Question
This is a question about Tony, the seller of durable goods, whom we have met before in HW4. This time he is selling to three
This is a question about Tony, the seller of durable goods, whom we have met before in HW4. This time he is selling to three potential consumers, H, M, L. Remember, since the good is durable, if a consumer buys it in period 1, she obtains utility from it for two periods. If she buys in period 2, then she obtains utility only in period 2.
The utilities, which are in equivalent dollar units, of each consumer is given in the table below:
Period | 1 | 2 |
H utility | 3000 | 1400 |
M utility | 2400 | 800 |
L utility | 1200 | 600 |
Thus, if H buys in period 1 at a price of $1000, he gets a payoff of 3000+ 1400 1000 = 3400. Similar calculations can be done for the other consumers. If any consumer does not buy, she gets a payoff of 0. Thus, L would be better o not buying than paying a price of $2000. You can assume that consumers who are indifferent will go ahead and buy.
If Tony charges a price of $1000 in the rst round and $100 in the second round while H and M buy in the rst period and L buys in the second period, then Tony's payoff is $1000 + $1000 + $100 = $2100.
The game is as follows: Tony announces a price p1 in round 1. The consumers simultaneously and independently decide whether or not to buy in round 1. Whoever buys leaves the game. Those who do not buy remain. Who remains is observable to everyone involved. Given this observation, Tony announces p2 in round 2.
Question: What is the subgame perfect pricing policy for Tony? Please make sure you write down the strategies for all players and show why it is subgame perfect. Record your answers on paper, then scan and upload them.
Step by Step Solution
There are 3 Steps involved in it
Step: 1
![blur-text-image](https://dsd5zvtm8ll6.cloudfront.net/includes/images/document_product_info/blur-text-image.webp)
Get Instant Access with AI-Powered Solutions
See step-by-step solutions with expert insights and AI powered tools for academic success
Step: 2
![blur-text-image](https://dsd5zvtm8ll6.cloudfront.net/includes/images/document_product_info/blur-subtext-image.webp)
Step: 3
![blur-text-image](https://dsd5zvtm8ll6.cloudfront.net/includes/images/document_product_info/blur-subtext-image.webp)
Ace Your Homework with AI
Get the answers you need in no time with our AI-driven, step-by-step assistance
Get Started