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... Problem Set 2: Posted on November 4 Advanced Microeconomics I (Fall, 1st, 2014) 1. Question 1 (7 points) A real-valued function f (x) is called homothetic if f (x) = g(h(x)) where g : R → R is a strictly ... 完全なドキュメントを参照

... A good is called normal (resp. inferior) if consumption of it increases (resp. declines) as income increases, holding prices constant.. Show the following claims.[r] ... 完全なドキュメントを参照

... Let w = (w 1 , w 2 , w 3 , w 4 ) ≫ 0 be factor prices and y be an (target) output. (a) Does the production function exhibit increasing, constant or decreasing returns to scale? Explain. (b) Calculate the ... 完全なドキュメントを参照

... Problem Set 2: Posted on November 18 Advanced Microeconomics I (Fall, 1st, 2013) 1. Question 1 (7 points) A real-valued function f (x) is called homothetic if f (x) = g(h(x)) where g : R → R is a strictly ... 完全なドキュメントを参照

... Problem Set 2: Due on May 14 Advanced Microeconomics I (Spring, 1st, 2013) 1. Question 1 (6 points) (a) Suppose the utility function is continuous and strictly increasing. Then, show that the associated indirect ... 完全なドキュメントを参照

... (d) Suppose that this game is played finitely many times, say T (≥ 2) times. De- rive the subgame perfect Nash equilibrium of such a finitely repeated game. Assume that payoff of each player is sum of each period ... 完全なドキュメントを参照

... Consider the following two-person dynamic game. In the …rst period, game A is played; after observing each player’s actions, they play game B in the second period. Assume that the payo¤s are simply the sum ... 完全なドキュメントを参照

... (d) What is the Nash equilibrium of this game? 4. Mixed Strategy (15 points) Three …rms (1, 2 and 3) put three items on the market and can advertise these products either on morning (= M ) or evening TV (= E). A ... 完全なドキュメントを参照

... 5. Bayesian Game (20 points) There are 10 envelopes and each of them contains a number 1 through 10. That is, one envelope contains 1, another envelope contains 2, and so on; these numbers cannot be observable ... 完全なドキュメントを参照

... Prisoners’ Dilemma: Analysis
 ( Silent , Silent ) looks mutually beneficial outcomes, though  Playing Confess is optimal regardless of other player’s choice!  Acting optimally ( Confess , Confess ) rends up ... 完全なドキュメントを参照

... Hint: Your answers in (a) – (c) may change depending on the value of θ. 4. Duopoly (20 points) Consider a duopoly game in which two firms, denoted by firm 1 and firm 2, simul- taneously and independently select ... 完全なドキュメントを参照

... 4. Auctions (30 points) Suppose that the government auctions one block of radio spectrum to two risk neu- tral mobile phone companies, i = 1, 2. The companies submit bids simultaneously, and the company with ... 完全なドキュメントを参照

... Suppose you are on the admission committee of the CRIPS, and must decide the minimum acceptance score of the entrance examination. There are two kinds of students, excellent and geniuses. All students would like to be ... 完全なドキュメントを参照

... That is, given that the incumbent’s information set is reached, choosing A is clearly optimal irrespective of her belief over nodes. → Choosing F looks non-credible. SPNE cannot eliminate this since there is no ... 完全なドキュメントを参照

... A belief about other players’ types is a conditional probability distribution of other players’ types given the player’s knowledge of her own type p i (t −i |t i ). When nature reveals t i to player i, she can ... 完全なドキュメントを参照

... First-Price: General Model (1) Consider a first-price auction with n bidders in which all the conditions in the previous theorem are satisfied. Assume that bidders play a symmetric equilibrium, β(x). Given some bidding ... 完全なドキュメントを参照

... Proof Sketch (2): Existence of Pivotal Voter Lemma 3 (Existence of Pivotal Voter) There is a voter n ∗ = n(b) who is extremely pivotal in the sense that by changing his vote at some profile he can move b from the ... 完全なドキュメントを参照

... Explain. (b) Show that any risk averse decision maker whose preference satisfies indepen- dence axiom must prefer L 2 to L 3 . 3. Question 3 (4 points) Suppose a monopolist with constant marginal costs prac- tices ... 完全なドキュメントを参照

... (c) Any finite game has at least one Nash equilibrium in pure strategies. 2. Expected Utility (16 points) Suppose that an individual can either exert effort or not. Her initial wealth is $100 and the cost of ... 完全なドキュメントを参照

... A bargaining situation is described by a tuple hX, D, % 1 , % 2 i: X is a set of possible agreements: a set of possible consequences that the two players can jointly achieve. D ∈ X is the disagreement outcome: the ... 完全なドキュメントを参照