# トップPDF Lec1 4 最近の更新履歴 yyasuda's website ### Lec1 4 最近の更新履歴 yyasuda's website

R n + := {(x 1 , ..., x n )|x i ≥ 0, i = 1, ..., n} ⊂ R n . For any x, y ∈ X, x % y means x is at least as preferred as y. Consumption set contains all conceivable alternatives. A budget set is a set of feasible consumption bundles, represented as B(p, ω) = {x ∈ X|px ≤ ω}, where p is an n-dimensional positive vector interpreted as prices, and ω is a positive number interpreted as the consumer’s wealth.

12 さらに読み込む ### PS1 最近の更新履歴 yyasuda's website

Continuous (a) Show that if % is represented by a linear utility function, i.e., u(x 1 ; x 2 ) = x 1 + x 2 with ; > 0, then % satis…es the above three properties. (b) Find the preference relation that is 1) Additive and Strictly monotone but not Continuous, and 2) Strictly monotone and Continuous but not Additive. ### Final 最近の更新履歴 yyasuda's website

2. Duopoly Game (20 points) Consider a duopoly game in which two firms, denoted by Firm 1 and Firm 2, simultaneously and independently select their own prices, p 1 and p 2 , respectively. The firms’ products are differentiated. After the prices are set, consumers demand A − p 1 + p 2 ### en 最近の更新履歴 yyasuda's website

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

84 さらに読み込む ### Midterm 最近の更新履歴 yyasuda's website

(a) Derive all pure strategy Nash equilibria. (b) Show that the following type of Nash equilibria does NOT exist: One firm chooses pure strategy M , and other two firms use mixed strategies. (c) Derive a symmetric mixed strategy Nash equilibria. You may assume that each firm chooses M with probability p and E with probability 1 − p, then calculate an equilibrium probability, p. ### Lec2 4 最近の更新履歴 yyasuda's website

u i (s ′ i , s − i ) > u i (s i , s − i ) for all s − i ∈ S − i . A strategy s ′ i is a weakly dominant strategy if playing s ′ i is optimal for any combination of other players’ strategies: u i (s ′ i , s −i ) ≥ u i (s i , s −i ) for all s ∈ S and

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Solve the following problems in Snyder and Nicholson (11th):. 1.[r] ### PS1 最近の更新履歴 yyasuda's website

(a) Show that if u(x 1 , x 2 ) and v(x 1 , x 2 ) are both homogeneous of degree r, then s (x 1 , x 2 ) := u(x 1 , x 2 ) + v(x 1 , x 2 ) is also homogeneous of degree r. (b) Show that if u(x 1 , x 2 ) and v(x 1 , x 2 ) are quasi-concave, then m(x 1 , x 2 ) := min{u(x 1 , x 2 ), v(x 1 , x 2 )} is also quasi-concave. ### Lec1 最近の更新履歴 yyasuda's website

 【戦略】 個々プレイヤーがとることできる行動  【利得】 起こり得る行動組み合わせに応じた満足度、効用 Q: ゲーム解（予測）はどうやって与えられる？ A: 実はノイマン達は一般的な解を生み出せなかった…

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More on Roy’s Identity | もっとロア恒等式 Roy’s identity says that the consumer’s Marshallian demand for good i is simply the ratio of the partial derivatives of indirect utility with respect to p i and ω after a sign change.

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“Soon after Nash ’s work, game-theoretic models began to be used in economic theory and political science,. and psychologists began studying how human subjects behave in experimental [r]

26 さらに読み込む ### Final1 14 最近の更新履歴 yyasuda's website

(b) Does this production function display increasing, constant, or decreasing re- turns to scale? Explain why. (c) Formulate the cost minimization problem (you may denote a target output level by y). Then, solve it and derive the (minimum) cost function, c(w 1 , w 2 , y). ### Final1 12 最近の更新履歴 yyasuda's website

4. Exchange Economy (12 points) Consider the following exchange economies with two agents and two goods. Derive competitive equilibrium prices and allocations in each case. (a) Two agents, 1 and 2, have the following indirect utility functions: v 1 (p 1 , p 2 , ω ) = ln ω − a ln p 1 − (1 − a) ln p 2 ### Final1 13 最近の更新履歴 yyasuda's website

endowment of time is 2ω 1 units. There is no (initial) endowment of consumption good. Each individual has a common utility function U (x) = ln x 1 + 2a ln x 2 . Sup- pose that only Ann owns the firm and its production function is y 2 = √z 1 , where y 2 is the output of consumption good and z 1 is the input of (total) labor. Let the ### Midterm1 14 最近の更新履歴 yyasuda's website

problem with equality constraints. 2. Consumer Theory (30 points) A consumer gets utility from 2 sources: drinking (measured in liters x) and time spent on the phone (measured in hours y). Each liter of drink costs \$4 and each hour on the phone costs \$4. She has a total of \$120 available for spending. Her utility function is given by: ### Lec2 1 最近の更新履歴 yyasuda's website

vNM Utility Function (1) Note the function U is a utility function representing the preferences on L(S) while v is a utility function defined over S, which is the building block for the construction of U (p). We refer to v as a vNM (Von Neumann-Morgenstern) utility function.

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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 ### PracticeM 最近の更新履歴 yyasuda's website

Consider a consumer problem. Suppose that a choice function x(p; !) satis…es Walras’s law and WA. Then, show that x(p; !) is homogeneous of degree zero. 6. Lagrange’s Method You have two …nal exams upcoming, Mathematics (M) and Japanese (J), and have to decide how to allocate your time to study each subject. After eating, sleeping, exercising, and maintaining some human contact, you will have T hours each day in which to study for your exams. You have …gured out that your grade point average (G) from your two courses takes the form ### PracticeF 最近の更新履歴 yyasuda's website

long-run total, average, and marginal cost functions. 7. Expected Utility Suppose that an individual can either exert e¤ort or not. The cost of e¤ort is c. Her initial wealth is 100. Her probability of facing a loss 75 (that is, her wealth becomes 25) is 1 ### PS1 最近の更新履歴 yyasuda's website

with x = (y, z) where y is a scalar, z is an n-dimensional consumption vector, and V (·) is a real valued function. The consumption set X = R n +1 + . (a) Show that if V is concave, U is quasi-concave. (b) Show that if U is quasi-concave, V is concave. 5. Question 5 (4 points)