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Test 1 Solutions.pdf

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Department
Economics
Course
ECO204Y5
Professor
Kathleen Wong
Semester
Fall

Description
ECO204: Solutions to Test 1 1. (20 points total) Peter Van Houten is a writer and has just finished writing his first manuscript, titled “An Imperial Affliction”. Note: A manuscript is an unpublished book. Peter wants to submit his manuscript to the three publishing firms to have it published. If accepted, assume that the manuscript can only be published as a book by one firm. In other words, Peter can’t accept multiple offers.  House 1 is the ranked as the number 1 firm and will pay Peter $10,000 if they publish his book. Because of their reputation, they also have the lowest acceptance rate: they accept only 15% of all manuscripts they receive.  House 2 is the second-ranked firm and will pay Peter $7,500 if they accept and publish his book. Their acceptance rate is 20%.  House 3 has the lowest reputation and will pay Peter only $3,000 if they accept and publish his book. They accept 45% of all book submissions.  There is also the possibility that all three firms will reject Peter’s manuscript, which means Peter won’t receive any financial compensation for his work. a. (5 points) What is the expected value of the compensation Peter will receive if he sends his book to all three publishing firms? EV 1 (Prob House 1 accepts)(Payment from House 1) + (Prob House 2 accepts)(Payment from House 2) + (Prob House 3 accepts)(Payment from House 3) + (Prob of no offers)(Payment from no offers) Probability of no offers is 1 – 0.15 – 0.20 – 0.45 = 0.20 or 20% EV 1 = (0.15)($10,000) + (0.20)($7,500) + (0.45)($3,000) + (0.20)($0) EV 1 $1,500 + $1,500 + $1,350 + $0 = $4,350 b. (15 points) After doing some research, Peter realizes there is a second option. Instead of getting the manuscript published as a physical book, he can upload the manuscript onto a website for people to download onto their e-readers (to read on devices like an iPad, Kindle, or Kobo). The website will pay Peter according to the users’ review of the book. The website provides Peter with the following information about other books that have used the website:  For books that receive a 4-star rating (the highest possible rating), the author receives $8,000.  For books that receive a 3-star rating, the author receives $6,000.  For books that receive a 2-star rating, the author receives $4,000.  For books that receive a 1-star rating (the lowest possible rating), the author receives $2,000.  The likelihood of receiving any of the four possible rating is the same: they all occur with 25% probability. 1 Assume Peter only cares about the money he’ll receive. Based on the payoffs described in part (a) and (b), which option will be more risky? You must support your answer with empirical (numerical) evidence and explain how you arrived at your conclusion. Hint: you’re dealing with large numbers here, so be careful. Don’t skip steps when entering the numbers in your calculator. EV =2(Prob of 4-star rating)(Payment from 4-star rating) + (Prob of 3-star rating)(Payment from 3-star rating) + (Prob of 2-star rating)(Payment from 2-star rating) + (Prob of 1-star rating)(Payment from 1-star rating) EV =2(0.25)($8,000) + (0.25)($6,000) + (0.25)($4,000) + (0.25)($2,000) EV =2$2,000 + $1,500 + $1,000 + $500 = $5,000 --- 2 2 σ 2 (Prob of 4-star rating)(Payment from 4-star rating – EV ) + (Prob2of 3-star rating)(Payment from 3-star rating – EV ) + (Prob of 2-star rating)(Payment from 2-star rating – 2 2 2 EV 2) + (Prob of 1-star rating)(Payment from 1-star rating – EV ) 2 2 2 2 2 σ 2 (0.25)($8,000 – $5,000) + (0.25)($6,000 – $5,000) + (0.25)($4,000 – $5,000) + (0.25)($2,000 – $5,000) 2 σ 2= (0.25)($3,000) + (0.25)($1,000) + (0.25)( –$1000) + (0.25)( –$3,000) 2 2 σ = $2,250,000 + $250,000 + $250,000 + $2,250,000 = $5,000,000 or $5 million 2 --- σ = (Prob House 1 accepts)(Payment from House 1 – EV ) + (Prob House 2 accepts)(Payment 1 2 1 2 from House 2 – EV 1) + (Prob House 3 accepts)(Payment from House 3 – EV ) + (Prob o1 no offers)(Payment from no offers – EV ) 2 1 σ = (0.15)($10,000 – $4,350) + (0.20)($7,500 – $4,350) + (0.45)($3,000 – $4,350) + 2 1 2 (0.20)($0 – $4,350) 2 2 2 2 2 σ 1 (0.15)($5,650) + (0.20)($3,150) + (0.45)( –$1,350) + (0.20)(–$4,350) 2 σ 1 = $4,788,375 + $1,984,500 + $820,125 + $3,784,500 = $11,377,500 --- By comparing the variance from each of the two options, we can determine which option requires Peter to bear more risk. Since σ > σ , we can conclude that the first option requires 1 2 Peter to bear a relatively larger amount of risk. 2. (20 points) Augustus Waters maximizes his utility by allocating his entire income to purchase only two goods: cheese and tomato sandwiches (S) and cigarettes (C). His utility 0.25 0.75 function can be described as U(S, C) = 0.8S C . Augustus initially has $6,500 to spend on the two goods each year. The price of cigarettes is $6.25, while cheese and tomato sandwiches cost $5 each. Unexpectedly, he receives a significant and large income increase of $1,000 (so that his new income is $7,500). 2 a. Calculate his income elasticity for each good. b. Based on your answer, does Augustus views S and C as normal or inferior goods? Notes: You must utilize the Lagrange method to show numerical evidence and explain how you arrived at your conclusion. Round intermediate answers to 3 decimal places (example: 0.001) and final answe
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