A seller sells a good of quality q at a price t. The cost of producing at quality level q is given by q2/2. There is a buyer who receives a utility of Xq − t by consuming the unit of quality q at price t. If he decides not to buy, he gets a utility of zero. X can take two values X1 = 1 and X2 = 4. (a) Suppose the seller can observe X. Derive the profit maximizing price-quality pairs offered when the type is X1 = 1 and when the type is X2 = 4. (b) Show that the full information price-quality pairs are not incentive compatible if the seller cannot observe X.

A seller sells a good of quality q at a price t. The cost of producing at quality level q is given by q2/2. There is a buyer who receives a utility of Xq − t by consuming the unit of quality q at price t. If he decides not to buy, he gets a utility of zero. X can take two values X1 = 1 and X2 = 4. (a) Suppose the seller can observe X. Derive the profit maximizing price-quality pairs offered when the type is X1 = 1 and when the type is X2 = 4. (b) Show that the full information price-quality pairs are not incentive compatible if the seller cannot observe X.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter7: Uncertainty

Section: Chapter Questions

Problem 7.8P

See similar textbooks

Similar questions

If a person lives for 3 years with a disease and the current standard of care for that disease means he/she lives with a utility level of 0.7.-What is the QALY? Answer in not less than 300 words
Chris Traeger is trying to decide whether or not to purchase health insurance. Chris knows that if he is healthy, his wealth will be $2,000 this year. However, if he gets sick his wealth will only be $500. Chris knows the probability of getting sick is 40%. His utility function is written below. U = (2) What is utility if the individual purchases insurance at the actuarially fair price? 25.29 utils 26.46 utils 31.62 utils 18.97 utils
b) If U = X0.75 y 0.25 and P = 5 ,P, = 10,Income = 200 then find out the utility maximizing values of X and Y.
Suppose that you are the owner of a bakery. The customers who buy the cakes you bake have different tastes x for the chocolate content, with x ranging from 0 to 1. The total number of customers is N = 100 are equally distributed along the [0,1] line. If x is the customer's most preferred chocolate content (location of the customer), and the cakes have chocolate content z, then customer x bears a unit utility cost of $1. Suppose that all customers' reservation price for a slice of a cake is $3. The marginal cost of producing one slice of a cake of any chocolate content is equal to $1. Suppose that you would always like to serve all the customers. a. Your company offers just one type of cake, say regular, with z =1/2 What price will you set for a slice of a cake? b. Suppose that in addition to regular chocolate cake z=1/2 you are also considering offering the high-chocolate variety, that is zHC = 3/4. What price will you set for the slice of your new cake? If running the high-chocolate…
Your own a chocolate producing company which can advertise on both television (T) and internet(I). The effect of TV and online commercials on sales is again given byS(T,I) = 500 + 48T−6T2+ 112I−6I2+ 4TI. You have a budget of $25 that you can spend on T and I. The price of aTV commercial is $12per unit and the price of an online commercial is also $12 per unit. 1. Determine the optimal level of TV commercials T and online commercials I if you have to spend all of your budget. You should provide two methods to solve this, by direct substitution and by setting up the Lagrangian. Is the Lagrange multiplier positive or negative? Give an intuitive interpretation of why this is the case? 2. Now determine the optimal level of TV commercials T and online commercials I if you DO NOT have to spend all of your budget. Do you obtain the same answer as subquestion 5.1? What is the Lagrange multiplier equal to in this case? Discuss.
Suppose that you are the owner of a bakery. The customers who buy the cakes you bake have different tastes x for the chocolate content, with x ranging from 0 to 1. The total number of customers is N = 100 are equally distributed along the [0,1] line. If x is the customer’s most preferred chocolate content (location of the customer), and the cakes have chocolate content z, then customer x bears a unit utility cost of $1. Suppose that all customers' reservation price for a slice of a cake is $3. The marginal cost of producing one slice of a cake of any chocolate content is equal to $1. Suppose that you would always like to serve all the customers. What is the "marginal cost of each unit is (c)" ? What is the "set up cost of each store is F" ? What is the number of the retail shop (n)? What is the transportation cost ( t ) ? What is the reservation price (V) ?
Diluted Happiness: Consider a relationship between a bartender and a customer. The bartender serves bourbon to the customer and chooses x ∈ [0, 1], which is the proportion of bourbon in the drink served, while 1− x is the proportion of water. The cost of supplying such a drink (standard 4-ounce glass) is cx, where c > 0. The customer, without knowing x, decides on whether or not to buy the drink at the market price p. If he buys the drink his payoff is vx − p, and the bartender’s payoff is p − cx. Assume that v>c and all payoffs are common knowledge. If the customer does not buy the drink he gets 0 and the bartender gets −cx. Because the customer has some experience, once the drink is bought and he tastes it, he learns the value of x, but this is only after he pays for the drink. a. Find all the Nash equilibria of this game. b. Now assume that the customer is visiting town for 10 days, and this “bar game” will be played on each of the 10 evenings that the customer is in town.…
Diluted Happiness: Consider a relationship between a bartender and a customer. The bartender serves bourbon to the customer and chooses x ∈ [0, 1], which is the proportion of bourbon in the drink served, while 1− x is the proportion of water. The cost of supplying such a drink (standard 4-ounce glass) is cx, where c > 0. The customer, without knowing x, decides on whether or not to buy the drink at the market price p. If he buys the drink his payoff is vx − p, and the bartender’s payoff is p − cx. Assume that v>c and all payoffs are common knowledge. If the customer does not buy the drink he gets 0 and the bartender gets −cx. Because the customer has some experience, once the drink is bought and he tastes it, he learns the value of x, but this is only after he pays for the drink. a. Find all the Nash equilibria of this game. b. Now assume that the customer is a local, and the players perceive the game as repeated infinitely many times. Assume that each player tries to maximize…
When X=2 and Y=5 Mu of X=10 and MU of Y=20 if Price of X is 2 and Price of Y is 4 and income is 30 Select an answer and submit. For keyboard navigation, use the up/down arrow keys to select an answer. a: Utility is maximum b: utility is minimum c: utility is not maxium d: none of the above.
A computer reseller needs to decide how many laptops to order next month. The lowest end laptop costs $220 and the retailer can sell these for $300. However, the laptop manufacturer already announced that they are coming out with a new model in a couple of months. Any laptops that will not be sold by the end of next month will have to be heavily discounted at half-price. The reseller also needs to consider that every time he fails to fulfill a laptop order, he stands to lose $25 for every unit. Based on the past months’ sales, the reseller estimates the demand probabilities for sales (S) as follows: P(0 units) = 0.3; P(1 units) = 0.4; P(2 units) = 0.2; P(3 units) =0.1. The reseller thinks it’s a good idea to conduct a survey on whether or not his customers are going to buy laptops and how many. The survey results will either be Yes (Y), No (N) or Don’t Know (DK). The probability estimates of the results based on the demand for number of units are: P(Y|S = 0 units) = 0.1 P(Y|S = 1…
A computer reseller needs to decide how many laptops to order next month. The lowest end laptop costs $220 and the retailer can sell these for $300. However, the laptop manufacturer already announced that they are coming out with a new model in a couple of months. Any laptops that will not be sold by the end of next month will have to be heavily discounted at half-price. The reseller also needs to consider that every time he fails to fulfill a laptop order, he stands to lose $25 for every unit. Based on the past months’ sales, the reseller estimates the demand probabilities for sales (S) as follows: P(0 units) = 0.3; P(1 units) = 0.4; P(2 units) = 0.2; P(3 units) =0.1. The reseller thinks it’s a good idea to conduct a survey on whether or not his customers are going to buy laptops and how many. The survey results will either be Yes (Y), No (N) or Don’t Know (DK). The probability estimates of the results based on the demand for number of units are: P(Y|S = 0 units) = 0.1 P(Y|S = 1…
A computer reseller needs to decide how many laptops to order next month. The lowest end laptop costs $220 and the retailer can sell these for $300. However, the laptop manufacturer already announced that they are coming out with a new model in a couple of months. Any laptops that will not be sold by the end of next month will have to be heavily discounted at half-price. The reseller also needs to consider that every time he fails to fulfill a laptop order, he stands to lose $25 for every unit. Based on the past months’ sales, the reseller estimates the demand probabilities for sales (S) as follows: P(0 units) = 0.3; P(1 units) = 0.4; P(2 units) = 0.2; P(3 units) =0.1. The reseller thinks it’s a good idea to conduct a survey on whether or not his customers are going to buy laptops and how many. The survey results will either be Yes (Y), No (N), or Don’t Know (DK). The probability estimates of the results based on the demand for the number of units are: P(Y|S = 0 units) = 0.1…