Assignment 3
T. Joy
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. T. Joy
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. I was in a 10 person group. I chose my bid definetely less than 10 and basing it mostly off of the bid the person before me received the chocolate bar. For the ask, I put 10 so that I could get some sort of value out of selling the chocolate bar.
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? if you bid above your true value because you wouldn’t get the chocolate bar at your value that means the second highest bid is higher than your true value and you would pay more than your value of the chocolate bar. If you bid less than your true value means you don’t get the chocolate bar then you get no or less value from bidding lower. In both cases it only effects your best interest if it changes the outcome of the bid. Due to the scenarios mentioned above, bidding your true value is the dominant strategy.
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?
If you were to get the chocolate bar in the first place you would not want to sell it for less than the amount you paid for it otherwise the entire transaction is a loss. So if you cannot sell at your value but can sell lower than your value then the second price is still below your value and your transaction is a loss. If you ask more than your value and do not sell it then you are giving up potential value because if you sold the bar for the second price, it would have given you excess values from your perceived value. This is the same logic as the second price sealed bid auction and the dominant strategy is asking your value.
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<-group_by(mydf, oneid)
mydf<-mutate(mydf, 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))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 is just a line with a slope of 1 that represents 1 increase of a bid is accompanied with 1 increase of a ask. Although it is difficult to see a pattern the data does seem to cluster around the white line meaning people bid the same as their ask. Both large groups had a larger dispersion of bids compared to the the small groups.
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? the average mean/ask data seems to be concentrated around the white line, specifically around the point (5,5). Small groups seem to have more data dispersed over the white line, while larger group data is much more concentrated. It seems as though the average value of the chocolate bar is around 5.
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<-group_by(mydf, 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? The larger group had the highest bids, while the smaller groups had smaller bids. Most of the bids and asks are centralized around the point (5,5). With larger groups it was more competitive to get a chocolate bar and so people bid more just to take part in the experiment. It is the same data as second plot, it is just shaped and colored to be more visually interpretable.
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 large groups have much more dispersion of their standard deviation bid and asks. This is likely because their are more people with different values of the goods, they also likely didn’t get the chocolate bar at their bid so they changed their bids just take part instead of their true value of receiving the bar. Most of the standard deviations are close to zero meaning people didn’t change their bid or asks all that much which may mean they were bidding at their value or where the chocolate bar was being sold at. # (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<-group_by(mydf, treatment)%>%
slice( chull(sd_bid, sd_ask))14 (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.
15 (5 marks)
What pattern can you see in the data? Much of the standard deviation bid and asks are below 1.5. Yet the large groups have much more dispersion. The large groups had more people with different values for their bid and asks making their standard deviation bid and asks wider. It is the same data as fourth plot just easier to find a pattern because the shapes make it easier to interpret.
# (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.
16 (10 marks)
What pattern can you see in the data?
Small groups had higher ask than bids because they had lower competition and likely had their bids and asks filled where they wanted and more often, while larger groups with more competition likely got bored bid and more than their values to win the auction and their bids were larger than asks. Again, smoothing the data makess it much easier to interpret.