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Homework 3

Monopoly

Question 1: (2 + 3 + 5 = 10 points)

a) What is the price and quantity a uniform-price monopoly charges in the short-run (in the long-run it will shut down). Figure 1: Caption

b) Consider the figure below. What is the uniform price monopolist’s profit? 1 Figure 2: Caption

c) In the figure above, what is the monopolist’s total revenue if it engages in first-degree price discrimination?

Question 2: (5 × 6 = 30 points)

State if the following examples are 1st degree, 2nd degree, or 3rd degree price discrimination:

a) A discount when you buy soda with your meal at a restaurant b) A discount for veterans when renting a car

c) iPhones cost \$200 more in Switzerland than in the United States d) A promotion that gives costumers a \$25 gift card if they spend \$100

e) After analyzing your search history, an online retailer sells a good to you at your exact maximum willingness to pay for the good

f) An airline charges different prices for economy and business class flights 2

Duopoly and Game Theory

Question: (10 + 10 + 10 + 5 + 15 + 10 = 60 points) Cournot Duopoly (quantity Competition)

Consider a duopoly with two firms A and B where firm A and firm B have as level of production qA and qB. We assume that qA and qB belongs to {2, 3, 4, 5} and that both firms face an identical average or per unit cost of \$5. They face the inverse demand P = 20 − qA − qB

a) If firm B output is known to be 0. What is the price and the quantity that firm A would charge and trade in the market? What would be the profit of firm A? (Hint: you can draw a graph using the inverse demand.)

b) Now, we no more have the assumption that firm B’s output is 0. Assume that firm A and B form a Cartel and no firm cheats, what are the equi librium quantities

For the remaining question, we assume that there is no Cartel. c) In a table, present price of the good for different values of (qA, qB). d) In a table, present unit profit of a firm for different (qA, qB).

e) In a table, present profit of each firm, together with best response for different (qA, qb)

f) Determine all Nash Equilibrium (NE) of this Cournot duopoly 3