Assignment 3
Solutions
Section #: 01
Students must abide by UVic academic regulations and observe standards of scholarly integrity (i.e. no plagiarism or cheating). Therefore, this assignment must be taken individually and not with a friend, classmate, or group. You are also prohibited from sharing any information about the assignment with others. I affirm that I will not give or receive any aid on this assignment and that all work will be my own. name here
A big part of environmental economics is estimating peoples willingness to pay for an improvement in environmental quality and/or their willingness to accept for a degradation in environmental quality. Theoretically these two measures should be very close for small changes for the good in question. Nevertheless there are countless studies that show that these two measures can be significantly different even for inconsequential i.e. small value goods… like chocolate bars. One possibility explanation for this divergence is that humans suffer from what is known an endowment effect. I emphasized suffer because this is an irrational behaviour. The endowment effect, in a nutshell, is that you demand more to give up something than what you are willing to pay for it in the first place. It is as if possessing a good makes it more valuable to you. In the context of environmental economics, people demand more compensation for a slight decrease in environmental quality than what they are willing to pay for a slight improvement. It is as if possessing the current level of environmental quality makes it more valuable that what your were willing to pay to get that level of environmental quality in the first place. It is an open question whether or not the endowment effect is an actual feature of human behaviour or is:
- an artifact of subject confusion regarding the mechanisms we use to measure their willingness to pay and willingness to accept.
- an artifact of random choice in an environment where little is at stake: this is known as the flat optimum problem.
Recall that in experiment 3 there were 3 separate parts:
- A second price sealed bid auction where you bid on a chocolate bar.
- You were asked with what probability you think you won the auction in part 1.
- Finally, you stated the minimum that you would be willing to sell a chocolate bar back to me (if you in fact won the auction in part 1).
The treatments were designed to manipulate both alternative explanations of the endowment effect.
Half of the subjects were provided hints regarding the optimal bidding and asking behaviour: i.e. “Hint: in a second price auction bidding your value maximizes your expected payoff.” and “Hint: In a second price procurement auction, asking your forgone value maximizes your expected payoff.” If subjects are confused about how to optimally bid and ask, then hints should reduce this confusion.
Half of the subjects were in two person groups and the other half of the class was in 10 person groups. In a two person group if you have “normal” preferences then you have some incentive to bid and ask your value, whereas in a 10 person group your expected payoff function is basically flat (at zero): the only mistake you can make is to bid too much or ask too little, resulting in negative payoffs.
Note that this is a very demanding test of the endowment effect: The probability of you becoming endowed (winning the auction) is low and unknown, so very little opportunity to become attached to the chocolate bar.
1 (0 marks)
If you participated in the experiment, tell me which treatment you were in and describe how you decided to what to bid and ask.
2 (10 marks)
In words, why is it in your best interest to bid your true value in a second price sealed bid auction, regardless of the number of bidders?
In a second price auction your bid only influences your probability of winning the auction, not the price you have to pay if you win. Contrast this to a first price auction where if you win, you pay your bid. In a first price auction you face a trade-off between the probability of winning and the amount of surplus you get if you win: i.e. a bid lower than your value ensures some surplus if you win, but you have a lower probability of winning than if your bid your value. In a second price auction bidding less than your value only reduces the probability of winning the auction in the situations where winning the auction would have yielded a positive payoff.
3 (10 marks)
In words, why is it in your best interest to ask your forgone value in a second price procurement auction, regardless of the number of askers?
Same reasoning as above: Your ask only influences the probability that you sell, not the price you receive if you sell. There is no incentive to ask for more than your value because this has no effect on the surplus you get if you do sell. Asking more than your value only reduces the probability of selling in the situations where you would have received positive surplus by selling.
4 (5 marks)
In your .R file use the assignment operator <- and the pipe operator %>% overwrite mydf using mydf as the input to the following functions: i.e. start with mydf <- mydf %>%, THEN do the following: group_by() variable oneid, THEN create new variables using the mutate() function: mean_bid=mean(bid), mean_ask=mean(ask), sd_bid=sd(bid), sd_ask=sd(ask), ask_minus_bid=ask-bid, mean_ask_minus_bid=mean(ask_minus_bid). Put a copy of your code into the chunk below, noting eval=FALSE, which means that the code is not evaluated (run).
mydf <- mydf%>%
group_by(oneid)%>%
mutate(sd_bid=sd(bid),
sd_ask=sd(ask),
mean_bid=mean(bid),
mean_ask=mean(ask),
ask_minus_bid=ask-bid,
mean_ask_minus_bid=mean(ask_minus_bid))5 (5 marks)
In your .R file use functions ggplot() with argument data=mydf and aes() with arguments x=bid, y=ask and col=treatment to create first_plot. To this blank plot add (using the + operator) geom_abline() with arguments slope=1,intercept=0,col="white",lwd=2 and geom_jitter() with arguments alpha=.5,width=1,height=1. Give the plot a descriptive title using function labs() with argument title="a short description of what I think the plot shows".
6 (5 marks)
What is the significance of the white diagonal line? What pattern can you see in the data?
The white diagonal line indicates where bids are equal to asks, which is what neoclassical economics would predict. It is hard to pick out any patterns in the data because there are so many data points. If you really squint, it might seem that blue and purple points (2 person auctions) tend to be above the line, and red and green groups (10 person auctions) tend to be below the line.
7 (5 marks)
In your .R file use functions ggplot() with argument data=mydf and aes() with arguments x=mean_bid, y=mean_ask,col=treatment,label=oneid to create second_plot. To this blank plot add (using the + operator) geom_abline() with arguments slope=1,intercept=0,col="white",lwd=2 and geom_text() with no arguments.
8 (5 marks)
What pattern can you see in the data?
In this plot each subject’s id is located at the mean of all their bids and asks. The fact that blue and purple points (2 person auctions) tend to be above the line, and red and green groups (10 person auctions) tend to be below the line is a bit more obvious.
9 (5 marks)
In your .R file create a dataframe called second_hull which uses dataframe mydf as an input, THEN group_by() treatment THEN slice(chull(mean_bid,mean_ask)). Copy your code into the chunk below, noting eval=FALSE, which means that the code is not evaluated (run).
second_hull <- mydf %>%
group_by(treatment) %>%
slice(chull(mean_bid,mean_ask))10 (5 marks)
In your .R file create third_plot, by adding to second_plot using the assignment <- and addition + operators: ie. third_plot<-second_plot+. To the plot add a geom_polygon() with arguments data=second_hull, alpha=.3 and mapping=aes() with arguments fill=treatment, col=treatment.
11 (5 marks)
What pattern can you see in the data?
To the plot we have added the convex hull around each treatment (connect the outermost points in each treatment). This just makes the treatment groups a bit more obvious.
12 (5 marks)
In your .R file use functions ggplot() with argument data=mydf and aes() with arguments x=sd_bid, y=sd_ask,col=treatment,label=oneid to create fourth_plot. To this blank plot add (using the + operator) geom_text() with no arguments.
13 (5 marks)
What pattern can you see in the data?
The variability of bids and asks tends to be higher in the 10 person treatments when compared to the 2 person treatments.
14 (5 marks)
In your .R file create a dataframe called fourth_hull which uses dataframe mydf as an input, THEN group_by() treatment THEN slice(chull(sd_bid,sd_ask)). Copy your code into the chunk below, noting eval=FALSE, which means that the code is not evaluated (run).
fourth_hull <- mydf %>%
group_by(treatment) %>%
slice(chull(sd_bid,sd_ask))15 (5 marks)
In your .R file create fifth_plot, by adding to fourth_plot using the assignment <- and addition + operators: ie. fifth_plot<-fourth_plot+. To the plot add a geom_polygon() with arguments data=second_hull, alpha=.3 and mapping=aes() with arguments fill=treatment, col=treatment.
16 (5 marks)
What pattern can you see in the data?
To the plot we have added the convex hull around each treatment (connect the outermost points in each treatment). This just makes the treatment groups a bit more obvious.
17 (5 marks)
In your .R file use functions ggplot() with argument data=mydf and aes() with arguments x=round,y=ask_minus_bid to create a blank plot called sixth_plot. Use the addition operator + to add geom_hline() with arguments yintercept = 0,lwd=2,col="white" and geom_line() with arguments aes(group=oneid, col=mean_ask_minus_bid). Add the colour palette scale_colour_viridis_c() and a geom_smooth() with arguments col="black",lwd=2,se=FALSE. Finally, create a separate plot for each treatment using facet_grid() with arguments group_size~hints.
18 (10 marks)
What pattern can you see in the data?
Greatest evidence of endowment effect in 2 person groups with hints… Not expected. In the 10 person groups there was no endowment effect to begin with, and then by the end of the experiment there was the opposite effect, where asks were lower than bids. My conjecture is that this behaviour was an attempt to overcome the boredom of being in a 10 person group where your expected payoff function is basically flat. i.e “winning” the auction might be fun, even if it results in a negative payoff.