Assignment 3
Z Xiaoyang
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?
Because you paid the second highest price in a Second Price Auction, your bid will only affect the probability of winning the auction, not your price if you win. If you bid lower, it will only effect your chances of winning the auction, not the price you pay.
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?
Your asking price at a Second Price Auction simply influences how likely you are to sell, not how much you really get. The leftover income will not be increased if the asking price is too high. As a result, without knowing the reserve price, the bid is equivalent to the value forgone, implying that the likelihood of selling is likewise the highest.
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(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?
In the scatter plot, the white line is a straight line with a slope of 1. Colors vary depending on the treatment. Small group with a hint at ask>bid; huge group with no clue in the lower right, presumably representing ask>bid
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 ask and bid for various treatments are plotted in the second plot. Mean ask>mean bid in a small group with a hint concentrated on the upper left. The majority of the mean ask in a large group with no indication focused towards the lower right.
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?
The painting appears to be identical to the previous one. The call is slightly larger in the big group than in the small group without the hint. They have a tendency to have issues with their left hand.
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 standard deviation of the distribution of different treatments is depicted in the diagram above. The sd values of the small group with hints will be modest, indicating a huge difference in value size, whereas the sd values of the large group with no hint will be all too large, indicating a great difference in value size. Distributed
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?
The prior theory is also supported by polygons. The sd value of a huge group with no suggestions is very high.
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?
The vertical axis of the above graphic represents ask-bid, while the horizontal axis is round for each round. The ask-bid of small with clues>0, and the ask-bid of large with no hints ask-bid0, can be shown. The other two treatments have a constant value of 0.