Select a subway station in Tokyo, and write down its name. You should NOT write more than one name. If you will successfully choose the most popular answer, you would get 4 points. Oth[r]

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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 third-degree price discrimination. Group A’**s** elasticity of demand is ǫ A and

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(b) If consumer’**s** choice satis…es the weak axiom of revealed preferences, we can always construct a utility function which is consistent with such choice behav- iour.
(c) If a consumer problem has a **solution**, then it must be unique whenever the consumer’**s** preference relation is convex.

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Exist exactly one for ANY exchange problem. Always Pareto efficient and individually rational[r]

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Paul Romer (1955-, 内生的成長理論) → 学界から消えた！？
Ben Bernanke (1953-, マクロ、金融) → FRB議長を辞めた**の**は好材料？ Douglas Diamond (1953-, 銀行取付) → 金融は無い？
清滝信宏 (1955-, マクロ、金融) → まだ早い

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2 units of the firm 1’**s** good and A − p 2 + p 1
2 units of the firm 2’**s** good. Assume that the firms have identical (and constant) marginal costs c(< A), and the payoff for each firm is equal to the firm’**s** profit, denoted by π 1 and π 2 .

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Q = K 1 =4
L 1 =8 Then, answer the following questions.
(a) In the short run, the …rm is committed to hire a …xed amount of capital K(+1), and can vary its output Q only by employing an appropriate amount of labor L . Derive the …rm’**s** short-run total, average, and marginal cost functions. (b) In the long run, the …rm can vary both capital and labor. Derive the …rm’**s**

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3(a - e)/4, is greater than aggregate quantity in the Nash equilib- rium of the Cournot game, 2(a - e)/3, so the market-clearing price is lower in the Stackelberg game.. Thus, i[r]

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Introduction to Market Design and its Applications to School Choice.. Yosuke YASUDA.[r]

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Two neighboring homeowners, 1 and 2, simultaneously choose how many hours to spend maintaining a beautiful lawn (denoted by l 1 and l 2 ). Since the appearance of one’**s** property depends in part on the beauty of the surrounding neighborhood, homeowner’**s** benefit is increasing in the hours that neighbor spends on his own lawn. Suppose that 1’**s** payoff is expressed by

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Substituting into p+q = 3=4, we achieve q = 1=2. Since the game is symmetric, we can derive exactly the same result for Player 1’**s** mixed action as well. Therefore, we get the mixed-strategy Nash equilibrium: both players choose Rock, Paper and Scissors with probabilities 1=4; 1=2; 1=4 respectively.

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If the stage game has a unique NE, then for any T , the finitely repeated game has a unique SPNE: the NE of the stage game is played in every stage irrespective of the histor[r]

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A tree starts with the initial node and ends at.. terminal nodes where payoffs are specified..[r]

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The main theorem shows that the condition that a schools’ priority profile ≻ C
has a common priority order for every type t ∈ T is sufficient for the existence of feasible assignments which are both fair and non-wasteful. This condition may be strong and hard to be satisfied when the classification of types is coarse. For instance, if the type set is {high income, low income} and there is a priority for students who live in each school’**s** walk zone, priority orders for high income students will differ across schools in general. However, this can be modified by making a finer type classification, {high income, low income} × {c 1 ’**s** walk zone, c 2 ’**s** walk zone,...}.

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(a) If an agent is risk averse, her risk premium is ALWAYS positive.
(b) When every player has a (strictly) dominant strategy, the strategy profile that consists of each player’**s** dominant strategy MUST be a Nash equilibrium. (c) If there are two Nash equilibria in pure-strategy, they can ALWAYS be Pareto

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elimination of strictly dominated strategies can never be selected (with positive probability) in a mixed-strategy Nash equilibrium.[r]

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e z . The prices of the three goods are given by (p, q, 1) and the consumer’**s** wealth is given by ω.
(a) Formulate the utility maximization problem of this consumer.
(b) Note that this consumer’**s** preference can be expressed in the form of U (x, y, z) = V (x, y) + z. Derive V (x, y).

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Find (all) pure‐strategy Nash equilibrium if it exists. iii.[r]

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5. Bayesian Nash Equilibrium (**12** points)
There are three different bills, $5, $10, and $20. Two individuals randomly receive one bill each. The (ex ante) probability of an individual receiving each bill is therefore 1/3. Each individual knows only her own bill, and is simultaneously given the option of exchanging her bill for the other individual’**s** bill. The bills will be exchanged if and only if both individuals wish to do so; otherwise no exchange occurs. That is, each individuals can choose either exchange (E) or not (N), and exchange occurs only when both choose E. We assume that individuals’ objective is to maximize their expected monetary payoff ($).

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(c) Solve for the total saving S by all types who save and the total borrowing B.. by all types who borrow.[r]

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