Rick thinks either Morty or Summer broke his TV. Morty and Summer each have to decide simultaneously whether to take the blame or blame the other person. If they both blame the same person (both blame Morty or both blame Summer), the person they blame gets a small punishment and utility of -2, while the blameless person gets a utility of 0. Otherwise (if they both blame the other or both blame themselves), they both get a more severe punishment and a utility of -10.a.Draw the normal (matrix) form of this game, with Morty choosing the row and Summer choosing the column. Does either Morty or Summer have a dominant strategy? Explain your answer. Note: only Morty and Summer are players in this Game. Rick designed the game and is not a player. )b.Find all Nash equilibria of this game. )c.Suppose instead there are three suspects: Morty, Summer, and Jerry. Otherwise, the rules are the same as before. Draw the normal (matrix) form of the game. Hint: draw three matrices, with Morty choosing the row, Summer choosing the column, and Jerry choosing between the three matrices.
3. Rick thinks either Morty or Summer broke his TV. Morty and Summer each have to decide simultaneously whether to take the blame or blame the other person. If they both blame the same person (both blame Morty or both blame Summer), the person they blame gets a small punishment and utility of -2, while the blameless person gets a utility of 0. Otherwise (if they both blame the other or both blame themselves), they both get a more severe punishment and a utility of -10.a.Draw the normal (matrix) form of this game, with Morty choosing the row and Summer choosing the column. Does either Morty or Summer have a dominant strategy? Explain your answer. Note: only Morty and Summer are players in this Game. Rick designed the game and is not a player. )b.Find all Nash equilibria of this game. )c.Suppose instead there are three suspects: Morty, Summer, and Jerry. Otherwise, the rules are the same as before. Draw the normal (matrix) form of the game. Hint: draw three matrices, with Morty choosing the row, Summer choosing the column, and Jerry choosing between the three matrices. (d.Find all Nash equilibria of the three-player game from part (c). (e.Suppose the game is played sequentially, with Summer moving first, Morty second, and Jerry third. Draw the game tree and find all subgame-perfect equilibria of the sequential game. )f.Does the sequential game have a Nash equilibrium that is not subgame perfect? Explain your answer.
4. Suppose the demand for pickles on The Citadel is Qd=500-4P, and the supply is Qs=6P. Assume this market is perfectly competitive.a.On the back of the page, graph the
2. U-To is a price leader in the market for truck rentals. There are many small follower firms that take U-To’s price P as given and then supply truck rentals according to the supply function S(P)=P-50 for P≥50, and S(P)=0 for P<50. Thedemand for truck rentals is given by QD(P)=100-P. U-To’s cost function is C(QL)=100+40QL. a.Find the residual demand curve facing U-To. ()b.Find the inverse residual demand curve facing U-To. )c.Write down U-To’s profit function, taking into account the follower firms response to U-To’s decision. ()d.Find U-To’s first order condition for profit-maximization. ()e.Find the profit-maximizing price and quantity chosen by U-To, and the quantity supplied by the follower firms. )f.Suppose demand decreased to QD(P)=60-P. Redo parts (a) – (e) with the new demand curve.
5. Needful Things sells cursed antiques (A) using two inputs: labor (L), and the owners’ time (T). The shop’s production function is A=L1/4T1/4. Needful Things sells cursed antiques in a competitive market at a price of $100. Labor costs $P per unit, and the owner’s time costs $1 per unit.a.Write down Needful Things’ profit function. b.Suppose in the short run, the owner’s time is fixed at T=16. Find the first order condition for the short-run profit maximizing amount of labor. c.Solve for the amount of labor that the shop uses in the short run to maximize profit as a function of P. Is your answer consistent with the
6. Curse Purge Plus is a monopolist in the curse removal market They face an inverse demand curve given by P=200-4Q, where Q is the number of curse removals they sell. Their cost function is C(Q)=10+8Q.
a.Write down the company’s profit function )b.Find the first-order condition for profit maximization. c.Find the profit-maximizing price and quantity, and the maximum profit. d.Calculate the consumer surplus in the market at the
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