Homework 5 Managerial Economics - where Congress and the President

Managerial Economics Questions

Homework 5 Managerial Economics  

Instructions: Show all of your work! 

1. Consider the following sequential game, where Congress and the President are trying to pass a spending bill. Congress first decides to what bill to pass, at which point the President can either sign the legislation or veto it. There are two potential components of the spending bill – infrastructure (I) spending which is preferred by Congress, and defense (D) spending which is preferred by the President. The legislation passed can include any combination of these components. Solve for the Subgame-Perfect Nash Equilibrium and the equilibrium path for the following game, where payoffs are in the order of (Congress, President). President I&D Sign (3 , 3) Veto Sign (2 , 2) I Congress D Neither Veto Sign (4 , 1) (2 , 2) (1 , 4) (2 , 2) Veto Sign (2 , 2) Veto (2 , 2)

2. Consider the following game where a potential market Entrant is trying to decide whether or not to enter the market. The Incumbent firm is established and can choose to cut the price, maintain the price, or raise the price of the god in hopes of deterring the Entrant from entering. The payouts are given in the matrix below. Cut Price Maintain Price Raise Price Enter -4,4 4,6 5,5 Stay Out 0,9 0,12 0, 13

a) Suppose the players move sequentially, and that the Entrant moves first. First set up the game tree. What will be the subgame perfect Nash equilibrium outcome? Can the Incumbent deter entry? Explain intuitively why or why not.

b) Now suppose that the Incumbent moves first. Again, set up the game tree. What is the subgame perfect Nash equilibrium outcome now? Can the Incumbent deter entry now?

3. Consider the 3rd problem from your last homework, where Xbox and Playstation are competing: Playstation Gaming XBox Media Both Gaming 11 , 8 6 , 12 10 , 14 Media 12 , 9 8 , 10 9, 8 Both 11, 6 12, 11 4,6

a) Suppose Playstation moves first. Solve for the equilibrium path for this sequential move game.

b) Suppose instead that Xbox can move first. What will be the equilibrium path now? Will Xbox want to move first? Will Playstation want them to? Explain.

4. Consider 2 firms (Firm A and Firm B) selling airplanes, competing as Cournot duopolists. The market demand function facing the airplane market is ???? = ????(???? − ????), where ???? = ???????? + ???????? . The ???? cost function for Firm A is given by ????(????????) = ???????? ???? , and the cost function for Firm B is given by ???? ???? ???? ????(???????? ) = ???????? ???? .

a) Find the Cournot Nash equilibrium where the firms choose output simultaneously.

5. Consider 2 airplane manufacturers that compete as Cournot duopolists in the market for ???? ???? commercial aircraft. Arrowing (firm A) has a cost function given by ????(???????? ) = ???????? , whereas ???? ???? SkyTrain (firm S) has a cost function given by ????(???????? ) = ???????? ???? . The market demand function for commercial airliners is given by: ???? = ???????????? − ???????? where ???? is the sum of the quantity of planes available for purchase.

a) If the two companies choose the quantities of trips supplied simultaneously, find the Cournot equilibrium quantities supplied for each firm and the equilibrium price.