Benefit Cost Analysis - Problem Set 3
Dan Killian
Sunday, April 26, 2015
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## intersect, setdiff, setequal, union- Excessive and improper use of antibiotics is contributing to the resistance of many diseases to existing antibiotics. Consider a regulatory program in the United States that would monitor antibiotic prescribing by physicians. Analysts estimate the direct costs of enforcement to be $40 million, the time costs to doctors and health professionals to be $220 million, and the convenience costs to patients to be $180 million (all annually). The annual benefits of the program are estimated to be $350 million in avoided resistance costs in the United States, $70 million in health benefits in the United States from better compliance with prescriptions, and $280 million in avoided resistance costs in the rest of the world.
Category <- c("Regulatory enforcement","Time cost to doctors","Convenience cost to patients","Total US costs","Avoided US resistance costs","better drug compliance","Total US benefits","Avoided non-US resistance costs","Fraction counted as US benefits","US benefits with fraction of non-US benefits","Total US net benefits")
Amount <- c(40,220,180,440,350,70,420,280,0,420,-20)
q1 <- data.frame(cbind(Category,Amount))
q1## Category Amount
## 1 Regulatory enforcement 40
## 2 Time cost to doctors 220
## 3 Convenience cost to patients 180
## 4 Total US costs 440
## 5 Avoided US resistance costs 350
## 6 better drug compliance 70
## 7 Total US benefits 420
## 8 Avoided non-US resistance costs 280
## 9 Fraction counted as US benefits 0
## 10 US benefits with fraction of non-US benefits 420
## 11 Total US net benefits -20- Does the program have positive net benefits from the national perspective?
No - net benefits are -$20 million
- If not, what fraction of benefits accruing in the rest of the world would have to be counted for the program to have positive net benefits?
20/280## [1] 0.07142857.07142857
Taking this fraction of non-US benefits makes benefits and costs equal.
Category <- c("Regulatory enforcement","Time cost to doctors","Convenience cost to patients","Total US costs","Avoided US resistance costs","better drug compliance","Total US benefits","Avoided non-US resistance costs","Fraction counted as US benefits","US benefits with fraction of non-US benefits","Total US net benefits")
Amount <- c(40,220,180,440,350,70,420,280,.07142857,440,0)
q1 <- data.frame(cbind(Category,Amount))
q1## Category Amount
## 1 Regulatory enforcement 40
## 2 Time cost to doctors 220
## 3 Convenience cost to patients 180
## 4 Total US costs 440
## 5 Avoided US resistance costs 350
## 6 better drug compliance 70
## 7 Total US benefits 420
## 8 Avoided non-US resistance costs 280
## 9 Fraction counted as US benefits 0.07142857
## 10 US benefits with fraction of non-US benefits 440
## 11 Total US net benefits 0- Write a short (1-2 paragraph) note to a policymaker about this issue of standing and whether you recommend a national or global approach.
As a matter of policy, I would not generally recommend incorporating global net benefits into cost benefit analyses, although I can imagine there to be a limited number of cases where such analyses would be useful for context. In this case, we only need to take 7% of the global benefits to justify the cost domestically, so I would consider this fact not only contextually relevant but worthy of justifying the cost. We could probably draw up a scenario where the non-US benefits eventually accrue to the US. Consider how reduced antibiotic resistance might reduce the chances of some superbug entering the US, or consider how international migration also creates an interest among US policymakers in contributing to non-US benefits.
I would recommend that the policymaker enact this program based on the US and non-US benefits.
- A proposed government project in a rural area with one hundred unemployed would require the hiring of 20 workers. The project would offer wages of $12 per hour. Imagine that the reservation wages of the one hundred unemployed fall between $2 and $20.
set.seed(1)
res <- round(data.frame(rnorm(100,11,3.9)),digits=2)
colnames(res) <- "ReservationPrice"
describe(res)## vars n mean sd median trimmed mad min max range
## ReservationPrice 1 100 11.42 3.5 11.45 11.46 3.4 2.36 20.37 18.01
## skew kurtosis se
## ReservationPrice -0.07 -0.05 0.35res$Accept <- ifelse(res$ReservationPrice>12, 0,1)
res## ReservationPrice Accept
## 1 8.56 1
## 2 11.72 1
## 3 7.74 1
## 4 17.22 0
## 5 12.29 0
## 6 7.80 1
## 7 12.90 0
## 8 13.88 0
## 9 13.25 0
## 10 9.81 1
## 11 16.90 0
## 12 12.52 0
## 13 8.58 1
## 14 2.36 1
## 15 15.39 0
## 16 10.82 1
## 17 10.94 1
## 18 14.68 0
## 19 14.20 0
## 20 13.32 0
## 21 14.58 0
## 22 14.05 0
## 23 11.29 1
## 24 3.24 1
## 25 13.42 0
## 26 10.78 1
## 27 10.39 1
## 28 5.26 1
## 29 9.14 1
## 30 12.63 0
## 31 16.30 0
## 32 10.60 1
## 33 12.51 0
## 34 10.79 1
## 35 5.63 1
## 36 9.38 1
## 37 9.46 1
## 38 10.77 1
## 39 15.29 0
## 40 13.98 0
## 41 10.36 1
## 42 10.01 1
## 43 13.72 0
## 44 13.17 0
## 45 8.31 1
## 46 8.24 1
## 47 12.42 0
## 48 14.00 0
## 49 10.56 1
## 50 14.44 0
## 51 12.55 0
## 52 8.61 1
## 53 12.33 0
## 54 6.60 1
## 55 16.59 0
## 56 18.72 0
## 57 9.57 1
## 58 6.93 1
## 59 13.22 0
## 60 10.47 1
## 61 20.37 0
## 62 10.85 1
## 63 13.69 0
## 64 11.11 1
## 65 8.10 1
## 66 11.74 1
## 67 3.96 1
## 68 16.72 0
## 69 11.60 1
## 70 19.47 0
## 71 12.85 0
## 72 8.23 1
## 73 13.38 0
## 74 7.36 1
## 75 6.11 1
## 76 12.14 0
## 77 9.27 1
## 78 11.00 1
## 79 11.29 1
## 80 8.70 1
## 81 8.78 1
## 82 10.47 1
## 83 15.59 0
## 84 5.06 1
## 85 13.32 0
## 86 12.30 0
## 87 15.15 0
## 88 9.81 1
## 89 12.44 0
## 90 12.04 0
## 91 8.88 1
## 92 15.71 0
## 93 15.53 0
## 94 13.73 0
## 95 17.19 0
## 96 13.18 0
## 97 6.02 1
## 98 8.76 1
## 99 6.22 1
## 100 9.15 1## subset data to the job offers up to 20 accepts
subRes <- res[1:37,]
subRes## ReservationPrice Accept
## 1 8.56 1
## 2 11.72 1
## 3 7.74 1
## 4 17.22 0
## 5 12.29 0
## 6 7.80 1
## 7 12.90 0
## 8 13.88 0
## 9 13.25 0
## 10 9.81 1
## 11 16.90 0
## 12 12.52 0
## 13 8.58 1
## 14 2.36 1
## 15 15.39 0
## 16 10.82 1
## 17 10.94 1
## 18 14.68 0
## 19 14.20 0
## 20 13.32 0
## 21 14.58 0
## 22 14.05 0
## 23 11.29 1
## 24 3.24 1
## 25 13.42 0
## 26 10.78 1
## 27 10.39 1
## 28 5.26 1
## 29 9.14 1
## 30 12.63 0
## 31 16.30 0
## 32 10.60 1
## 33 12.51 0
## 34 10.79 1
## 35 5.63 1
## 36 9.38 1
## 37 9.46 1sum(subRes$ReservationPrice)## [1] 414.33414.33
(Not sure what the units would be here? Person dollars?)
- Estimate the opportunity cost of the labor required for the project assuming that the government can identify and hire the 20 unemployed with the lowest reservation wages. This can be done by copying your list of random, unsorted reservation wages and paste them in a different column and then using Data-Sort from the pull down menu to sort these reservation wages in ascending order.
resSort <- arrange(res, ReservationPrice)
resSort## ReservationPrice Accept
## 1 2.36 1
## 2 3.24 1
## 3 3.96 1
## 4 5.06 1
## 5 5.26 1
## 6 5.63 1
## 7 6.02 1
## 8 6.11 1
## 9 6.22 1
## 10 6.60 1
## 11 6.93 1
## 12 7.36 1
## 13 7.74 1
## 14 7.80 1
## 15 8.10 1
## 16 8.23 1
## 17 8.24 1
## 18 8.31 1
## 19 8.56 1
## 20 8.58 1
## 21 8.61 1
## 22 8.70 1
## 23 8.76 1
## 24 8.78 1
## 25 8.88 1
## 26 9.14 1
## 27 9.15 1
## 28 9.27 1
## 29 9.38 1
## 30 9.46 1
## 31 9.57 1
## 32 9.81 1
## 33 9.81 1
## 34 10.01 1
## 35 10.36 1
## 36 10.39 1
## 37 10.47 1
## 38 10.47 1
## 39 10.56 1
## 40 10.60 1
## 41 10.77 1
## 42 10.78 1
## 43 10.79 1
## 44 10.82 1
## 45 10.85 1
## 46 10.94 1
## 47 11.00 1
## 48 11.11 1
## 49 11.29 1
## 50 11.29 1
## 51 11.60 1
## 52 11.72 1
## 53 11.74 1
## 54 12.04 0
## 55 12.14 0
## 56 12.29 0
## 57 12.30 0
## 58 12.33 0
## 59 12.42 0
## 60 12.44 0
## 61 12.51 0
## 62 12.52 0
## 63 12.55 0
## 64 12.63 0
## 65 12.85 0
## 66 12.90 0
## 67 13.17 0
## 68 13.18 0
## 69 13.22 0
## 70 13.25 0
## 71 13.32 0
## 72 13.32 0
## 73 13.38 0
## 74 13.42 0
## 75 13.69 0
## 76 13.72 0
## 77 13.73 0
## 78 13.88 0
## 79 13.98 0
## 80 14.00 0
## 81 14.05 0
## 82 14.20 0
## 83 14.44 0
## 84 14.58 0
## 85 14.68 0
## 86 15.15 0
## 87 15.29 0
## 88 15.39 0
## 89 15.53 0
## 90 15.59 0
## 91 15.71 0
## 92 16.30 0
## 93 16.59 0
## 94 16.72 0
## 95 16.90 0
## 96 17.19 0
## 97 17.22 0
## 98 18.72 0
## 99 19.47 0
## 100 20.37 0resLow <- resSort[1:20,]
resLow## ReservationPrice Accept
## 1 2.36 1
## 2 3.24 1
## 3 3.96 1
## 4 5.06 1
## 5 5.26 1
## 6 5.63 1
## 7 6.02 1
## 8 6.11 1
## 9 6.22 1
## 10 6.60 1
## 11 6.93 1
## 12 7.36 1
## 13 7.74 1
## 14 7.80 1
## 15 8.10 1
## 16 8.23 1
## 17 8.24 1
## 18 8.31 1
## 19 8.56 1
## 20 8.58 1describe(resLow)## vars n mean sd median trimmed mad min max range
## ReservationPrice 1 20 6.52 1.83 6.76 6.72 2.08 2.36 8.58 6.22
## Accept 2 20 1.00 0.00 1.00 1.00 0.00 1.00 1.00 0.00
## skew kurtosis se
## ReservationPrice -0.72 -0.6 0.41
## Accept NaN NaN 0.00sum(resLow$ReservationPrice)## [1] 130.31The opportunity cost for those who most want to work is 130.31
- Repeat parts (a) and (b) 15 times to get a distribution for the opportunity cost using both methods. Compute and report the mean and standard deviation for both methods.
See Annex 1 for the simulations. The summary:
names <- c("seed","resRandom","resLow")
seed <- 1:15
resRandom <- c(414.33,436.38,237.74,484.68,331.33,387.89,459.54,318.25,311.97,269.07,244.94,276.84,375.7,501.58,464.06)
resLow <- c(130.31,95.93,128.8,133.13,125.34,115.53,131.87,92.8,122.17,105.35,118.98,125.33,111.62,128.75,122.52)
simul <- data.frame(cbind(seed,resRandom,resLow))
simul## seed resRandom resLow
## 1 1 414.33 130.31
## 2 2 436.38 95.93
## 3 3 237.74 128.80
## 4 4 484.68 133.13
## 5 5 331.33 125.34
## 6 6 387.89 115.53
## 7 7 459.54 131.87
## 8 8 318.25 92.80
## 9 9 311.97 122.17
## 10 10 269.07 105.35
## 11 11 244.94 118.98
## 12 12 276.84 125.33
## 13 13 375.70 111.62
## 14 14 501.58 128.75
## 15 15 464.06 122.52describe(simul)## vars n mean sd median trimmed mad min max range
## seed 1 15 8.00 4.47 8.00 8.00 5.93 1.00 15.00 14.00
## resRandom 2 15 367.62 90.04 375.70 367.31 124.30 237.74 501.58 263.84
## resLow 3 15 119.23 12.70 122.52 120.19 10.36 92.80 133.13 40.33
## skew kurtosis se
## seed 0.00 -1.44 1.15
## resRandom 0.00 -1.59 23.25
## resLow -0.84 -0.64 3.28For the random draw of reservation wages: mean 367.62 standard deviation 90.04
For those who most want to work: mean 119.23 standard deviation 12.7
Visually:
data <- melt(simul,id="seed")
ggplot(data,aes(x=value,fill=variable)) + geom_density(alpha=.25)
- What does this tell you about calculating the opportunity cost of unemployed labor?
I’m not sure what to make of the distributions or whether I’ve constructed them correctly, but at face value I would say that the opportunity cost among those who most want to work is defined much more tightly around the mean, while the distribution for a random sample of reservation prices looks almost uniform. If it’s a correct characterization to say it approximates a uniform distribution, is that somehow a consequence of taking the random sample of reservation wages?
Given the difference in distributions, I find it reassuring to think that a government program to help the unemployed or underemployed can be tightly targeted to those who need/want it most.
A government data processing center has been plagued in recent years by complaints from employees of back pain. Consultants have estimated that upgrading office furniture at a net cost of $425,000 would reduce the incidence and severity of back injuries, allowing the center to avoid medical care that currently costs $68,000 each year. They estimate that the new furniture would also provide yearly benefits of avoided losses in work time and employee comfort worth $18,000. The furniture would have a useful life of five years, after which it would have a positive salvage value equal to 10 percent of its initial net cost. The consultants made their estimates of avoided costs assuming that they would be treated as occurring at the beginning of each year.
In its investment decisions, the center uses a nominal discount rate of 9.5 percent and an assumed general inflation rate of 3 percent. It expects the inflation rate for medical care will run between 3 percent and 5 percent but is uncertain as to the exact rate. In other words, it is uncertain as to whether the cost of medical care will inflate at the same rate as other prices or rise 2 percent faster. Should the center purchase the new furniture?
See Excel sheet for calculations. In summary:
At 3% inflation of medical costs, present value of net benefits is $133,600
At 5% inflation of medical costs, present value of net benefits is $154,895
The company should purchase the chairs.
As a personal aside, I feel like there is a missing benefit, which is the avoided reputational cost to the firm providing the chairs. A decision like this should not strictly be about avoided medical costs or increased comfort - it should be about projecting and executing a commitment to the well being of their workers in fundamental matters such as the things they use very day, and which accrue over many years to make a career.
- Imagine that a rancher would have an income of $80,000 if his county remains free from a cattle parasite but only $50,000 if the county is exposed to the parasite. Imagine that a county program to limit the impact of exposure to the parasite would reduce his income to $76,000 if the county remains free of the parasite but increase it to $70,000 if the county is exposed to the parasite. Assume that there is a 60 percent chance of exposure to the parasite and that the rancher’s utility is the natural logarithm of his income.
exposure <- c("parasite","no_parasite")
program <- as.numeric(c(70000,76000))
no_program <- as.numeric(c(50000,80000))
prob <- as.numeric(c(.6,.4))
data <- data.frame(cbind(exposure,program,no_program,prob))
data[,2:4] <- lapply(data[,2:4],as.character)
data[,2:4] <- lapply(data[,2:4],as.numeric)
data$surplus <- data$program-data$no_program
data## exposure program no_program prob surplus
## 1 parasite 70000 50000 0.6 20000
## 2 no_parasite 76000 80000 0.4 -4000- Find the expected surplus in both outcomes (i.e., parasite-free and parasite exposed). Find the expected value of the world with the program and without the program. What is the expected surplus of the program? What is the change in variance of income both with and without the program?
The surplus with exposure to the parasite is 20,000.
The surplus without exposure to the parasite is -4,000.
(20000*.6) + (-4000*.4)## [1] 10400The expected surplus is 10,400
var(data$program)## [1] 1.8e+07sd(data$program)## [1] 4242.641var(data$no_program)## [1] 4.5e+08sd(data$no_program)## [1] 21213.2Income variance is much lower with the program. The standard deviation in income is $21,213 without the program, and $4,243 with the program.
- What is the rancher’s option price for the county program? This can be found by calculating the utility without the program. Then calculate the option price by finding the amount of income that must be taken away in both outcomes to maintain this level of utility. What is the option value for the program?
Expected utility without the program is:
log(50000)*.6 + log(80000)*.4## [1] 11.0077811
We set expected utility without the program equal to expected utility with the program minus the amount needed to equal expected utility without the program:
11 = .6U(70000-OP) + .4U(76000-OP)
I’m not sure how to solve algebraically when the unknown is inside the log operator. But Wolfram Alpha tells me the solution is 12,455 which seems about right.
- Suppose there is uncertainty in the percent chance of exposure to the parasite. Instead of a 60% chance, it ranges from 50% to 70%. What is the farmers option price at each of these extremes?
At 50%:
11 = .5U(70000-OP) + .5U(76000-OP)
13,051
At 70%:
11 = .7U(70000-OP) + .3U(76000-OP)
11,864
I’m confused here. I thought OP was the conceptually correct measure of willingness to pay. Why would it go down when the risk of exposure goes up?
- Given the uncertainty in (c), what is the “breakeven” percent chance of exposure for finding positive benefits to this program?
Using the expected surplus measure and a bit of trial and error:
(20000*.1675) + (-4000*.8325)## [1] 20Expected suprlus is around zero at a 16.7% risk of exposure.
- The following table gives cost and benefit estimates in real dollars for dredging a navigable channel from an inland port to the open sea.
year <- 0:7
costs <- c(2548000, 60000,60000,70000,70000,80000,80000,90000)
benefit1 <- c(0,400000,440000,440000,440000,440000,440000,440000)
benefit2 <- c(0,60000,175000,175000,175000,175000,175000,175000)
data <- data.frame(cbind(year,costs,benefit1,benefit2))
data## year costs benefit1 benefit2
## 1 0 2548000 0 0
## 2 1 60000 400000 60000
## 3 2 60000 440000 175000
## 4 3 70000 440000 175000
## 5 4 70000 440000 175000
## 6 5 80000 440000 175000
## 7 6 80000 440000 175000
## 8 7 90000 440000 175000The channel would be navigable for seven years, after which silting would render it un-navigable. Local economists estimate that 75 percent of the savings to shippers would be directly invested by the firms, or their shareholders, and the remaining 25 percent would be used by shareholders for consumption. They also estimate that all government expenditures come at the expense of private investment. The social marginal rate of time preference is assumed to be 3 percent, the marginal rate of return on private investment is assumed to be 7 percent, and the shadow price of capital is assumed to be 1.3. Assuming that the costs and benefits accrue at the end of each year, calculate the present value of net benefits of the project using each of the following methods:
- Discount at the marginal rate of return on private investment.
data$TotalBenefit <- data$benefit1 + data$benefit2
data$PV_a <- data$TotalBenefit/1.07
data## year costs benefit1 benefit2 TotalBenefit PV_a
## 1 0 2548000 0 0 0 0.0
## 2 1 60000 400000 60000 460000 429906.5
## 3 2 60000 440000 175000 615000 574766.4
## 4 3 70000 440000 175000 615000 574766.4
## 5 4 70000 440000 175000 615000 574766.4
## 6 5 80000 440000 175000 615000 574766.4
## 7 6 80000 440000 175000 615000 574766.4
## 8 7 90000 440000 175000 615000 574766.4sum(data$PV_a) ## [1] 38785053,878,505
- Discount at the social marginal rate of time preference.
data$PV_b <- data$TotalBenefit/1.03
data## year costs benefit1 benefit2 TotalBenefit PV_a PV_b
## 1 0 2548000 0 0 0 0.0 0.0
## 2 1 60000 400000 60000 460000 429906.5 446601.9
## 3 2 60000 440000 175000 615000 574766.4 597087.4
## 4 3 70000 440000 175000 615000 574766.4 597087.4
## 5 4 70000 440000 175000 615000 574766.4 597087.4
## 6 5 80000 440000 175000 615000 574766.4 597087.4
## 7 6 80000 440000 175000 615000 574766.4 597087.4
## 8 7 90000 440000 175000 615000 574766.4 597087.4sum(data$PV_b)## [1] 40291264,029,126
- Discount using the shadow price of capital method.
data$SPKCosts <- (1.3*data$costs*.75) + (.25*data$costs)
data$SPKBenefits <- (1.3*data$TotalBenefit*.75) + (.25*data$TotalBenefit)
data$PV_c <- data$SPKBenefits/1.03
data ## year costs benefit1 benefit2 TotalBenefit PV_a PV_b SPKCosts
## 1 0 2548000 0 0 0 0.0 0.0 3121300
## 2 1 60000 400000 60000 460000 429906.5 446601.9 73500
## 3 2 60000 440000 175000 615000 574766.4 597087.4 73500
## 4 3 70000 440000 175000 615000 574766.4 597087.4 85750
## 5 4 70000 440000 175000 615000 574766.4 597087.4 85750
## 6 5 80000 440000 175000 615000 574766.4 597087.4 98000
## 7 6 80000 440000 175000 615000 574766.4 597087.4 98000
## 8 7 90000 440000 175000 615000 574766.4 597087.4 110250
## SPKBenefits PV_c
## 1 0 0.0
## 2 563500 547087.4
## 3 753375 731432.0
## 4 753375 731432.0
## 5 753375 731432.0
## 6 753375 731432.0
## 7 753375 731432.0
## 8 753375 731432.0sum(data$PV_c) ## [1] 49356804,935,680
- Using the shadow price of capital method, what are the implications if only 20% of the savings to shippers would be directly invested by the firms or shareholders, and the remainder used for consumption?
data$SPKCosts2 <- (1.3*data$costs*.2) + (.8*data$costs)
data$SPKBenefits2 <- (1.3*data$TotalBenefit*.2) + (.8*data$TotalBenefit)
data$PV_d <- data$SPKBenefits2/1.03
data ## year costs benefit1 benefit2 TotalBenefit PV_a PV_b SPKCosts
## 1 0 2548000 0 0 0 0.0 0.0 3121300
## 2 1 60000 400000 60000 460000 429906.5 446601.9 73500
## 3 2 60000 440000 175000 615000 574766.4 597087.4 73500
## 4 3 70000 440000 175000 615000 574766.4 597087.4 85750
## 5 4 70000 440000 175000 615000 574766.4 597087.4 85750
## 6 5 80000 440000 175000 615000 574766.4 597087.4 98000
## 7 6 80000 440000 175000 615000 574766.4 597087.4 98000
## 8 7 90000 440000 175000 615000 574766.4 597087.4 110250
## SPKBenefits PV_c SPKCosts2 SPKBenefits2 PV_d
## 1 0 0.0 2700880 0 0.0
## 2 563500 547087.4 63600 487600 473398.1
## 3 753375 731432.0 63600 651900 632912.6
## 4 753375 731432.0 74200 651900 632912.6
## 5 753375 731432.0 74200 651900 632912.6
## 6 753375 731432.0 84800 651900 632912.6
## 7 753375 731432.0 84800 651900 632912.6
## 8 753375 731432.0 95400 651900 632912.6sum(data$PV_d) ## [1] 42708744,270,874
About 650,000 less than if 75% were allocated to investment.
- Write a short summary (1-2 paragraphs) to a policy maker explaining why there is a difference in the present value of net benefits under parts (c) and (d)
I don’t fully grasp the theoretical basis of using the shadow price of capital, but it has something to do with the value of investment vs. consumption, and whether the project expenditure is government or private sector financed. Investment generally provides a stream of benefits over time, while consumption provides benefit in only one time period. Therefore, investment flows need to be weighted in a way that makes them equal to consumption, so that costs or benefits of investment and consumption may be treated together as a single cost or benefit category. In this example, the benefits go down because more of the benefits are used for consumption rather than investment.
- An analyst was asked to predict the gross social benefits of building a public swimming pool in Dryville, which has a population of 70,230 people and a median household income of $31,500. The analyst identified 24 towns in the region that already had public swimming pools. She conducted a telephone interview with the recreation department in each town to find out what fee it charged per visit (FEE) and how many visits it had during the most recent summer season (VISITS). In addition, she was able to find each town’s population (POP) and median household income (INCOME) in the most recent census. Her data are as follows:
q6 <- read.xlsx("q6 data.xlsx",colNames=T, startRow=1)
q6## town visits fee income pop
## 1 1 168590 0.00 20600 36879
## 2 2 179599 0.00 33400 64520
## 3 3 198595 0.00 39700 104123
## 4 4 206662 0.00 32600 103073
## 5 5 170259 0.00 24900 58386
## 6 6 209995 0.25 38000 116592
## 7 7 172018 0.25 26700 49945
## 8 8 190802 0.25 20800 79789
## 9 9 197019 0.25 26300 98234
## 10 10 186515 0.50 35600 71762
## 11 11 152679 0.50 38900 40178
## 12 12 137423 0.50 21700 22928
## 13 13 158056 0.50 37900 39031
## 14 14 157424 0.50 35100 44685
## 15 15 179490 0.50 35700 67882
## 16 16 164657 0.75 22900 69625
## 17 17 184428 0.75 38600 98408
## 18 18 183822 0.75 20500 93429
## 19 19 174510 1.00 39300 98077
## 20 20 187820 1.00 25800 104068
## 21 21 196318 1.25 23800 117940
## 22 22 166694 1.50 34000 59757
## 23 23 161716 1.50 29600 88305
## 24 24 167505 2.00 33800 84102describe(q6)## vars n mean sd median trimmed mad min
## town 1 24 12.50 7.07 12.5 12.50 8.90 1
## visits 2 24 177191.50 17876.56 177000.0 177291.85 17170.73 137423
## fee 3 24 0.60 0.54 0.5 0.55 0.37 0
## income 4 24 30675.00 6843.67 33000.0 30805.00 9043.86 20500
## pop 5 24 75488.25 27360.70 75775.5 75868.95 33425.96 22928
## max range skew kurtosis se
## town 24 23 0.00 -1.35 1.44
## visits 209995 72572 -0.08 -0.66 3649.04
## fee 2 2 0.86 -0.07 0.11
## income 39700 19200 -0.18 -1.61 1396.96
## pop 117940 95012 -0.19 -1.24 5584.98- Use these data to run a simple linear regression to predict the gross benefits of opening a public swimming pool in Dryville and allowing free admission. (Note: this is simply estimating a linear demand function for visits.)
visits <- lm(visits~fee+income+pop, data=q6)
summary(visits)##
## Call:
## lm(formula = visits ~ fee + income + pop, data = q6)
##
## Residuals:
## Min 1Q Median 3Q Max
## -10499.6 -4707.5 551.1 5122.7 12106.6
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.405e+05 7.135e+03 19.698 1.44e-14 ***
## fee -1.464e+04 2.634e+03 -5.557 1.94e-05 ***
## income -1.127e-03 2.054e-01 -0.005 0.996
## pop 6.031e-01 5.242e-02 11.504 2.86e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6686 on 20 degrees of freedom
## Multiple R-squared: 0.8784, Adjusted R-squared: 0.8601
## F-statistic: 48.14 on 3 and 20 DF, p-value: 2.474e-09140546.7-(.001127*31500) + (.603*70230)## [1] 182859.9182,860
- Predict gross benefits for Dryville if admission is set at $1.00.
140546.7 - 14638.37 -(.001127*31500) + (.603*70230)## [1] 168221.5168,222
- Predict gross benefits if admission is set to $1.00 and Dryville has marginal excess tax burden of 0.25. In answering this question, assume that the fees are used to reduce taxes that would otherwise have to be collected from the citizens of Dryville to pay for expenses incurred in operating the pool. (Note: we did not cover marginal excess tax burden in class so you will need to use your text for this part. See Chapter 3.)
140546.7 - (1.25*14638.37) -(.001127*31500) + (.603*70230)## [1] 164561.9164,561.9
- Two alternative mosquito control programs have been proposed to reduce the health risks of West Nile disease in a state over the next five years. The costs and effectiveness of each program in each of the next five years are displayed below:
SEE EXCEL SHEET
Calculate CE ratios for each program without discounting.
Calculate CE ratios discounting cost but not effectiveness assuming a discount rate of 4 percent.
Calculate CE ratios discounting both costs and effectiveness at 4 percent.
Assume that the uncertainty range for each of the yearly effectiveness estimates is plus or minus 20 percent, and the uncertainty in each of the yearly cost estimates is 10 percent. Assuming uniform distributions of errors, produce Monte Carlo distributions of CE ratios for each program and compare them. Include the mean, standard deviation, minimum, and maximum for each alternative. (Note: See Appendix 7A in your textbook for doing Monte Carlo Sensitivity Analysis with a Simple Spreadsheet. The same techniques were used for the rural hiring question earlier in this problem set.)
A <- data.frame(rnorm(1000,1.9,.18))
costA <- data.frame(rnorm(1000,3.8,.35))
simA <- data.frame(cbind(A, costA))
colnames(simA) <- c("qaly","cost")
simA$ratio <- simA$cost / simA$qaly
describe(simA)## vars n mean sd median trimmed mad min max range skew
## qaly 1 1000 1.90 0.19 1.89 1.90 0.19 1.36 2.59 1.23 -0.01
## cost 2 1000 3.79 0.37 3.78 3.79 0.37 2.66 5.07 2.41 0.03
## ratio 3 1000 2.02 0.28 2.00 2.01 0.28 1.20 2.98 1.78 0.45
## kurtosis se
## qaly -0.07 0.01
## cost -0.02 0.01
## ratio 0.28 0.01ggplot(simA, aes(x=ratio)) + geom_density()
qalyB <- rnorm(1000,2,.19)
costB <- rnorm(1000,4,.38)
simB <- data.frame(cbind(qalyB,costB))
colnames(simB) <- c("qaly","cost")
simB$ratio <- simB$cost / simB$qaly
describe(simB)## vars n mean sd median trimmed mad min max range skew
## qaly 1 1000 2.01 0.20 2.00 2.01 0.19 1.33 2.54 1.22 -0.10
## cost 2 1000 4.00 0.39 4.00 4.00 0.40 2.78 5.16 2.38 -0.05
## ratio 3 1000 2.01 0.28 1.99 2.00 0.27 1.19 3.26 2.07 0.48
## kurtosis se
## qaly -0.05 0.01
## cost -0.04 0.01
## ratio 0.89 0.01ggplot(simB, aes(x=ratio)) + geom_density()
Annex 1: Simulations from question 2c
set.seed(2)
res <- round(data.frame(rnorm(100,11,3.9)),digits=2)
colnames(res) <- "ReservationPrice"
describe(res)## vars n mean sd median trimmed mad min max range
## ReservationPrice 1 100 10.88 4.52 10.46 10.85 4.48 1.44 19.15 17.71
## skew kurtosis se
## ReservationPrice 0.11 -0.8 0.45res$Accept <- ifelse(res$ReservationPrice>12, 0,1)
res## ReservationPrice Accept
## 1 7.50 1
## 2 11.72 1
## 3 17.19 0
## 4 6.59 1
## 5 10.69 1
## 6 11.52 1
## 7 13.76 0
## 8 10.07 1
## 9 18.74 0
## 10 10.46 1
## 11 12.63 0
## 12 14.83 0
## 13 9.47 1
## 14 6.95 1
## 15 17.95 0
## 16 1.99 1
## 17 14.43 0
## 18 11.14 1
## 19 14.95 0
## 20 12.69 0
## 21 19.15 0
## 22 6.32 1
## 23 17.20 0
## 24 18.62 0
## 25 11.02 1
## 26 1.44 1
## 27 12.86 0
## 28 8.67 1
## 29 14.09 0
## 30 12.13 0
## 31 13.88 0
## 32 12.24 0
## 33 15.20 0
## 34 9.89 1
## 35 7.97 1
## 36 8.68 1
## 37 4.27 1
## 38 7.48 1
## 39 8.82 1
## 40 10.04 1
## 41 9.50 1
## 42 3.36 1
## 43 7.72 1
## 44 18.42 0
## 45 13.43 0
## 46 18.76 0
## 47 9.81 1
## 48 10.65 1
## 49 10.28 1
## 50 6.32 1
## 51 7.73 1
## 52 19.06 0
## 53 8.81 1
## 54 15.98 0
## 55 6.91 1
## 56 3.33 1
## 57 9.74 1
## 58 14.65 0
## 59 15.44 0
## 60 17.52 0
## 61 4.03 1
## 62 18.92 0
## 63 8.26 1
## 64 11.62 1
## 65 12.97 0
## 66 7.80 1
## 67 3.20 1
## 68 9.13 1
## 69 11.33 1
## 70 7.51 1
## 71 7.41 1
## 72 12.29 0
## 73 10.45 1
## 74 12.70 0
## 75 10.79 1
## 76 7.46 1
## 77 16.08 0
## 78 14.01 0
## 79 15.10 0
## 80 5.50 1
## 81 14.88 0
## 82 4.39 1
## 83 8.92 1
## 84 5.65 1
## 85 2.39 1
## 86 18.11 0
## 87 8.45 1
## 88 9.89 1
## 89 9.49 1
## 90 12.51 0
## 91 17.24 0
## 92 17.56 0
## 93 6.38 1
## 94 5.70 1
## 95 5.10 1
## 96 6.11 1
## 97 18.64 0
## 98 11.03 1
## 99 7.71 1
## 100 8.66 1## subset data to the job offers up to 12 accepts
subRes <- res[1:38,]
subRes## ReservationPrice Accept
## 1 7.50 1
## 2 11.72 1
## 3 17.19 0
## 4 6.59 1
## 5 10.69 1
## 6 11.52 1
## 7 13.76 0
## 8 10.07 1
## 9 18.74 0
## 10 10.46 1
## 11 12.63 0
## 12 14.83 0
## 13 9.47 1
## 14 6.95 1
## 15 17.95 0
## 16 1.99 1
## 17 14.43 0
## 18 11.14 1
## 19 14.95 0
## 20 12.69 0
## 21 19.15 0
## 22 6.32 1
## 23 17.20 0
## 24 18.62 0
## 25 11.02 1
## 26 1.44 1
## 27 12.86 0
## 28 8.67 1
## 29 14.09 0
## 30 12.13 0
## 31 13.88 0
## 32 12.24 0
## 33 15.20 0
## 34 9.89 1
## 35 7.97 1
## 36 8.68 1
## 37 4.27 1
## 38 7.48 1sum(subRes$ReservationPrice)## [1] 436.38436.38
resSort <- arrange(res, ReservationPrice)
resSort## ReservationPrice Accept
## 1 1.44 1
## 2 1.99 1
## 3 2.39 1
## 4 3.20 1
## 5 3.33 1
## 6 3.36 1
## 7 4.03 1
## 8 4.27 1
## 9 4.39 1
## 10 5.10 1
## 11 5.50 1
## 12 5.65 1
## 13 5.70 1
## 14 6.11 1
## 15 6.32 1
## 16 6.32 1
## 17 6.38 1
## 18 6.59 1
## 19 6.91 1
## 20 6.95 1
## 21 7.41 1
## 22 7.46 1
## 23 7.48 1
## 24 7.50 1
## 25 7.51 1
## 26 7.71 1
## 27 7.72 1
## 28 7.73 1
## 29 7.80 1
## 30 7.97 1
## 31 8.26 1
## 32 8.45 1
## 33 8.66 1
## 34 8.67 1
## 35 8.68 1
## 36 8.81 1
## 37 8.82 1
## 38 8.92 1
## 39 9.13 1
## 40 9.47 1
## 41 9.49 1
## 42 9.50 1
## 43 9.74 1
## 44 9.81 1
## 45 9.89 1
## 46 9.89 1
## 47 10.04 1
## 48 10.07 1
## 49 10.28 1
## 50 10.45 1
## 51 10.46 1
## 52 10.65 1
## 53 10.69 1
## 54 10.79 1
## 55 11.02 1
## 56 11.03 1
## 57 11.14 1
## 58 11.33 1
## 59 11.52 1
## 60 11.62 1
## 61 11.72 1
## 62 12.13 0
## 63 12.24 0
## 64 12.29 0
## 65 12.51 0
## 66 12.63 0
## 67 12.69 0
## 68 12.70 0
## 69 12.86 0
## 70 12.97 0
## 71 13.43 0
## 72 13.76 0
## 73 13.88 0
## 74 14.01 0
## 75 14.09 0
## 76 14.43 0
## 77 14.65 0
## 78 14.83 0
## 79 14.88 0
## 80 14.95 0
## 81 15.10 0
## 82 15.20 0
## 83 15.44 0
## 84 15.98 0
## 85 16.08 0
## 86 17.19 0
## 87 17.20 0
## 88 17.24 0
## 89 17.52 0
## 90 17.56 0
## 91 17.95 0
## 92 18.11 0
## 93 18.42 0
## 94 18.62 0
## 95 18.64 0
## 96 18.74 0
## 97 18.76 0
## 98 18.92 0
## 99 19.06 0
## 100 19.15 0resLow <- resSort[1:20,]
resLow## ReservationPrice Accept
## 1 1.44 1
## 2 1.99 1
## 3 2.39 1
## 4 3.20 1
## 5 3.33 1
## 6 3.36 1
## 7 4.03 1
## 8 4.27 1
## 9 4.39 1
## 10 5.10 1
## 11 5.50 1
## 12 5.65 1
## 13 5.70 1
## 14 6.11 1
## 15 6.32 1
## 16 6.32 1
## 17 6.38 1
## 18 6.59 1
## 19 6.91 1
## 20 6.95 1describe(resLow)## vars n mean sd median trimmed mad min max range
## ReservationPrice 1 20 4.8 1.72 5.3 4.92 1.74 1.44 6.95 5.51
## Accept 2 20 1.0 0.00 1.0 1.00 0.00 1.00 1.00 0.00
## skew kurtosis se
## ReservationPrice -0.44 -1.21 0.38
## Accept NaN NaN 0.00sum(resLow$ReservationPrice)## [1] 95.93The opportunity cost for those who most want to work is 95.93
set.seed(3)
res <- round(data.frame(rnorm(100,11,3.9)),digits=2)
colnames(res) <- "ReservationPrice"
describe(res)## vars n mean sd median trimmed mad min max range
## ReservationPrice 1 100 11.04 3.34 11.13 11.09 4.23 2.16 17.77 15.61
## skew kurtosis se
## ReservationPrice -0.13 -0.77 0.33res$Accept <- ifelse(res$ReservationPrice>12, 0,1)
res## ReservationPrice Accept
## 1 7.25 1
## 2 9.86 1
## 3 12.01 0
## 4 6.51 1
## 5 11.76 1
## 6 11.12 1
## 7 11.33 1
## 8 15.35 0
## 9 6.25 1
## 10 15.94 0
## 11 8.10 1
## 12 6.59 1
## 13 8.21 1
## 14 11.99 1
## 15 11.59 1
## 16 9.80 1
## 17 7.28 1
## 18 8.47 1
## 19 15.77 0
## 20 11.78 1
## 21 8.74 1
## 22 7.33 1
## 23 10.21 1
## 24 4.50 1
## 25 9.11 1
## 26 8.11 1
## 27 15.53 0
## 28 14.95 0
## 29 10.72 1
## 30 6.57 1
## 31 14.51 0
## 32 14.32 0
## 33 13.84 0
## 34 13.87 0
## 35 9.63 1
## 36 13.75 0
## 37 16.07 0
## 38 11.15 1
## 39 7.18 1
## 40 14.10 0
## 41 14.07 0
## 42 9.79 1
## 43 17.63 0
## 44 7.90 1
## 45 12.36 0
## 46 2.16 1
## 47 10.37 1
## 48 15.41 0
## 49 9.22 1
## 50 7.49 1
## 51 13.83 0
## 52 7.84 1
## 53 12.04 0
## 54 4.22 1
## 55 5.50 1
## 56 9.23 1
## 57 6.96 1
## 58 16.31 0
## 59 14.58 0
## 60 7.94 1
## 61 13.24 0
## 62 14.58 0
## 63 12.00 1
## 64 12.37 0
## 65 15.58 0
## 66 9.12 1
## 67 9.37 1
## 68 14.72 0
## 69 5.97 1
## 70 11.73 1
## 71 10.88 1
## 72 12.82 0
## 73 14.99 0
## 74 12.04 0
## 75 11.90 1
## 76 13.92 0
## 77 15.75 0
## 78 12.50 0
## 79 7.15 1
## 80 10.39 1
## 81 17.77 0
## 82 9.63 1
## 83 13.69 0
## 84 15.78 0
## 85 14.10 0
## 86 10.98 1
## 87 11.85 1
## 88 7.54 1
## 89 12.72 0
## 90 7.54 1
## 91 7.67 1
## 92 7.14 1
## 93 8.46 1
## 94 15.11 0
## 95 9.48 1
## 96 10.72 1
## 97 9.20 1
## 98 13.11 0
## 99 14.63 0
## 100 10.18 1## subset data to the job offers up to 12 accepts
subRes <- res[1:24,]
subRes## ReservationPrice Accept
## 1 7.25 1
## 2 9.86 1
## 3 12.01 0
## 4 6.51 1
## 5 11.76 1
## 6 11.12 1
## 7 11.33 1
## 8 15.35 0
## 9 6.25 1
## 10 15.94 0
## 11 8.10 1
## 12 6.59 1
## 13 8.21 1
## 14 11.99 1
## 15 11.59 1
## 16 9.80 1
## 17 7.28 1
## 18 8.47 1
## 19 15.77 0
## 20 11.78 1
## 21 8.74 1
## 22 7.33 1
## 23 10.21 1
## 24 4.50 1sum(subRes$ReservationPrice)## [1] 237.74237.74
resSort <- arrange(res, ReservationPrice)
resSort## ReservationPrice Accept
## 1 2.16 1
## 2 4.22 1
## 3 4.50 1
## 4 5.50 1
## 5 5.97 1
## 6 6.25 1
## 7 6.51 1
## 8 6.57 1
## 9 6.59 1
## 10 6.96 1
## 11 7.14 1
## 12 7.15 1
## 13 7.18 1
## 14 7.25 1
## 15 7.28 1
## 16 7.33 1
## 17 7.49 1
## 18 7.54 1
## 19 7.54 1
## 20 7.67 1
## 21 7.84 1
## 22 7.90 1
## 23 7.94 1
## 24 8.10 1
## 25 8.11 1
## 26 8.21 1
## 27 8.46 1
## 28 8.47 1
## 29 8.74 1
## 30 9.11 1
## 31 9.12 1
## 32 9.20 1
## 33 9.22 1
## 34 9.23 1
## 35 9.37 1
## 36 9.48 1
## 37 9.63 1
## 38 9.63 1
## 39 9.79 1
## 40 9.80 1
## 41 9.86 1
## 42 10.18 1
## 43 10.21 1
## 44 10.37 1
## 45 10.39 1
## 46 10.72 1
## 47 10.72 1
## 48 10.88 1
## 49 10.98 1
## 50 11.12 1
## 51 11.15 1
## 52 11.33 1
## 53 11.59 1
## 54 11.73 1
## 55 11.76 1
## 56 11.78 1
## 57 11.85 1
## 58 11.90 1
## 59 11.99 1
## 60 12.00 1
## 61 12.01 0
## 62 12.04 0
## 63 12.04 0
## 64 12.36 0
## 65 12.37 0
## 66 12.50 0
## 67 12.72 0
## 68 12.82 0
## 69 13.11 0
## 70 13.24 0
## 71 13.69 0
## 72 13.75 0
## 73 13.83 0
## 74 13.84 0
## 75 13.87 0
## 76 13.92 0
## 77 14.07 0
## 78 14.10 0
## 79 14.10 0
## 80 14.32 0
## 81 14.51 0
## 82 14.58 0
## 83 14.58 0
## 84 14.63 0
## 85 14.72 0
## 86 14.95 0
## 87 14.99 0
## 88 15.11 0
## 89 15.35 0
## 90 15.41 0
## 91 15.53 0
## 92 15.58 0
## 93 15.75 0
## 94 15.77 0
## 95 15.78 0
## 96 15.94 0
## 97 16.07 0
## 98 16.31 0
## 99 17.63 0
## 100 17.77 0resLow <- resSort[1:20,]
resLow## ReservationPrice Accept
## 1 2.16 1
## 2 4.22 1
## 3 4.50 1
## 4 5.50 1
## 5 5.97 1
## 6 6.25 1
## 7 6.51 1
## 8 6.57 1
## 9 6.59 1
## 10 6.96 1
## 11 7.14 1
## 12 7.15 1
## 13 7.18 1
## 14 7.25 1
## 15 7.28 1
## 16 7.33 1
## 17 7.49 1
## 18 7.54 1
## 19 7.54 1
## 20 7.67 1describe(resLow)## vars n mean sd median trimmed mad min max range
## ReservationPrice 1 20 6.44 1.4 7.05 6.7 0.72 2.16 7.67 5.51
## Accept 2 20 1.00 0.0 1.00 1.0 0.00 1.00 1.00 0.00
## skew kurtosis se
## ReservationPrice -1.62 2.01 0.31
## Accept NaN NaN 0.00sum(resLow$ReservationPrice)## [1] 128.8The opportunity cost for those who most want to work is 128.8
set.seed(4)
res <- round(data.frame(rnorm(100,11,3.9)),digits=2)
colnames(res) <- "ReservationPrice"
describe(res)## vars n mean sd median trimmed mad min max range
## ReservationPrice 1 100 11.38 3.56 10.95 11.3 3.7 3.99 20.09 16.1
## skew kurtosis se
## ReservationPrice 0.23 -0.57 0.36res$Accept <- ifelse(res$ReservationPrice>12, 0,1)
res## ReservationPrice Accept
## 1 11.85 1
## 2 8.88 1
## 3 14.48 0
## 4 13.32 0
## 5 17.38 0
## 6 13.69 0
## 7 6.00 1
## 8 10.17 1
## 9 18.40 0
## 10 17.93 0
## 11 13.21 0
## 12 11.06 1
## 13 12.49 0
## 14 10.82 1
## 15 11.13 1
## 16 11.66 1
## 17 15.54 0
## 18 10.83 1
## 19 10.61 1
## 20 9.89 1
## 21 17.01 0
## 22 11.64 1
## 23 16.10 0
## 24 16.02 0
## 25 13.31 0
## 26 9.90 1
## 27 15.90 0
## 28 14.55 0
## 29 7.38 1
## 30 15.84 0
## 31 11.60 1
## 32 15.10 0
## 33 8.06 1
## 34 5.22 1
## 35 14.36 0
## 36 9.42 1
## 37 10.11 1
## 38 14.64 0
## 39 9.18 1
## 40 8.51 1
## 41 16.24 0
## 42 11.71 1
## 43 16.04 0
## 44 4.42 1
## 45 7.80 1
## 46 7.64 1
## 47 11.39 1
## 48 9.53 1
## 49 13.82 0
## 50 3.99 1
## 51 8.41 1
## 52 8.57 1
## 53 10.69 1
## 54 12.70 0
## 55 18.69 0
## 56 8.67 1
## 57 8.85 1
## 58 13.71 0
## 59 10.39 1
## 60 16.26 0
## 61 6.83 1
## 62 15.15 0
## 63 5.88 1
## 64 19.05 0
## 65 11.51 1
## 66 10.10 1
## 67 9.45 1
## 68 14.47 0
## 69 13.05 0
## 70 10.33 1
## 71 11.62 1
## 72 9.11 1
## 73 7.26 1
## 74 11.70 1
## 75 13.81 0
## 76 9.56 1
## 77 11.93 1
## 78 8.40 1
## 79 7.89 1
## 80 10.80 1
## 81 16.02 0
## 82 10.16 1
## 83 8.76 1
## 84 5.26 1
## 85 6.97 1
## 86 5.90 1
## 87 7.73 1
## 88 6.59 1
## 89 12.44 0
## 90 10.21 1
## 91 6.02 1
## 92 7.89 1
## 93 11.62 1
## 94 13.40 0
## 95 13.68 0
## 96 10.82 1
## 97 20.09 0
## 98 8.75 1
## 99 14.78 0
## 100 9.92 1## subset data to the job offers up to 12 accepts
subRes <- res[1:39,]
subRes## ReservationPrice Accept
## 1 11.85 1
## 2 8.88 1
## 3 14.48 0
## 4 13.32 0
## 5 17.38 0
## 6 13.69 0
## 7 6.00 1
## 8 10.17 1
## 9 18.40 0
## 10 17.93 0
## 11 13.21 0
## 12 11.06 1
## 13 12.49 0
## 14 10.82 1
## 15 11.13 1
## 16 11.66 1
## 17 15.54 0
## 18 10.83 1
## 19 10.61 1
## 20 9.89 1
## 21 17.01 0
## 22 11.64 1
## 23 16.10 0
## 24 16.02 0
## 25 13.31 0
## 26 9.90 1
## 27 15.90 0
## 28 14.55 0
## 29 7.38 1
## 30 15.84 0
## 31 11.60 1
## 32 15.10 0
## 33 8.06 1
## 34 5.22 1
## 35 14.36 0
## 36 9.42 1
## 37 10.11 1
## 38 14.64 0
## 39 9.18 1sum(subRes$ReservationPrice)## [1] 484.68484.68
resSort <- arrange(res, ReservationPrice)
resSort## ReservationPrice Accept
## 1 3.99 1
## 2 4.42 1
## 3 5.22 1
## 4 5.26 1
## 5 5.88 1
## 6 5.90 1
## 7 6.00 1
## 8 6.02 1
## 9 6.59 1
## 10 6.83 1
## 11 6.97 1
## 12 7.26 1
## 13 7.38 1
## 14 7.64 1
## 15 7.73 1
## 16 7.80 1
## 17 7.89 1
## 18 7.89 1
## 19 8.06 1
## 20 8.40 1
## 21 8.41 1
## 22 8.51 1
## 23 8.57 1
## 24 8.67 1
## 25 8.75 1
## 26 8.76 1
## 27 8.85 1
## 28 8.88 1
## 29 9.11 1
## 30 9.18 1
## 31 9.42 1
## 32 9.45 1
## 33 9.53 1
## 34 9.56 1
## 35 9.89 1
## 36 9.90 1
## 37 9.92 1
## 38 10.10 1
## 39 10.11 1
## 40 10.16 1
## 41 10.17 1
## 42 10.21 1
## 43 10.33 1
## 44 10.39 1
## 45 10.61 1
## 46 10.69 1
## 47 10.80 1
## 48 10.82 1
## 49 10.82 1
## 50 10.83 1
## 51 11.06 1
## 52 11.13 1
## 53 11.39 1
## 54 11.51 1
## 55 11.60 1
## 56 11.62 1
## 57 11.62 1
## 58 11.64 1
## 59 11.66 1
## 60 11.70 1
## 61 11.71 1
## 62 11.85 1
## 63 11.93 1
## 64 12.44 0
## 65 12.49 0
## 66 12.70 0
## 67 13.05 0
## 68 13.21 0
## 69 13.31 0
## 70 13.32 0
## 71 13.40 0
## 72 13.68 0
## 73 13.69 0
## 74 13.71 0
## 75 13.81 0
## 76 13.82 0
## 77 14.36 0
## 78 14.47 0
## 79 14.48 0
## 80 14.55 0
## 81 14.64 0
## 82 14.78 0
## 83 15.10 0
## 84 15.15 0
## 85 15.54 0
## 86 15.84 0
## 87 15.90 0
## 88 16.02 0
## 89 16.02 0
## 90 16.04 0
## 91 16.10 0
## 92 16.24 0
## 93 16.26 0
## 94 17.01 0
## 95 17.38 0
## 96 17.93 0
## 97 18.40 0
## 98 18.69 0
## 99 19.05 0
## 100 20.09 0resLow <- resSort[1:20,]
resLow## ReservationPrice Accept
## 1 3.99 1
## 2 4.42 1
## 3 5.22 1
## 4 5.26 1
## 5 5.88 1
## 6 5.90 1
## 7 6.00 1
## 8 6.02 1
## 9 6.59 1
## 10 6.83 1
## 11 6.97 1
## 12 7.26 1
## 13 7.38 1
## 14 7.64 1
## 15 7.73 1
## 16 7.80 1
## 17 7.89 1
## 18 7.89 1
## 19 8.06 1
## 20 8.40 1describe(resLow)## vars n mean sd median trimmed mad min max range skew
## ReservationPrice 1 20 6.66 1.27 6.9 6.77 1.4 3.99 8.4 4.41 -0.52
## Accept 2 20 1.00 0.00 1.0 1.00 0.0 1.00 1.0 0.00 NaN
## kurtosis se
## ReservationPrice -0.95 0.28
## Accept NaN 0.00sum(resLow$ReservationPrice)## [1] 133.13The opportunity cost for those who most want to work is 133.13
set.seed(5)
res <- round(data.frame(rnorm(100,11,3.9)),digits=2)
colnames(res) <- "ReservationPrice"
describe(res)## vars n mean sd median trimmed mad min max range
## ReservationPrice 1 100 11.12 3.69 10.63 11.08 3.6 2.48 20.31 17.83
## skew kurtosis se
## ReservationPrice 0.12 -0.26 0.37res$Accept <- ifelse(res$ReservationPrice>12, 0,1)
res## ReservationPrice Accept
## 1 7.72 1
## 2 16.40 0
## 3 6.10 1
## 4 11.27 1
## 5 17.67 0
## 6 8.65 1
## 7 9.16 1
## 8 8.52 1
## 9 9.89 1
## 10 11.54 1
## 11 15.79 0
## 12 7.87 1
## 13 6.79 1
## 14 10.39 1
## 15 6.82 1
## 16 10.46 1
## 17 8.67 1
## 18 2.48 1
## 19 11.94 1
## 20 9.99 1
## 21 14.51 0
## 22 14.67 0
## 23 16.73 0
## 24 13.76 0
## 25 14.19 0
## 26 9.86 1
## 27 16.53 0
## 28 16.85 0
## 29 8.44 1
## 30 7.67 1
## 31 12.23 0
## 32 15.33 0
## 33 19.64 0
## 34 15.75 0
## 35 16.77 0
## 36 14.71 0
## 37 7.06 1
## 38 3.20 1
## 39 4.13 1
## 40 10.44 1
## 41 17.05 0
## 42 7.87 1
## 43 10.71 1
## 44 18.39 0
## 45 9.22 1
## 46 13.19 0
## 47 7.54 1
## 48 9.21 1
## 49 8.18 1
## 50 10.73 1
## 51 16.71 0
## 52 11.73 1
## 53 14.99 0
## 54 8.69 1
## 55 10.56 1
## 56 7.39 1
## 57 13.94 0
## 58 10.56 1
## 59 10.75 1
## 60 11.91 1
## 61 6.57 1
## 62 14.33 0
## 63 8.74 1
## 64 12.94 0
## 65 8.04 1
## 66 9.67 1
## 67 2.80 1
## 68 9.82 1
## 69 6.04 1
## 70 9.91 1
## 71 10.20 1
## 72 10.12 1
## 73 12.35 0
## 74 11.13 1
## 75 12.61 0
## 76 10.39 1
## 77 14.80 0
## 78 11.47 1
## 79 11.74 1
## 80 8.80 1
## 81 12.94 0
## 82 4.21 1
## 83 14.80 0
## 84 10.91 1
## 85 13.64 0
## 86 8.23 1
## 87 20.31 0
## 88 9.15 1
## 89 10.70 1
## 90 8.96 1
## 91 14.61 0
## 92 6.86 1
## 93 13.17 0
## 94 14.51 0
## 95 14.86 0
## 96 12.50 0
## 97 9.65 1
## 98 8.89 1
## 99 10.29 1
## 100 10.77 1## subset data to the job offers up to 12 accepts
subRes <- res[1:30,]
subRes## ReservationPrice Accept
## 1 7.72 1
## 2 16.40 0
## 3 6.10 1
## 4 11.27 1
## 5 17.67 0
## 6 8.65 1
## 7 9.16 1
## 8 8.52 1
## 9 9.89 1
## 10 11.54 1
## 11 15.79 0
## 12 7.87 1
## 13 6.79 1
## 14 10.39 1
## 15 6.82 1
## 16 10.46 1
## 17 8.67 1
## 18 2.48 1
## 19 11.94 1
## 20 9.99 1
## 21 14.51 0
## 22 14.67 0
## 23 16.73 0
## 24 13.76 0
## 25 14.19 0
## 26 9.86 1
## 27 16.53 0
## 28 16.85 0
## 29 8.44 1
## 30 7.67 1sum(subRes$ReservationPrice)## [1] 331.33331.33
resSort <- arrange(res, ReservationPrice)
resSort## ReservationPrice Accept
## 1 2.48 1
## 2 2.80 1
## 3 3.20 1
## 4 4.13 1
## 5 4.21 1
## 6 6.04 1
## 7 6.10 1
## 8 6.57 1
## 9 6.79 1
## 10 6.82 1
## 11 6.86 1
## 12 7.06 1
## 13 7.39 1
## 14 7.54 1
## 15 7.67 1
## 16 7.72 1
## 17 7.87 1
## 18 7.87 1
## 19 8.04 1
## 20 8.18 1
## 21 8.23 1
## 22 8.44 1
## 23 8.52 1
## 24 8.65 1
## 25 8.67 1
## 26 8.69 1
## 27 8.74 1
## 28 8.80 1
## 29 8.89 1
## 30 8.96 1
## 31 9.15 1
## 32 9.16 1
## 33 9.21 1
## 34 9.22 1
## 35 9.65 1
## 36 9.67 1
## 37 9.82 1
## 38 9.86 1
## 39 9.89 1
## 40 9.91 1
## 41 9.99 1
## 42 10.12 1
## 43 10.20 1
## 44 10.29 1
## 45 10.39 1
## 46 10.39 1
## 47 10.44 1
## 48 10.46 1
## 49 10.56 1
## 50 10.56 1
## 51 10.70 1
## 52 10.71 1
## 53 10.73 1
## 54 10.75 1
## 55 10.77 1
## 56 10.91 1
## 57 11.13 1
## 58 11.27 1
## 59 11.47 1
## 60 11.54 1
## 61 11.73 1
## 62 11.74 1
## 63 11.91 1
## 64 11.94 1
## 65 12.23 0
## 66 12.35 0
## 67 12.50 0
## 68 12.61 0
## 69 12.94 0
## 70 12.94 0
## 71 13.17 0
## 72 13.19 0
## 73 13.64 0
## 74 13.76 0
## 75 13.94 0
## 76 14.19 0
## 77 14.33 0
## 78 14.51 0
## 79 14.51 0
## 80 14.61 0
## 81 14.67 0
## 82 14.71 0
## 83 14.80 0
## 84 14.80 0
## 85 14.86 0
## 86 14.99 0
## 87 15.33 0
## 88 15.75 0
## 89 15.79 0
## 90 16.40 0
## 91 16.53 0
## 92 16.71 0
## 93 16.73 0
## 94 16.77 0
## 95 16.85 0
## 96 17.05 0
## 97 17.67 0
## 98 18.39 0
## 99 19.64 0
## 100 20.31 0resLow <- resSort[1:20,]
resLow## ReservationPrice Accept
## 1 2.48 1
## 2 2.80 1
## 3 3.20 1
## 4 4.13 1
## 5 4.21 1
## 6 6.04 1
## 7 6.10 1
## 8 6.57 1
## 9 6.79 1
## 10 6.82 1
## 11 6.86 1
## 12 7.06 1
## 13 7.39 1
## 14 7.54 1
## 15 7.67 1
## 16 7.72 1
## 17 7.87 1
## 18 7.87 1
## 19 8.04 1
## 20 8.18 1describe(resLow)## vars n mean sd median trimmed mad min max range
## ReservationPrice 1 20 6.27 1.85 6.84 6.49 1.27 2.48 8.18 5.7
## Accept 2 20 1.00 0.00 1.00 1.00 0.00 1.00 1.00 0.0
## skew kurtosis se
## ReservationPrice -0.88 -0.76 0.41
## Accept NaN NaN 0.00sum(resLow$ReservationPrice)## [1] 125.34The opportunity cost for those who most want to work is 125.34
set.seed(6)
res <- round(data.frame(rnorm(100,11,3.9)),digits=2)
colnames(res) <- "ReservationPrice"
describe(res)## vars n mean sd median trimmed mad min max range
## ReservationPrice 1 100 10.96 4.03 10.46 10.73 3.83 3.39 21.17 17.78
## skew kurtosis se
## ReservationPrice 0.46 -0.41 0.4res$Accept <- ifelse(res$ReservationPrice>12, 0,1)
res## ReservationPrice Accept
## 1 12.05 0
## 2 8.54 1
## 3 14.39 0
## 4 17.74 0
## 5 11.09 1
## 6 12.44 0
## 7 5.89 1
## 8 13.88 0
## 9 11.18 1
## 10 6.91 1
## 11 17.74 0
## 12 6.40 1
## 13 13.55 0
## 14 9.56 1
## 15 8.66 1
## 16 11.21 1
## 17 17.66 0
## 18 6.73 1
## 19 9.87 1
## 20 19.61 0
## 21 13.02 0
## 22 5.52 1
## 23 18.86 0
## 24 6.37 1
## 25 11.74 1
## 26 6.44 1
## 27 10.85 1
## 28 20.18 0
## 29 16.43 0
## 30 8.81 1
## 31 8.38 1
## 32 12.92 0
## 33 6.40 1
## 34 6.87 1
## 35 15.44 0
## 36 10.37 1
## 37 13.46 0
## 38 17.31 0
## 39 10.25 1
## 40 4.73 1
## 41 7.55 1
## 42 9.31 1
## 43 9.36 1
## 44 10.34 1
## 45 11.96 1
## 46 8.09 1
## 47 9.93 1
## 48 18.12 0
## 49 11.06 1
## 50 11.73 1
## 51 10.79 1
## 52 12.80 0
## 53 8.67 1
## 54 15.93 0
## 55 6.53 1
## 56 15.23 0
## 57 5.04 1
## 58 4.86 1
## 59 10.56 1
## 60 11.43 1
## 61 11.84 1
## 62 13.16 0
## 63 6.87 1
## 64 4.72 1
## 65 9.68 1
## 66 11.80 1
## 67 10.13 1
## 68 7.45 1
## 69 7.85 1
## 70 13.16 0
## 71 9.48 1
## 72 9.26 1
## 73 10.92 1
## 74 8.66 1
## 75 9.79 1
## 76 8.34 1
## 77 10.21 1
## 78 15.36 0
## 79 14.22 0
## 80 15.88 0
## 81 21.17 0
## 82 10.80 1
## 83 19.69 0
## 84 10.95 1
## 85 4.97 1
## 86 5.62 1
## 87 16.77 0
## 88 10.01 1
## 89 9.73 1
## 90 8.17 1
## 91 3.39 1
## 92 12.65 0
## 93 15.61 0
## 94 14.58 0
## 95 11.37 1
## 96 4.43 1
## 97 14.86 0
## 98 8.24 1
## 99 8.68 1
## 100 6.84 1## subset data to the job offers up to 12 accepts
subRes <- res[1:34,]
subRes## ReservationPrice Accept
## 1 12.05 0
## 2 8.54 1
## 3 14.39 0
## 4 17.74 0
## 5 11.09 1
## 6 12.44 0
## 7 5.89 1
## 8 13.88 0
## 9 11.18 1
## 10 6.91 1
## 11 17.74 0
## 12 6.40 1
## 13 13.55 0
## 14 9.56 1
## 15 8.66 1
## 16 11.21 1
## 17 17.66 0
## 18 6.73 1
## 19 9.87 1
## 20 19.61 0
## 21 13.02 0
## 22 5.52 1
## 23 18.86 0
## 24 6.37 1
## 25 11.74 1
## 26 6.44 1
## 27 10.85 1
## 28 20.18 0
## 29 16.43 0
## 30 8.81 1
## 31 8.38 1
## 32 12.92 0
## 33 6.40 1
## 34 6.87 1sum(subRes$ReservationPrice)## [1] 387.89387.89
resSort <- arrange(res, ReservationPrice)
resSort## ReservationPrice Accept
## 1 3.39 1
## 2 4.43 1
## 3 4.72 1
## 4 4.73 1
## 5 4.86 1
## 6 4.97 1
## 7 5.04 1
## 8 5.52 1
## 9 5.62 1
## 10 5.89 1
## 11 6.37 1
## 12 6.40 1
## 13 6.40 1
## 14 6.44 1
## 15 6.53 1
## 16 6.73 1
## 17 6.84 1
## 18 6.87 1
## 19 6.87 1
## 20 6.91 1
## 21 7.45 1
## 22 7.55 1
## 23 7.85 1
## 24 8.09 1
## 25 8.17 1
## 26 8.24 1
## 27 8.34 1
## 28 8.38 1
## 29 8.54 1
## 30 8.66 1
## 31 8.66 1
## 32 8.67 1
## 33 8.68 1
## 34 8.81 1
## 35 9.26 1
## 36 9.31 1
## 37 9.36 1
## 38 9.48 1
## 39 9.56 1
## 40 9.68 1
## 41 9.73 1
## 42 9.79 1
## 43 9.87 1
## 44 9.93 1
## 45 10.01 1
## 46 10.13 1
## 47 10.21 1
## 48 10.25 1
## 49 10.34 1
## 50 10.37 1
## 51 10.56 1
## 52 10.79 1
## 53 10.80 1
## 54 10.85 1
## 55 10.92 1
## 56 10.95 1
## 57 11.06 1
## 58 11.09 1
## 59 11.18 1
## 60 11.21 1
## 61 11.37 1
## 62 11.43 1
## 63 11.73 1
## 64 11.74 1
## 65 11.80 1
## 66 11.84 1
## 67 11.96 1
## 68 12.05 0
## 69 12.44 0
## 70 12.65 0
## 71 12.80 0
## 72 12.92 0
## 73 13.02 0
## 74 13.16 0
## 75 13.16 0
## 76 13.46 0
## 77 13.55 0
## 78 13.88 0
## 79 14.22 0
## 80 14.39 0
## 81 14.58 0
## 82 14.86 0
## 83 15.23 0
## 84 15.36 0
## 85 15.44 0
## 86 15.61 0
## 87 15.88 0
## 88 15.93 0
## 89 16.43 0
## 90 16.77 0
## 91 17.31 0
## 92 17.66 0
## 93 17.74 0
## 94 17.74 0
## 95 18.12 0
## 96 18.86 0
## 97 19.61 0
## 98 19.69 0
## 99 20.18 0
## 100 21.17 0resLow <- resSort[1:20,]
resLow## ReservationPrice Accept
## 1 3.39 1
## 2 4.43 1
## 3 4.72 1
## 4 4.73 1
## 5 4.86 1
## 6 4.97 1
## 7 5.04 1
## 8 5.52 1
## 9 5.62 1
## 10 5.89 1
## 11 6.37 1
## 12 6.40 1
## 13 6.40 1
## 14 6.44 1
## 15 6.53 1
## 16 6.73 1
## 17 6.84 1
## 18 6.87 1
## 19 6.87 1
## 20 6.91 1describe(resLow)## vars n mean sd median trimmed mad min max range
## ReservationPrice 1 20 5.78 1.02 6.13 5.87 1.07 3.39 6.91 3.52
## Accept 2 20 1.00 0.00 1.00 1.00 0.00 1.00 1.00 0.00
## skew kurtosis se
## ReservationPrice -0.59 -0.81 0.23
## Accept NaN NaN 0.00sum(resLow$ReservationPrice)## [1] 115.53The opportunity cost for those who most want to work is 115.53
set.seed(7)
res <- round(data.frame(rnorm(100,11,3.9)),digits=2)
colnames(res) <- "ReservationPrice"
describe(res)## vars n mean sd median trimmed mad min max range
## ReservationPrice 1 100 11.54 3.74 11.41 11.39 3.65 4.04 21.6 17.56
## skew kurtosis se
## ReservationPrice 0.37 -0.13 0.37res$Accept <- ifelse(res$ReservationPrice>12, 0,1)
res## ReservationPrice Accept
## 1 19.92 0
## 2 6.33 1
## 3 8.29 1
## 4 9.39 1
## 5 7.21 1
## 6 7.31 1
## 7 13.92 0
## 8 10.54 1
## 9 11.60 1
## 10 19.54 0
## 11 12.39 0
## 12 21.60 0
## 13 19.90 0
## 14 12.26 0
## 15 18.39 0
## 16 12.82 0
## 17 7.51 1
## 18 9.80 1
## 19 10.98 1
## 20 14.85 0
## 21 14.28 0
## 22 13.75 0
## 23 16.09 0
## 24 5.59 1
## 25 15.96 0
## 26 11.72 1
## 27 13.93 0
## 28 13.31 0
## 29 7.17 1
## 30 9.92 1
## 31 7.60 1
## 32 13.80 0
## 33 11.43 1
## 34 10.69 1
## 35 9.36 1
## 36 8.81 1
## 37 14.89 0
## 38 6.69 1
## 39 10.45 1
## 40 12.23 0
## 41 15.75 0
## 42 8.27 1
## 43 9.89 1
## 44 5.88 1
## 45 9.48 1
## 46 9.43 1
## 47 16.27 0
## 48 13.31 0
## 49 11.39 1
## 50 14.63 0
## 51 9.98 1
## 52 10.97 1
## 53 12.43 0
## 54 17.66 0
## 55 13.82 0
## 56 12.88 0
## 57 4.89 1
## 58 12.24 0
## 59 11.65 1
## 60 7.49 1
## 61 11.30 1
## 62 11.62 1
## 63 13.12 0
## 64 13.75 0
## 65 12.24 0
## 66 15.33 0
## 67 14.00 0
## 68 15.50 0
## 69 15.92 0
## 70 13.73 0
## 71 12.69 0
## 72 7.40 1
## 73 8.60 1
## 74 7.62 1
## 75 4.61 1
## 76 5.83 1
## 77 7.53 1
## 78 8.83 1
## 79 10.76 1
## 80 20.45 0
## 81 12.34 0
## 82 11.02 1
## 83 11.11 1
## 84 9.47 1
## 85 7.91 1
## 86 9.78 1
## 87 9.65 1
## 88 9.81 1
## 89 4.04 1
## 90 13.29 0
## 91 17.38 0
## 92 8.48 1
## 93 13.41 0
## 94 11.92 1
## 95 14.30 0
## 96 8.76 1
## 97 15.36 0
## 98 4.99 1
## 99 9.29 1
## 100 10.41 1## subset data to the job offers up to 12 accepts
subRes <- res[1:38,]
subRes## ReservationPrice Accept
## 1 19.92 0
## 2 6.33 1
## 3 8.29 1
## 4 9.39 1
## 5 7.21 1
## 6 7.31 1
## 7 13.92 0
## 8 10.54 1
## 9 11.60 1
## 10 19.54 0
## 11 12.39 0
## 12 21.60 0
## 13 19.90 0
## 14 12.26 0
## 15 18.39 0
## 16 12.82 0
## 17 7.51 1
## 18 9.80 1
## 19 10.98 1
## 20 14.85 0
## 21 14.28 0
## 22 13.75 0
## 23 16.09 0
## 24 5.59 1
## 25 15.96 0
## 26 11.72 1
## 27 13.93 0
## 28 13.31 0
## 29 7.17 1
## 30 9.92 1
## 31 7.60 1
## 32 13.80 0
## 33 11.43 1
## 34 10.69 1
## 35 9.36 1
## 36 8.81 1
## 37 14.89 0
## 38 6.69 1sum(subRes$ReservationPrice)## [1] 459.54459.54
resSort <- arrange(res, ReservationPrice)
resSort## ReservationPrice Accept
## 1 4.04 1
## 2 4.61 1
## 3 4.89 1
## 4 4.99 1
## 5 5.59 1
## 6 5.83 1
## 7 5.88 1
## 8 6.33 1
## 9 6.69 1
## 10 7.17 1
## 11 7.21 1
## 12 7.31 1
## 13 7.40 1
## 14 7.49 1
## 15 7.51 1
## 16 7.53 1
## 17 7.60 1
## 18 7.62 1
## 19 7.91 1
## 20 8.27 1
## 21 8.29 1
## 22 8.48 1
## 23 8.60 1
## 24 8.76 1
## 25 8.81 1
## 26 8.83 1
## 27 9.29 1
## 28 9.36 1
## 29 9.39 1
## 30 9.43 1
## 31 9.47 1
## 32 9.48 1
## 33 9.65 1
## 34 9.78 1
## 35 9.80 1
## 36 9.81 1
## 37 9.89 1
## 38 9.92 1
## 39 9.98 1
## 40 10.41 1
## 41 10.45 1
## 42 10.54 1
## 43 10.69 1
## 44 10.76 1
## 45 10.97 1
## 46 10.98 1
## 47 11.02 1
## 48 11.11 1
## 49 11.30 1
## 50 11.39 1
## 51 11.43 1
## 52 11.60 1
## 53 11.62 1
## 54 11.65 1
## 55 11.72 1
## 56 11.92 1
## 57 12.23 0
## 58 12.24 0
## 59 12.24 0
## 60 12.26 0
## 61 12.34 0
## 62 12.39 0
## 63 12.43 0
## 64 12.69 0
## 65 12.82 0
## 66 12.88 0
## 67 13.12 0
## 68 13.29 0
## 69 13.31 0
## 70 13.31 0
## 71 13.41 0
## 72 13.73 0
## 73 13.75 0
## 74 13.75 0
## 75 13.80 0
## 76 13.82 0
## 77 13.92 0
## 78 13.93 0
## 79 14.00 0
## 80 14.28 0
## 81 14.30 0
## 82 14.63 0
## 83 14.85 0
## 84 14.89 0
## 85 15.33 0
## 86 15.36 0
## 87 15.50 0
## 88 15.75 0
## 89 15.92 0
## 90 15.96 0
## 91 16.09 0
## 92 16.27 0
## 93 17.38 0
## 94 17.66 0
## 95 18.39 0
## 96 19.54 0
## 97 19.90 0
## 98 19.92 0
## 99 20.45 0
## 100 21.60 0resLow <- resSort[1:20,]
resLow## ReservationPrice Accept
## 1 4.04 1
## 2 4.61 1
## 3 4.89 1
## 4 4.99 1
## 5 5.59 1
## 6 5.83 1
## 7 5.88 1
## 8 6.33 1
## 9 6.69 1
## 10 7.17 1
## 11 7.21 1
## 12 7.31 1
## 13 7.40 1
## 14 7.49 1
## 15 7.51 1
## 16 7.53 1
## 17 7.60 1
## 18 7.62 1
## 19 7.91 1
## 20 8.27 1describe(resLow)## vars n mean sd median trimmed mad min max range skew
## ReservationPrice 1 20 6.59 1.24 7.19 6.69 0.9 4.04 8.27 4.23 -0.6
## Accept 2 20 1.00 0.00 1.00 1.00 0.0 1.00 1.00 0.00 NaN
## kurtosis se
## ReservationPrice -1.07 0.28
## Accept NaN 0.00sum(resLow$ReservationPrice)## [1] 131.87The opportunity cost for those who most want to work is 131.87
set.seed(8)
res <- round(data.frame(rnorm(100,11,3.9)),digits=2)
colnames(res) <- "ReservationPrice"
describe(res)## vars n mean sd median trimmed mad min max range
## ReservationPrice 1 100 10.64 4.21 10.7 10.73 3.92 -0.76 20.27 21.03
## skew kurtosis se
## ReservationPrice -0.29 0.13 0.42res$Accept <- ifelse(res$ReservationPrice>12, 0,1)
res## ReservationPrice Accept
## 1 10.67 1
## 2 14.28 0
## 3 9.19 1
## 4 8.85 1
## 5 13.87 0
## 6 10.58 1
## 7 10.34 1
## 8 6.76 1
## 9 -0.74 1
## 10 8.69 1
## 11 8.04 1
## 12 12.14 0
## 13 12.64 0
## 14 5.95 1
## 15 11.27 1
## 16 7.83 1
## 17 16.89 0
## 18 9.94 1
## 19 17.08 0
## 20 10.07 1
## 21 16.00 0
## 22 10.96 1
## 23 9.44 1
## 24 11.09 1
## 25 17.80 0
## 26 6.68 1
## 27 6.86 1
## 28 18.61 0
## 29 13.35 0
## 30 3.12 1
## 31 16.88 0
## 32 14.76 0
## 33 4.94 1
## 34 7.98 1
## 35 15.92 0
## 36 12.67 0
## 37 14.29 0
## 38 8.27 1
## 39 10.75 1
## 40 12.84 0
## 41 12.42 0
## 42 8.60 1
## 43 11.89 1
## 44 9.98 1
## 45 13.39 0
## 46 3.37 1
## 47 8.41 1
## 48 12.11 0
## 49 12.05 0
## 50 8.50 1
## 51 15.21 0
## 52 9.58 1
## 53 13.30 0
## 54 10.63 1
## 55 14.79 0
## 56 13.26 0
## 57 7.97 1
## 58 8.66 1
## 59 5.15 1
## 60 13.94 0
## 61 13.17 0
## 62 11.37 1
## 63 4.05 1
## 64 6.68 1
## 65 9.96 1
## 66 6.80 1
## 67 9.08 1
## 68 17.39 0
## 69 12.55 0
## 70 4.77 1
## 71 5.28 1
## 72 15.06 0
## 73 14.05 0
## 74 9.14 1
## 75 11.37 1
## 76 13.34 0
## 77 -0.30 1
## 78 13.28 0
## 79 20.27 0
## 80 8.48 1
## 81 11.95 1
## 82 7.92 1
## 83 6.73 1
## 84 18.97 0
## 85 4.44 1
## 86 15.74 0
## 87 10.63 1
## 88 7.29 1
## 89 13.34 0
## 90 -0.76 1
## 91 14.00 0
## 92 17.12 0
## 93 9.04 1
## 94 8.59 1
## 95 5.73 1
## 96 14.00 0
## 97 12.28 0
## 98 10.83 1
## 99 8.51 1
## 100 10.73 1## subset data to the job offers up to 12 accepts
subRes <- res[1:30,]
subRes## ReservationPrice Accept
## 1 10.67 1
## 2 14.28 0
## 3 9.19 1
## 4 8.85 1
## 5 13.87 0
## 6 10.58 1
## 7 10.34 1
## 8 6.76 1
## 9 -0.74 1
## 10 8.69 1
## 11 8.04 1
## 12 12.14 0
## 13 12.64 0
## 14 5.95 1
## 15 11.27 1
## 16 7.83 1
## 17 16.89 0
## 18 9.94 1
## 19 17.08 0
## 20 10.07 1
## 21 16.00 0
## 22 10.96 1
## 23 9.44 1
## 24 11.09 1
## 25 17.80 0
## 26 6.68 1
## 27 6.86 1
## 28 18.61 0
## 29 13.35 0
## 30 3.12 1sum(subRes$ReservationPrice)## [1] 318.25318.25
resSort <- arrange(res, ReservationPrice)
resSort## ReservationPrice Accept
## 1 -0.76 1
## 2 -0.74 1
## 3 -0.30 1
## 4 3.12 1
## 5 3.37 1
## 6 4.05 1
## 7 4.44 1
## 8 4.77 1
## 9 4.94 1
## 10 5.15 1
## 11 5.28 1
## 12 5.73 1
## 13 5.95 1
## 14 6.68 1
## 15 6.68 1
## 16 6.73 1
## 17 6.76 1
## 18 6.80 1
## 19 6.86 1
## 20 7.29 1
## 21 7.83 1
## 22 7.92 1
## 23 7.97 1
## 24 7.98 1
## 25 8.04 1
## 26 8.27 1
## 27 8.41 1
## 28 8.48 1
## 29 8.50 1
## 30 8.51 1
## 31 8.59 1
## 32 8.60 1
## 33 8.66 1
## 34 8.69 1
## 35 8.85 1
## 36 9.04 1
## 37 9.08 1
## 38 9.14 1
## 39 9.19 1
## 40 9.44 1
## 41 9.58 1
## 42 9.94 1
## 43 9.96 1
## 44 9.98 1
## 45 10.07 1
## 46 10.34 1
## 47 10.58 1
## 48 10.63 1
## 49 10.63 1
## 50 10.67 1
## 51 10.73 1
## 52 10.75 1
## 53 10.83 1
## 54 10.96 1
## 55 11.09 1
## 56 11.27 1
## 57 11.37 1
## 58 11.37 1
## 59 11.89 1
## 60 11.95 1
## 61 12.05 0
## 62 12.11 0
## 63 12.14 0
## 64 12.28 0
## 65 12.42 0
## 66 12.55 0
## 67 12.64 0
## 68 12.67 0
## 69 12.84 0
## 70 13.17 0
## 71 13.26 0
## 72 13.28 0
## 73 13.30 0
## 74 13.34 0
## 75 13.34 0
## 76 13.35 0
## 77 13.39 0
## 78 13.87 0
## 79 13.94 0
## 80 14.00 0
## 81 14.00 0
## 82 14.05 0
## 83 14.28 0
## 84 14.29 0
## 85 14.76 0
## 86 14.79 0
## 87 15.06 0
## 88 15.21 0
## 89 15.74 0
## 90 15.92 0
## 91 16.00 0
## 92 16.88 0
## 93 16.89 0
## 94 17.08 0
## 95 17.12 0
## 96 17.39 0
## 97 17.80 0
## 98 18.61 0
## 99 18.97 0
## 100 20.27 0resLow <- resSort[1:20,]
resLow## ReservationPrice Accept
## 1 -0.76 1
## 2 -0.74 1
## 3 -0.30 1
## 4 3.12 1
## 5 3.37 1
## 6 4.05 1
## 7 4.44 1
## 8 4.77 1
## 9 4.94 1
## 10 5.15 1
## 11 5.28 1
## 12 5.73 1
## 13 5.95 1
## 14 6.68 1
## 15 6.68 1
## 16 6.73 1
## 17 6.76 1
## 18 6.80 1
## 19 6.86 1
## 20 7.29 1describe(resLow)## vars n mean sd median trimmed mad min max range
## ReservationPrice 1 20 4.64 2.56 5.21 5.01 2.21 -0.76 7.29 8.05
## Accept 2 20 1.00 0.00 1.00 1.00 0.00 1.00 1.00 0.00
## skew kurtosis se
## ReservationPrice -1.08 -0.12 0.57
## Accept NaN NaN 0.00sum(resLow$ReservationPrice)## [1] 92.8The opportunity cost for those who most want to work is 92.8
set.seed(9)
res <- round(data.frame(rnorm(100,11,3.9)),digits=2)
colnames(res) <- "ReservationPrice"
describe(res)## vars n mean sd median trimmed mad min max range
## ReservationPrice 1 100 10.79 3.74 10.34 10.63 3.42 0.79 21.46 20.67
## skew kurtosis se
## ReservationPrice 0.31 0.13 0.37res$Accept <- ifelse(res$ReservationPrice>12, 0,1)
res## ReservationPrice Accept
## 1 8.01 1
## 2 7.82 1
## 3 10.45 1
## 4 9.92 1
## 5 12.70 0
## 6 6.37 1
## 7 15.65 0
## 8 10.93 1
## 9 10.03 1
## 10 9.58 1
## 11 15.98 0
## 12 9.17 1
## 13 11.28 1
## 14 9.96 1
## 15 18.20 0
## 16 7.73 1
## 17 10.70 1
## 18 0.79 1
## 19 14.46 0
## 20 8.24 1
## 21 17.85 0
## 22 11.71 1
## 23 9.96 1
## 24 14.61 0
## 25 8.30 1
## 26 21.46 0
## 27 11.87 1
## 28 8.24 1
## 29 12.63 0
## 30 12.44 0
## 31 7.44 1
## 32 9.76 1
## 33 15.09 0
## 34 11.66 1
## 35 11.12 1
## 36 7.06 1
## 37 12.49 0
## 38 7.80 1
## 39 12.41 0
## 40 11.36 1
## 41 7.85 1
## 42 3.12 1
## 43 8.12 1
## 44 12.49 0
## 45 17.75 0
## 46 10.21 1
## 47 7.11 1
## 48 5.90 1
## 49 7.11 1
## 50 8.80 1
## 51 17.83 0
## 52 8.86 1
## 53 7.65 1
## 54 11.19 1
## 55 10.22 1
## 56 6.69 1
## 57 11.94 1
## 58 12.49 0
## 59 19.70 0
## 60 15.68 0
## 61 12.10 0
## 62 6.31 1
## 63 12.81 0
## 64 12.37 0
## 65 8.70 1
## 66 7.67 1
## 67 10.04 1
## 68 17.00 0
## 69 13.13 0
## 70 17.10 0
## 71 11.97 1
## 72 3.35 1
## 73 7.84 1
## 74 9.06 1
## 75 12.19 0
## 76 9.87 1
## 77 16.69 0
## 78 14.41 0
## 79 7.28 1
## 80 10.88 1
## 81 11.44 1
## 82 6.89 1
## 83 11.61 1
## 84 16.07 0
## 85 6.49 1
## 86 11.84 1
## 87 14.14 0
## 88 8.14 1
## 89 4.69 1
## 90 14.27 0
## 91 9.63 1
## 92 8.21 1
## 93 7.33 1
## 94 13.85 0
## 95 9.29 1
## 96 10.03 1
## 97 8.38 1
## 98 14.12 0
## 99 5.19 1
## 100 12.77 0## subset data to the job offers up to 12 accepts
subRes <- res[1:28,]
subRes## ReservationPrice Accept
## 1 8.01 1
## 2 7.82 1
## 3 10.45 1
## 4 9.92 1
## 5 12.70 0
## 6 6.37 1
## 7 15.65 0
## 8 10.93 1
## 9 10.03 1
## 10 9.58 1
## 11 15.98 0
## 12 9.17 1
## 13 11.28 1
## 14 9.96 1
## 15 18.20 0
## 16 7.73 1
## 17 10.70 1
## 18 0.79 1
## 19 14.46 0
## 20 8.24 1
## 21 17.85 0
## 22 11.71 1
## 23 9.96 1
## 24 14.61 0
## 25 8.30 1
## 26 21.46 0
## 27 11.87 1
## 28 8.24 1sum(subRes$ReservationPrice)## [1] 311.97311.97
resSort <- arrange(res, ReservationPrice)
resSort## ReservationPrice Accept
## 1 0.79 1
## 2 3.12 1
## 3 3.35 1
## 4 4.69 1
## 5 5.19 1
## 6 5.90 1
## 7 6.31 1
## 8 6.37 1
## 9 6.49 1
## 10 6.69 1
## 11 6.89 1
## 12 7.06 1
## 13 7.11 1
## 14 7.11 1
## 15 7.28 1
## 16 7.33 1
## 17 7.44 1
## 18 7.65 1
## 19 7.67 1
## 20 7.73 1
## 21 7.80 1
## 22 7.82 1
## 23 7.84 1
## 24 7.85 1
## 25 8.01 1
## 26 8.12 1
## 27 8.14 1
## 28 8.21 1
## 29 8.24 1
## 30 8.24 1
## 31 8.30 1
## 32 8.38 1
## 33 8.70 1
## 34 8.80 1
## 35 8.86 1
## 36 9.06 1
## 37 9.17 1
## 38 9.29 1
## 39 9.58 1
## 40 9.63 1
## 41 9.76 1
## 42 9.87 1
## 43 9.92 1
## 44 9.96 1
## 45 9.96 1
## 46 10.03 1
## 47 10.03 1
## 48 10.04 1
## 49 10.21 1
## 50 10.22 1
## 51 10.45 1
## 52 10.70 1
## 53 10.88 1
## 54 10.93 1
## 55 11.12 1
## 56 11.19 1
## 57 11.28 1
## 58 11.36 1
## 59 11.44 1
## 60 11.61 1
## 61 11.66 1
## 62 11.71 1
## 63 11.84 1
## 64 11.87 1
## 65 11.94 1
## 66 11.97 1
## 67 12.10 0
## 68 12.19 0
## 69 12.37 0
## 70 12.41 0
## 71 12.44 0
## 72 12.49 0
## 73 12.49 0
## 74 12.49 0
## 75 12.63 0
## 76 12.70 0
## 77 12.77 0
## 78 12.81 0
## 79 13.13 0
## 80 13.85 0
## 81 14.12 0
## 82 14.14 0
## 83 14.27 0
## 84 14.41 0
## 85 14.46 0
## 86 14.61 0
## 87 15.09 0
## 88 15.65 0
## 89 15.68 0
## 90 15.98 0
## 91 16.07 0
## 92 16.69 0
## 93 17.00 0
## 94 17.10 0
## 95 17.75 0
## 96 17.83 0
## 97 17.85 0
## 98 18.20 0
## 99 19.70 0
## 100 21.46 0resLow <- resSort[1:20,]
resLow## ReservationPrice Accept
## 1 0.79 1
## 2 3.12 1
## 3 3.35 1
## 4 4.69 1
## 5 5.19 1
## 6 5.90 1
## 7 6.31 1
## 8 6.37 1
## 9 6.49 1
## 10 6.69 1
## 11 6.89 1
## 12 7.06 1
## 13 7.11 1
## 14 7.11 1
## 15 7.28 1
## 16 7.33 1
## 17 7.44 1
## 18 7.65 1
## 19 7.67 1
## 20 7.73 1describe(resLow)## vars n mean sd median trimmed mad min max range
## ReservationPrice 1 20 6.11 1.83 6.79 6.43 0.88 0.79 7.73 6.94
## Accept 2 20 1.00 0.00 1.00 1.00 0.00 1.00 1.00 0.00
## skew kurtosis se
## ReservationPrice -1.46 1.29 0.41
## Accept NaN NaN 0.00sum(resLow$ReservationPrice)## [1] 122.17The opportunity cost for those who most want to work is 122.17
set.seed(10)
res <- round(data.frame(rnorm(100,11,3.9)),digits=2)
colnames(res) <- "ReservationPrice"
describe(res)## vars n mean sd median trimmed mad min max range
## ReservationPrice 1 100 10.47 3.67 10.25 10.47 4.15 2.48 19.66 17.18
## skew kurtosis se
## ReservationPrice 0.03 -0.56 0.37res$Accept <- ifelse(res$ReservationPrice>12, 0,1)
res## ReservationPrice Accept
## 1 11.07 1
## 2 10.28 1
## 3 5.65 1
## 4 8.66 1
## 5 12.15 0
## 6 12.52 0
## 7 6.29 1
## 8 9.58 1
## 9 4.66 1
## 10 10.00 1
## 11 15.30 0
## 12 13.95 0
## 13 10.07 1
## 14 14.85 0
## 15 13.89 0
## 16 11.35 1
## 17 7.28 1
## 18 10.24 1
## 19 14.61 0
## 20 12.88 0
## 21 8.67 1
## 22 2.48 1
## 23 8.37 1
## 24 2.74 1
## 25 6.07 1
## 26 9.54 1
## 27 8.32 1
## 28 7.60 1
## 29 10.60 1
## 30 10.01 1
## 31 3.77 1
## 32 10.70 1
## 33 14.78 0
## 34 11.72 1
## 35 5.62 1
## 36 5.40 1
## 37 12.41 0
## 38 4.14 1
## 39 9.73 1
## 40 8.46 1
## 41 15.24 0
## 42 8.03 1
## 43 7.77 1
## 44 14.25 0
## 45 7.23 1
## 46 10.89 1
## 47 11.91 1
## 48 9.83 1
## 49 8.36 1
## 50 13.56 0
## 51 9.44 1
## 52 9.70 1
## 53 16.34 0
## 54 19.34 0
## 55 12.97 0
## 56 14.07 0
## 57 7.48 1
## 58 13.08 0
## 59 8.48 1
## 60 12.13 0
## 61 6.17 1
## 62 9.22 1
## 63 7.76 1
## 64 12.33 0
## 65 15.16 0
## 66 15.74 0
## 67 13.87 0
## 68 9.12 1
## 69 13.19 0
## 70 6.14 1
## 71 12.49 0
## 72 5.42 1
## 73 6.91 1
## 74 10.15 1
## 75 5.19 1
## 76 15.57 0
## 77 5.23 1
## 78 9.32 1
## 79 6.90 1
## 80 16.94 0
## 81 13.31 0
## 82 10.13 1
## 83 13.78 0
## 84 13.79 0
## 85 12.72 0
## 86 11.62 1
## 87 13.57 0
## 88 19.66 0
## 89 6.38 1
## 90 10.71 1
## 91 9.38 1
## 92 10.25 1
## 93 11.27 1
## 94 15.51 0
## 95 13.32 0
## 96 5.46 1
## 97 4.73 1
## 98 14.48 0
## 99 11.58 1
## 100 15.79 0## subset data to the job offers up to 12 accepts
subRes <- res[1:28,]
subRes## ReservationPrice Accept
## 1 11.07 1
## 2 10.28 1
## 3 5.65 1
## 4 8.66 1
## 5 12.15 0
## 6 12.52 0
## 7 6.29 1
## 8 9.58 1
## 9 4.66 1
## 10 10.00 1
## 11 15.30 0
## 12 13.95 0
## 13 10.07 1
## 14 14.85 0
## 15 13.89 0
## 16 11.35 1
## 17 7.28 1
## 18 10.24 1
## 19 14.61 0
## 20 12.88 0
## 21 8.67 1
## 22 2.48 1
## 23 8.37 1
## 24 2.74 1
## 25 6.07 1
## 26 9.54 1
## 27 8.32 1
## 28 7.60 1sum(subRes$ReservationPrice)## [1] 269.07269.07
resSort <- arrange(res, ReservationPrice)
resSort## ReservationPrice Accept
## 1 2.48 1
## 2 2.74 1
## 3 3.77 1
## 4 4.14 1
## 5 4.66 1
## 6 4.73 1
## 7 5.19 1
## 8 5.23 1
## 9 5.40 1
## 10 5.42 1
## 11 5.46 1
## 12 5.62 1
## 13 5.65 1
## 14 6.07 1
## 15 6.14 1
## 16 6.17 1
## 17 6.29 1
## 18 6.38 1
## 19 6.90 1
## 20 6.91 1
## 21 7.23 1
## 22 7.28 1
## 23 7.48 1
## 24 7.60 1
## 25 7.76 1
## 26 7.77 1
## 27 8.03 1
## 28 8.32 1
## 29 8.36 1
## 30 8.37 1
## 31 8.46 1
## 32 8.48 1
## 33 8.66 1
## 34 8.67 1
## 35 9.12 1
## 36 9.22 1
## 37 9.32 1
## 38 9.38 1
## 39 9.44 1
## 40 9.54 1
## 41 9.58 1
## 42 9.70 1
## 43 9.73 1
## 44 9.83 1
## 45 10.00 1
## 46 10.01 1
## 47 10.07 1
## 48 10.13 1
## 49 10.15 1
## 50 10.24 1
## 51 10.25 1
## 52 10.28 1
## 53 10.60 1
## 54 10.70 1
## 55 10.71 1
## 56 10.89 1
## 57 11.07 1
## 58 11.27 1
## 59 11.35 1
## 60 11.58 1
## 61 11.62 1
## 62 11.72 1
## 63 11.91 1
## 64 12.13 0
## 65 12.15 0
## 66 12.33 0
## 67 12.41 0
## 68 12.49 0
## 69 12.52 0
## 70 12.72 0
## 71 12.88 0
## 72 12.97 0
## 73 13.08 0
## 74 13.19 0
## 75 13.31 0
## 76 13.32 0
## 77 13.56 0
## 78 13.57 0
## 79 13.78 0
## 80 13.79 0
## 81 13.87 0
## 82 13.89 0
## 83 13.95 0
## 84 14.07 0
## 85 14.25 0
## 86 14.48 0
## 87 14.61 0
## 88 14.78 0
## 89 14.85 0
## 90 15.16 0
## 91 15.24 0
## 92 15.30 0
## 93 15.51 0
## 94 15.57 0
## 95 15.74 0
## 96 15.79 0
## 97 16.34 0
## 98 16.94 0
## 99 19.34 0
## 100 19.66 0resLow <- resSort[1:20,]
resLow## ReservationPrice Accept
## 1 2.48 1
## 2 2.74 1
## 3 3.77 1
## 4 4.14 1
## 5 4.66 1
## 6 4.73 1
## 7 5.19 1
## 8 5.23 1
## 9 5.40 1
## 10 5.42 1
## 11 5.46 1
## 12 5.62 1
## 13 5.65 1
## 14 6.07 1
## 15 6.14 1
## 16 6.17 1
## 17 6.29 1
## 18 6.38 1
## 19 6.90 1
## 20 6.91 1describe(resLow)## vars n mean sd median trimmed mad min max range
## ReservationPrice 1 20 5.27 1.23 5.44 5.4 1.07 2.48 6.91 4.43
## Accept 2 20 1.00 0.00 1.00 1.0 0.00 1.00 1.00 0.00
## skew kurtosis se
## ReservationPrice -0.81 -0.19 0.27
## Accept NaN NaN 0.00sum(resLow$ReservationPrice)## [1] 105.35The opportunity cost for those who most want to work is 105.35
set.seed(11)
res <- round(data.frame(rnorm(100,11,3.9)),digits=2)
colnames(res) <- "ReservationPrice"
describe(res)## vars n mean sd median trimmed mad min max range
## ReservationPrice 1 100 10.52 3.57 10.27 10.4 3.84 2.47 20.12 17.65
## skew kurtosis se
## ReservationPrice 0.32 -0.25 0.36res$Accept <- ifelse(res$ReservationPrice>12, 0,1)
res## ReservationPrice Accept
## 1 8.69 1
## 2 11.10 1
## 3 5.09 1
## 4 5.69 1
## 5 15.60 0
## 6 7.36 1
## 7 16.16 0
## 8 13.44 0
## 9 10.82 1
## 10 7.08 1
## 11 7.77 1
## 12 9.64 1
## 13 5.00 1
## 14 10.00 1
## 15 6.52 1
## 16 11.05 1
## 17 10.13 1
## 18 14.46 0
## 19 8.69 1
## 20 8.44 1
## 21 8.34 1
## 22 10.94 1
## 23 9.27 1
## 24 12.37 0
## 25 11.29 1
## 26 11.03 1
## 27 10.27 1
## 28 8.01 1
## 29 10.14 1
## 30 7.16 1
## 31 6.69 1
## 32 7.34 1
## 33 13.65 0
## 34 4.85 1
## 35 7.61 1
## 36 12.89 0
## 37 10.27 1
## 38 17.03 0
## 39 8.62 1
## 40 9.64 1
## 41 4.62 1
## 42 11.08 1
## 43 14.48 0
## 44 7.60 1
## 45 14.47 0
## 46 9.66 1
## 47 2.47 1
## 48 14.43 0
## 49 13.82 0
## 50 11.86 1
## 51 14.08 0
## 52 10.10 1
## 53 7.81 1
## 54 12.95 0
## 55 11.62 1
## 56 13.12 0
## 57 10.39 1
## 58 12.71 0
## 59 16.80 0
## 60 11.23 1
## 61 7.69 1
## 62 20.12 0
## 63 10.53 1
## 64 3.39 1
## 65 13.10 0
## 66 17.60 0
## 67 7.92 1
## 68 6.81 1
## 69 8.63 1
## 70 13.94 0
## 71 12.77 0
## 72 10.52 1
## 73 8.02 1
## 74 11.89 1
## 75 15.37 0
## 76 11.61 1
## 77 8.31 1
## 78 12.77 0
## 79 6.84 1
## 80 12.57 0
## 81 10.75 1
## 82 12.23 0
## 83 8.64 1
## 84 7.46 1
## 85 19.82 0
## 86 8.65 1
## 87 5.94 1
## 88 12.98 0
## 89 7.67 1
## 90 5.13 1
## 91 15.69 0
## 92 6.99 1
## 93 14.66 0
## 94 8.88 1
## 95 13.00 0
## 96 9.62 1
## 97 16.17 0
## 98 6.55 1
## 99 16.51 0
## 100 8.65 1## subset data to the job offers up to 12 accepts
subRes <- res[1:25,]
subRes## ReservationPrice Accept
## 1 8.69 1
## 2 11.10 1
## 3 5.09 1
## 4 5.69 1
## 5 15.60 0
## 6 7.36 1
## 7 16.16 0
## 8 13.44 0
## 9 10.82 1
## 10 7.08 1
## 11 7.77 1
## 12 9.64 1
## 13 5.00 1
## 14 10.00 1
## 15 6.52 1
## 16 11.05 1
## 17 10.13 1
## 18 14.46 0
## 19 8.69 1
## 20 8.44 1
## 21 8.34 1
## 22 10.94 1
## 23 9.27 1
## 24 12.37 0
## 25 11.29 1sum(subRes$ReservationPrice)## [1] 244.94244.94
resSort <- arrange(res, ReservationPrice)
resSort## ReservationPrice Accept
## 1 2.47 1
## 2 3.39 1
## 3 4.62 1
## 4 4.85 1
## 5 5.00 1
## 6 5.09 1
## 7 5.13 1
## 8 5.69 1
## 9 5.94 1
## 10 6.52 1
## 11 6.55 1
## 12 6.69 1
## 13 6.81 1
## 14 6.84 1
## 15 6.99 1
## 16 7.08 1
## 17 7.16 1
## 18 7.34 1
## 19 7.36 1
## 20 7.46 1
## 21 7.60 1
## 22 7.61 1
## 23 7.67 1
## 24 7.69 1
## 25 7.77 1
## 26 7.81 1
## 27 7.92 1
## 28 8.01 1
## 29 8.02 1
## 30 8.31 1
## 31 8.34 1
## 32 8.44 1
## 33 8.62 1
## 34 8.63 1
## 35 8.64 1
## 36 8.65 1
## 37 8.65 1
## 38 8.69 1
## 39 8.69 1
## 40 8.88 1
## 41 9.27 1
## 42 9.62 1
## 43 9.64 1
## 44 9.64 1
## 45 9.66 1
## 46 10.00 1
## 47 10.10 1
## 48 10.13 1
## 49 10.14 1
## 50 10.27 1
## 51 10.27 1
## 52 10.39 1
## 53 10.52 1
## 54 10.53 1
## 55 10.75 1
## 56 10.82 1
## 57 10.94 1
## 58 11.03 1
## 59 11.05 1
## 60 11.08 1
## 61 11.10 1
## 62 11.23 1
## 63 11.29 1
## 64 11.61 1
## 65 11.62 1
## 66 11.86 1
## 67 11.89 1
## 68 12.23 0
## 69 12.37 0
## 70 12.57 0
## 71 12.71 0
## 72 12.77 0
## 73 12.77 0
## 74 12.89 0
## 75 12.95 0
## 76 12.98 0
## 77 13.00 0
## 78 13.10 0
## 79 13.12 0
## 80 13.44 0
## 81 13.65 0
## 82 13.82 0
## 83 13.94 0
## 84 14.08 0
## 85 14.43 0
## 86 14.46 0
## 87 14.47 0
## 88 14.48 0
## 89 14.66 0
## 90 15.37 0
## 91 15.60 0
## 92 15.69 0
## 93 16.16 0
## 94 16.17 0
## 95 16.51 0
## 96 16.80 0
## 97 17.03 0
## 98 17.60 0
## 99 19.82 0
## 100 20.12 0resLow <- resSort[1:20,]
resLow## ReservationPrice Accept
## 1 2.47 1
## 2 3.39 1
## 3 4.62 1
## 4 4.85 1
## 5 5.00 1
## 6 5.09 1
## 7 5.13 1
## 8 5.69 1
## 9 5.94 1
## 10 6.52 1
## 11 6.55 1
## 12 6.69 1
## 13 6.81 1
## 14 6.84 1
## 15 6.99 1
## 16 7.08 1
## 17 7.16 1
## 18 7.34 1
## 19 7.36 1
## 20 7.46 1describe(resLow)## vars n mean sd median trimmed mad min max range
## ReservationPrice 1 20 5.95 1.39 6.54 6.14 1.21 2.47 7.46 4.99
## Accept 2 20 1.00 0.00 1.00 1.00 0.00 1.00 1.00 0.00
## skew kurtosis se
## ReservationPrice -0.91 -0.13 0.31
## Accept NaN NaN 0.00sum(resLow$ReservationPrice)## [1] 118.98The opportunity cost for those who most want to work is 118.98
set.seed(12)
res <- round(data.frame(rnorm(100,11,3.9)),digits=2)
colnames(res) <- "ReservationPrice"
describe(res)## vars n mean sd median trimmed mad min max range
## ReservationPrice 1 100 10.88 3.37 10.57 10.82 3.26 2.62 19.08 16.46
## skew kurtosis se
## ReservationPrice 0.17 -0.1 0.34res$Accept <- ifelse(res$ReservationPrice>12, 0,1)
res## ReservationPrice Accept
## 1 5.23 1
## 2 17.15 0
## 3 7.27 1
## 4 7.41 1
## 5 3.21 1
## 6 9.94 1
## 7 9.77 1
## 8 8.55 1
## 9 10.58 1
## 10 12.67 0
## 11 7.97 1
## 12 5.95 1
## 13 7.96 1
## 14 11.05 1
## 15 10.41 1
## 16 8.26 1
## 17 15.64 0
## 18 12.33 0
## 19 12.98 0
## 20 9.86 1
## 21 11.87 1
## 22 18.83 0
## 23 14.95 0
## 24 9.82 1
## 25 7.00 1
## 26 9.96 1
## 27 10.22 1
## 28 11.51 1
## 29 11.57 1
## 30 12.41 0
## 31 13.63 0
## 32 19.08 0
## 33 8.89 1
## 34 6.83 1
## 35 9.55 1
## 36 9.11 1
## 37 12.07 0
## 38 9.13 1
## 39 14.11 0
## 40 7.08 1
## 41 11.41 1
## 42 6.49 1
## 43 13.25 0
## 44 4.78 1
## 45 9.80 1
## 46 12.75 0
## 47 7.19 1
## 48 11.74 1
## 49 13.85 0
## 50 9.08 1
## 51 10.83 1
## 52 10.56 1
## 53 12.78 0
## 54 18.88 0
## 55 6.90 1
## 56 13.87 0
## 57 13.10 0
## 58 5.87 1
## 59 10.02 1
## 60 12.23 0
## 61 12.59 0
## 62 14.88 0
## 63 14.34 0
## 64 11.77 1
## 65 14.25 0
## 66 14.30 0
## 67 18.62 0
## 68 2.62 1
## 69 14.79 0
## 70 15.47 0
## 71 8.95 1
## 72 11.98 1
## 73 9.33 1
## 74 10.29 1
## 75 10.60 1
## 76 8.53 1
## 77 6.04 1
## 78 9.50 1
## 79 13.02 0
## 80 10.31 1
## 81 11.02 1
## 82 6.03 1
## 83 10.21 1
## 84 15.54 0
## 85 10.91 1
## 86 14.50 0
## 87 10.31 1
## 88 15.34 0
## 89 8.89 1
## 90 7.24 1
## 91 12.47 0
## 92 7.16 1
## 93 14.50 0
## 94 11.50 1
## 95 15.03 0
## 96 9.67 1
## 97 12.76 0
## 98 8.29 1
## 99 10.07 1
## 100 7.07 1## subset data to the job offers up to 12 accepts
subRes <- res[1:27,]
subRes## ReservationPrice Accept
## 1 5.23 1
## 2 17.15 0
## 3 7.27 1
## 4 7.41 1
## 5 3.21 1
## 6 9.94 1
## 7 9.77 1
## 8 8.55 1
## 9 10.58 1
## 10 12.67 0
## 11 7.97 1
## 12 5.95 1
## 13 7.96 1
## 14 11.05 1
## 15 10.41 1
## 16 8.26 1
## 17 15.64 0
## 18 12.33 0
## 19 12.98 0
## 20 9.86 1
## 21 11.87 1
## 22 18.83 0
## 23 14.95 0
## 24 9.82 1
## 25 7.00 1
## 26 9.96 1
## 27 10.22 1sum(subRes$ReservationPrice)## [1] 276.84276.84
resSort <- arrange(res, ReservationPrice)
resSort## ReservationPrice Accept
## 1 2.62 1
## 2 3.21 1
## 3 4.78 1
## 4 5.23 1
## 5 5.87 1
## 6 5.95 1
## 7 6.03 1
## 8 6.04 1
## 9 6.49 1
## 10 6.83 1
## 11 6.90 1
## 12 7.00 1
## 13 7.07 1
## 14 7.08 1
## 15 7.16 1
## 16 7.19 1
## 17 7.24 1
## 18 7.27 1
## 19 7.41 1
## 20 7.96 1
## 21 7.97 1
## 22 8.26 1
## 23 8.29 1
## 24 8.53 1
## 25 8.55 1
## 26 8.89 1
## 27 8.89 1
## 28 8.95 1
## 29 9.08 1
## 30 9.11 1
## 31 9.13 1
## 32 9.33 1
## 33 9.50 1
## 34 9.55 1
## 35 9.67 1
## 36 9.77 1
## 37 9.80 1
## 38 9.82 1
## 39 9.86 1
## 40 9.94 1
## 41 9.96 1
## 42 10.02 1
## 43 10.07 1
## 44 10.21 1
## 45 10.22 1
## 46 10.29 1
## 47 10.31 1
## 48 10.31 1
## 49 10.41 1
## 50 10.56 1
## 51 10.58 1
## 52 10.60 1
## 53 10.83 1
## 54 10.91 1
## 55 11.02 1
## 56 11.05 1
## 57 11.41 1
## 58 11.50 1
## 59 11.51 1
## 60 11.57 1
## 61 11.74 1
## 62 11.77 1
## 63 11.87 1
## 64 11.98 1
## 65 12.07 0
## 66 12.23 0
## 67 12.33 0
## 68 12.41 0
## 69 12.47 0
## 70 12.59 0
## 71 12.67 0
## 72 12.75 0
## 73 12.76 0
## 74 12.78 0
## 75 12.98 0
## 76 13.02 0
## 77 13.10 0
## 78 13.25 0
## 79 13.63 0
## 80 13.85 0
## 81 13.87 0
## 82 14.11 0
## 83 14.25 0
## 84 14.30 0
## 85 14.34 0
## 86 14.50 0
## 87 14.50 0
## 88 14.79 0
## 89 14.88 0
## 90 14.95 0
## 91 15.03 0
## 92 15.34 0
## 93 15.47 0
## 94 15.54 0
## 95 15.64 0
## 96 17.15 0
## 97 18.62 0
## 98 18.83 0
## 99 18.88 0
## 100 19.08 0resLow <- resSort[1:20,]
resLow## ReservationPrice Accept
## 1 2.62 1
## 2 3.21 1
## 3 4.78 1
## 4 5.23 1
## 5 5.87 1
## 6 5.95 1
## 7 6.03 1
## 8 6.04 1
## 9 6.49 1
## 10 6.83 1
## 11 6.90 1
## 12 7.00 1
## 13 7.07 1
## 14 7.08 1
## 15 7.16 1
## 16 7.19 1
## 17 7.24 1
## 18 7.27 1
## 19 7.41 1
## 20 7.96 1describe(resLow)## vars n mean sd median trimmed mad min max range skew
## ReservationPrice 1 20 6.27 1.39 6.87 6.51 0.7 2.62 7.96 5.34 -1.3
## Accept 2 20 1.00 0.00 1.00 1.00 0.0 1.00 1.00 0.00 NaN
## kurtosis se
## ReservationPrice 0.82 0.31
## Accept NaN 0.00sum(resLow$ReservationPrice)## [1] 125.33The opportunity cost for those who most want to work is 125.33
set.seed(13)
res <- round(data.frame(rnorm(100,11,3.9)),digits=2)
colnames(res) <- "ReservationPrice"
describe(res)## vars n mean sd median trimmed mad min max range
## ReservationPrice 1 100 10.76 3.71 10.69 10.73 3.74 3.09 18.16 15.07
## skew kurtosis se
## ReservationPrice 0.02 -0.68 0.37res$Accept <- ifelse(res$ReservationPrice>12, 0,1)
res## ReservationPrice Accept
## 1 13.16 0
## 2 9.91 1
## 3 17.92 0
## 4 11.73 1
## 5 15.46 0
## 6 12.62 0
## 7 15.80 0
## 8 11.92 1
## 9 9.58 1
## 10 15.31 0
## 11 6.73 1
## 12 12.80 0
## 13 5.69 1
## 14 3.76 1
## 15 9.28 1
## 16 10.24 1
## 17 16.45 0
## 18 11.39 1
## 19 10.55 1
## 20 13.74 0
## 21 12.02 0
## 22 18.16 0
## 23 12.39 0
## 24 6.92 1
## 25 13.42 0
## 26 11.58 1
## 27 5.31 1
## 28 3.09 1
## 29 6.88 1
## 30 8.16 1
## 31 10.97 1
## 32 14.31 0
## 33 9.50 1
## 34 8.95 1
## 35 9.93 1
## 36 8.64 1
## 37 9.70 1
## 38 10.06 1
## 39 7.64 1
## 40 7.70 1
## 41 11.39 1
## 42 17.20 0
## 43 13.21 0
## 44 17.30 0
## 45 9.17 1
## 46 8.17 1
## 47 7.01 1
## 48 3.44 1
## 49 12.08 0
## 50 16.49 0
## 51 12.07 0
## 52 13.95 0
## 53 9.64 1
## 54 8.87 1
## 55 11.91 1
## 56 9.84 1
## 57 7.72 1
## 58 14.22 0
## 59 16.79 0
## 60 13.73 0
## 61 6.08 1
## 62 12.16 0
## 63 10.42 1
## 64 7.53 1
## 65 14.95 0
## 66 7.41 1
## 67 8.76 1
## 68 15.49 0
## 69 15.46 0
## 70 10.07 1
## 71 6.76 1
## 72 10.76 1
## 73 8.98 1
## 74 3.56 1
## 75 11.42 1
## 76 6.41 1
## 77 17.81 0
## 78 9.45 1
## 79 12.73 0
## 80 12.76 0
## 81 10.70 1
## 82 12.16 0
## 83 6.34 1
## 84 3.21 1
## 85 16.42 0
## 86 10.68 1
## 87 12.53 0
## 88 6.78 1
## 89 17.25 0
## 90 14.92 0
## 91 12.48 0
## 92 8.79 1
## 93 6.27 1
## 94 5.68 1
## 95 5.48 1
## 96 10.00 1
## 97 6.22 1
## 98 11.83 1
## 99 11.26 1
## 100 14.34 0## subset data to the job offers up to 12 accepts
subRes <- res[1:34,]
subRes## ReservationPrice Accept
## 1 13.16 0
## 2 9.91 1
## 3 17.92 0
## 4 11.73 1
## 5 15.46 0
## 6 12.62 0
## 7 15.80 0
## 8 11.92 1
## 9 9.58 1
## 10 15.31 0
## 11 6.73 1
## 12 12.80 0
## 13 5.69 1
## 14 3.76 1
## 15 9.28 1
## 16 10.24 1
## 17 16.45 0
## 18 11.39 1
## 19 10.55 1
## 20 13.74 0
## 21 12.02 0
## 22 18.16 0
## 23 12.39 0
## 24 6.92 1
## 25 13.42 0
## 26 11.58 1
## 27 5.31 1
## 28 3.09 1
## 29 6.88 1
## 30 8.16 1
## 31 10.97 1
## 32 14.31 0
## 33 9.50 1
## 34 8.95 1sum(subRes$ReservationPrice)## [1] 375.7375.70
resSort <- arrange(res, ReservationPrice)
resSort## ReservationPrice Accept
## 1 3.09 1
## 2 3.21 1
## 3 3.44 1
## 4 3.56 1
## 5 3.76 1
## 6 5.31 1
## 7 5.48 1
## 8 5.68 1
## 9 5.69 1
## 10 6.08 1
## 11 6.22 1
## 12 6.27 1
## 13 6.34 1
## 14 6.41 1
## 15 6.73 1
## 16 6.76 1
## 17 6.78 1
## 18 6.88 1
## 19 6.92 1
## 20 7.01 1
## 21 7.41 1
## 22 7.53 1
## 23 7.64 1
## 24 7.70 1
## 25 7.72 1
## 26 8.16 1
## 27 8.17 1
## 28 8.64 1
## 29 8.76 1
## 30 8.79 1
## 31 8.87 1
## 32 8.95 1
## 33 8.98 1
## 34 9.17 1
## 35 9.28 1
## 36 9.45 1
## 37 9.50 1
## 38 9.58 1
## 39 9.64 1
## 40 9.70 1
## 41 9.84 1
## 42 9.91 1
## 43 9.93 1
## 44 10.00 1
## 45 10.06 1
## 46 10.07 1
## 47 10.24 1
## 48 10.42 1
## 49 10.55 1
## 50 10.68 1
## 51 10.70 1
## 52 10.76 1
## 53 10.97 1
## 54 11.26 1
## 55 11.39 1
## 56 11.39 1
## 57 11.42 1
## 58 11.58 1
## 59 11.73 1
## 60 11.83 1
## 61 11.91 1
## 62 11.92 1
## 63 12.02 0
## 64 12.07 0
## 65 12.08 0
## 66 12.16 0
## 67 12.16 0
## 68 12.39 0
## 69 12.48 0
## 70 12.53 0
## 71 12.62 0
## 72 12.73 0
## 73 12.76 0
## 74 12.80 0
## 75 13.16 0
## 76 13.21 0
## 77 13.42 0
## 78 13.73 0
## 79 13.74 0
## 80 13.95 0
## 81 14.22 0
## 82 14.31 0
## 83 14.34 0
## 84 14.92 0
## 85 14.95 0
## 86 15.31 0
## 87 15.46 0
## 88 15.46 0
## 89 15.49 0
## 90 15.80 0
## 91 16.42 0
## 92 16.45 0
## 93 16.49 0
## 94 16.79 0
## 95 17.20 0
## 96 17.25 0
## 97 17.30 0
## 98 17.81 0
## 99 17.92 0
## 100 18.16 0resLow <- resSort[1:20,]
resLow## ReservationPrice Accept
## 1 3.09 1
## 2 3.21 1
## 3 3.44 1
## 4 3.56 1
## 5 3.76 1
## 6 5.31 1
## 7 5.48 1
## 8 5.68 1
## 9 5.69 1
## 10 6.08 1
## 11 6.22 1
## 12 6.27 1
## 13 6.34 1
## 14 6.41 1
## 15 6.73 1
## 16 6.76 1
## 17 6.78 1
## 18 6.88 1
## 19 6.92 1
## 20 7.01 1describe(resLow)## vars n mean sd median trimmed mad min max range
## ReservationPrice 1 20 5.58 1.38 6.15 5.71 0.96 3.09 7.01 3.92
## Accept 2 20 1.00 0.00 1.00 1.00 0.00 1.00 1.00 0.00
## skew kurtosis se
## ReservationPrice -0.74 -1.1 0.31
## Accept NaN NaN 0.00sum(resLow$ReservationPrice)## [1] 111.62The opportunity cost for those who most want to work is 111.62
set.seed(14)
res <- round(data.frame(rnorm(100,11,3.9)),digits=2)
colnames(res) <- "ReservationPrice"
describe(res)## vars n mean sd median trimmed mad min max range
## ReservationPrice 1 100 11.17 3.53 10.95 11.11 3.6 2.67 19.27 16.6
## skew kurtosis se
## ReservationPrice 0.13 -0.44 0.35res$Accept <- ifelse(res$ReservationPrice>12, 0,1)
res## ReservationPrice Accept
## 1 8.42 1
## 2 17.70 0
## 3 19.27 0
## 4 16.84 0
## 5 10.86 1
## 6 15.80 0
## 7 10.75 1
## 8 15.17 0
## 9 9.53 1
## 10 15.07 0
## 11 9.51 1
## 12 12.17 0
## 13 13.63 0
## 14 9.86 1
## 15 12.90 0
## 16 14.44 0
## 17 18.26 0
## 18 17.29 0
## 19 11.53 1
## 20 15.24 0
## 21 6.06 1
## 22 10.23 1
## 23 11.54 1
## 24 9.91 1
## 25 13.76 0
## 26 8.01 1
## 27 16.63 0
## 28 14.30 0
## 29 9.44 1
## 30 5.43 1
## 31 5.45 1
## 32 9.72 1
## 33 12.11 0
## 34 13.81 0
## 35 12.69 0
## 36 9.63 1
## 37 12.16 0
## 38 9.98 1
## 39 16.10 0
## 40 11.06 1
## 41 9.32 1
## 42 12.49 0
## 43 11.16 1
## 44 10.77 1
## 45 5.94 1
## 46 2.67 1
## 47 7.51 1
## 48 13.39 0
## 49 13.27 0
## 50 10.98 1
## 51 3.72 1
## 52 18.14 0
## 53 7.13 1
## 54 5.34 1
## 55 10.94 1
## 56 13.09 0
## 57 7.84 1
## 58 9.76 1
## 59 15.33 0
## 60 10.45 1
## 61 10.20 1
## 62 8.34 1
## 63 10.83 1
## 64 6.47 1
## 65 7.99 1
## 66 7.42 1
## 67 11.35 1
## 68 8.05 1
## 69 17.82 0
## 70 11.66 1
## 71 14.22 0
## 72 10.93 1
## 73 12.92 0
## 74 12.39 0
## 75 11.44 1
## 76 15.43 0
## 77 8.79 1
## 78 13.16 0
## 79 10.95 1
## 80 8.77 1
## 81 8.33 1
## 82 15.56 0
## 83 12.44 0
## 84 9.01 1
## 85 8.54 1
## 86 17.68 0
## 87 10.13 1
## 88 7.26 1
## 89 11.15 1
## 90 4.60 1
## 91 14.08 0
## 92 6.88 1
## 93 6.99 1
## 94 15.29 0
## 95 8.61 1
## 96 9.65 1
## 97 11.34 1
## 98 8.47 1
## 99 12.19 0
## 100 7.99 1## subset data to the job offers up to 12 accepts
subRes <- res[1:41,]
subRes## ReservationPrice Accept
## 1 8.42 1
## 2 17.70 0
## 3 19.27 0
## 4 16.84 0
## 5 10.86 1
## 6 15.80 0
## 7 10.75 1
## 8 15.17 0
## 9 9.53 1
## 10 15.07 0
## 11 9.51 1
## 12 12.17 0
## 13 13.63 0
## 14 9.86 1
## 15 12.90 0
## 16 14.44 0
## 17 18.26 0
## 18 17.29 0
## 19 11.53 1
## 20 15.24 0
## 21 6.06 1
## 22 10.23 1
## 23 11.54 1
## 24 9.91 1
## 25 13.76 0
## 26 8.01 1
## 27 16.63 0
## 28 14.30 0
## 29 9.44 1
## 30 5.43 1
## 31 5.45 1
## 32 9.72 1
## 33 12.11 0
## 34 13.81 0
## 35 12.69 0
## 36 9.63 1
## 37 12.16 0
## 38 9.98 1
## 39 16.10 0
## 40 11.06 1
## 41 9.32 1sum(subRes$ReservationPrice)## [1] 501.58501.58
resSort <- arrange(res, ReservationPrice)
resSort## ReservationPrice Accept
## 1 2.67 1
## 2 3.72 1
## 3 4.60 1
## 4 5.34 1
## 5 5.43 1
## 6 5.45 1
## 7 5.94 1
## 8 6.06 1
## 9 6.47 1
## 10 6.88 1
## 11 6.99 1
## 12 7.13 1
## 13 7.26 1
## 14 7.42 1
## 15 7.51 1
## 16 7.84 1
## 17 7.99 1
## 18 7.99 1
## 19 8.01 1
## 20 8.05 1
## 21 8.33 1
## 22 8.34 1
## 23 8.42 1
## 24 8.47 1
## 25 8.54 1
## 26 8.61 1
## 27 8.77 1
## 28 8.79 1
## 29 9.01 1
## 30 9.32 1
## 31 9.44 1
## 32 9.51 1
## 33 9.53 1
## 34 9.63 1
## 35 9.65 1
## 36 9.72 1
## 37 9.76 1
## 38 9.86 1
## 39 9.91 1
## 40 9.98 1
## 41 10.13 1
## 42 10.20 1
## 43 10.23 1
## 44 10.45 1
## 45 10.75 1
## 46 10.77 1
## 47 10.83 1
## 48 10.86 1
## 49 10.93 1
## 50 10.94 1
## 51 10.95 1
## 52 10.98 1
## 53 11.06 1
## 54 11.15 1
## 55 11.16 1
## 56 11.34 1
## 57 11.35 1
## 58 11.44 1
## 59 11.53 1
## 60 11.54 1
## 61 11.66 1
## 62 12.11 0
## 63 12.16 0
## 64 12.17 0
## 65 12.19 0
## 66 12.39 0
## 67 12.44 0
## 68 12.49 0
## 69 12.69 0
## 70 12.90 0
## 71 12.92 0
## 72 13.09 0
## 73 13.16 0
## 74 13.27 0
## 75 13.39 0
## 76 13.63 0
## 77 13.76 0
## 78 13.81 0
## 79 14.08 0
## 80 14.22 0
## 81 14.30 0
## 82 14.44 0
## 83 15.07 0
## 84 15.17 0
## 85 15.24 0
## 86 15.29 0
## 87 15.33 0
## 88 15.43 0
## 89 15.56 0
## 90 15.80 0
## 91 16.10 0
## 92 16.63 0
## 93 16.84 0
## 94 17.29 0
## 95 17.68 0
## 96 17.70 0
## 97 17.82 0
## 98 18.14 0
## 99 18.26 0
## 100 19.27 0resLow <- resSort[1:20,]
resLow## ReservationPrice Accept
## 1 2.67 1
## 2 3.72 1
## 3 4.60 1
## 4 5.34 1
## 5 5.43 1
## 6 5.45 1
## 7 5.94 1
## 8 6.06 1
## 9 6.47 1
## 10 6.88 1
## 11 6.99 1
## 12 7.13 1
## 13 7.26 1
## 14 7.42 1
## 15 7.51 1
## 16 7.84 1
## 17 7.99 1
## 18 7.99 1
## 19 8.01 1
## 20 8.05 1describe(resLow)## vars n mean sd median trimmed mad min max range
## ReservationPrice 1 20 6.44 1.52 6.94 6.64 1.52 2.67 8.05 5.38
## Accept 2 20 1.00 0.00 1.00 1.00 0.00 1.00 1.00 0.00
## skew kurtosis se
## ReservationPrice -0.87 -0.2 0.34
## Accept NaN NaN 0.00sum(resLow$ReservationPrice)## [1] 128.75The opportunity cost for those who most want to work is 128.75
set.seed(15)
res <- round(data.frame(rnorm(100,11,3.9)),digits=2)
colnames(res) <- "ReservationPrice"
describe(res)## vars n mean sd median trimmed mad min max range
## ReservationPrice 1 100 11.4 3.88 11.05 11.33 4.05 1.49 20.69 19.2
## skew kurtosis se
## ReservationPrice 0.12 -0.45 0.39res$Accept <- ifelse(res$ReservationPrice>12, 0,1)
res## ReservationPrice Accept
## 1 12.01 0
## 2 18.14 0
## 3 9.68 1
## 4 14.50 0
## 5 12.90 0
## 6 6.10 1
## 7 11.09 1
## 8 15.25 0
## 9 10.48 1
## 10 6.81 1
## 11 14.33 0
## 12 9.58 1
## 13 11.65 1
## 14 6.15 1
## 15 16.69 0
## 16 10.99 1
## 17 10.92 1
## 18 11.13 1
## 19 6.45 1
## 20 8.97 1
## 21 16.36 0
## 22 16.51 0
## 23 9.43 1
## 24 9.29 1
## 25 14.94 0
## 26 12.68 0
## 27 13.86 0
## 28 8.35 1
## 29 12.27 0
## 30 14.54 0
## 31 9.20 1
## 32 11.02 1
## 33 16.66 0
## 34 13.94 0
## 35 14.77 0
## 36 12.83 0
## 37 10.06 1
## 38 15.03 0
## 39 8.50 1
## 40 5.87 1
## 41 12.41 0
## 42 13.81 0
## 43 20.69 0
## 44 7.16 1
## 45 9.68 1
## 46 15.89 0
## 47 6.60 1
## 48 17.08 0
## 49 13.76 0
## 50 14.64 0
## 51 13.67 0
## 52 14.97 0
## 53 10.06 1
## 54 17.54 0
## 55 12.60 0
## 56 7.53 1
## 57 8.27 1
## 58 13.03 0
## 59 15.51 0
## 60 10.57 1
## 61 12.16 0
## 62 9.33 1
## 63 8.70 1
## 64 5.94 1
## 65 5.20 1
## 66 6.47 1
## 67 9.70 1
## 68 13.11 0
## 69 8.11 1
## 70 15.84 0
## 71 5.05 1
## 72 3.68 1
## 73 5.82 1
## 74 9.06 1
## 75 11.16 1
## 76 8.88 1
## 77 12.40 0
## 78 14.91 0
## 79 7.17 1
## 80 18.96 0
## 81 11.01 1
## 82 20.11 0
## 83 11.60 1
## 84 9.18 1
## 85 9.17 1
## 86 9.06 1
## 87 9.74 1
## 88 13.40 0
## 89 11.50 1
## 90 10.41 1
## 91 7.97 1
## 92 5.86 1
## 93 19.21 0
## 94 12.48 0
## 95 10.13 1
## 96 17.05 0
## 97 10.34 1
## 98 16.01 0
## 99 7.09 1
## 100 1.49 1## subset data to the job offers up to 12 accepts
subRes <- res[1:39,]
subRes## ReservationPrice Accept
## 1 12.01 0
## 2 18.14 0
## 3 9.68 1
## 4 14.50 0
## 5 12.90 0
## 6 6.10 1
## 7 11.09 1
## 8 15.25 0
## 9 10.48 1
## 10 6.81 1
## 11 14.33 0
## 12 9.58 1
## 13 11.65 1
## 14 6.15 1
## 15 16.69 0
## 16 10.99 1
## 17 10.92 1
## 18 11.13 1
## 19 6.45 1
## 20 8.97 1
## 21 16.36 0
## 22 16.51 0
## 23 9.43 1
## 24 9.29 1
## 25 14.94 0
## 26 12.68 0
## 27 13.86 0
## 28 8.35 1
## 29 12.27 0
## 30 14.54 0
## 31 9.20 1
## 32 11.02 1
## 33 16.66 0
## 34 13.94 0
## 35 14.77 0
## 36 12.83 0
## 37 10.06 1
## 38 15.03 0
## 39 8.50 1sum(subRes$ReservationPrice)## [1] 464.06464.06
resSort <- arrange(res, ReservationPrice)
resSort## ReservationPrice Accept
## 1 1.49 1
## 2 3.68 1
## 3 5.05 1
## 4 5.20 1
## 5 5.82 1
## 6 5.86 1
## 7 5.87 1
## 8 5.94 1
## 9 6.10 1
## 10 6.15 1
## 11 6.45 1
## 12 6.47 1
## 13 6.60 1
## 14 6.81 1
## 15 7.09 1
## 16 7.16 1
## 17 7.17 1
## 18 7.53 1
## 19 7.97 1
## 20 8.11 1
## 21 8.27 1
## 22 8.35 1
## 23 8.50 1
## 24 8.70 1
## 25 8.88 1
## 26 8.97 1
## 27 9.06 1
## 28 9.06 1
## 29 9.17 1
## 30 9.18 1
## 31 9.20 1
## 32 9.29 1
## 33 9.33 1
## 34 9.43 1
## 35 9.58 1
## 36 9.68 1
## 37 9.68 1
## 38 9.70 1
## 39 9.74 1
## 40 10.06 1
## 41 10.06 1
## 42 10.13 1
## 43 10.34 1
## 44 10.41 1
## 45 10.48 1
## 46 10.57 1
## 47 10.92 1
## 48 10.99 1
## 49 11.01 1
## 50 11.02 1
## 51 11.09 1
## 52 11.13 1
## 53 11.16 1
## 54 11.50 1
## 55 11.60 1
## 56 11.65 1
## 57 12.01 0
## 58 12.16 0
## 59 12.27 0
## 60 12.40 0
## 61 12.41 0
## 62 12.48 0
## 63 12.60 0
## 64 12.68 0
## 65 12.83 0
## 66 12.90 0
## 67 13.03 0
## 68 13.11 0
## 69 13.40 0
## 70 13.67 0
## 71 13.76 0
## 72 13.81 0
## 73 13.86 0
## 74 13.94 0
## 75 14.33 0
## 76 14.50 0
## 77 14.54 0
## 78 14.64 0
## 79 14.77 0
## 80 14.91 0
## 81 14.94 0
## 82 14.97 0
## 83 15.03 0
## 84 15.25 0
## 85 15.51 0
## 86 15.84 0
## 87 15.89 0
## 88 16.01 0
## 89 16.36 0
## 90 16.51 0
## 91 16.66 0
## 92 16.69 0
## 93 17.05 0
## 94 17.08 0
## 95 17.54 0
## 96 18.14 0
## 97 18.96 0
## 98 19.21 0
## 99 20.11 0
## 100 20.69 0resLow <- resSort[1:20,]
resLow## ReservationPrice Accept
## 1 1.49 1
## 2 3.68 1
## 3 5.05 1
## 4 5.20 1
## 5 5.82 1
## 6 5.86 1
## 7 5.87 1
## 8 5.94 1
## 9 6.10 1
## 10 6.15 1
## 11 6.45 1
## 12 6.47 1
## 13 6.60 1
## 14 6.81 1
## 15 7.09 1
## 16 7.16 1
## 17 7.17 1
## 18 7.53 1
## 19 7.97 1
## 20 8.11 1describe(resLow)## vars n mean sd median trimmed mad min max range
## ReservationPrice 1 20 6.13 1.51 6.3 6.33 0.96 1.49 8.11 6.62
## Accept 2 20 1.00 0.00 1.0 1.00 0.00 1.00 1.00 0.00
## skew kurtosis se
## ReservationPrice -1.4 2.2 0.34
## Accept NaN NaN 0.00sum(resLow$ReservationPrice)## [1] 122.52The opportunity cost for those who most want to work is 122.52