# トップPDF Lec1 12 最近の更新履歴 yyasuda's website ### Lec1 12 最近の更新履歴 yyasuda's website

for i = 1, · · · , n. We now have to show that p ∗ is a competitive equilibrium. Using Warlas’ law, we can show that z i (p ∗ ) = 0 for all i. It is common to show the existence of equilibrium by applying a version of fixed-point theorems in Economics.

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i (p, u) denote the Hicksian demand function of good i and e(p, u) denote the expenditure function. Then, state the Shephard’s lemma. (c) Using envelope theorem, derive either (a) Roy’s identity, or (b) Shephard’s lemma. You can assume that the first order conditions guarantee the optimal solution, i.e., ignore the second order conditions. ### Lec1 最近の更新履歴 yyasuda's website

いよいよゲーム理論中身を見ていこう！  まずは1時点（静学的な）ゲームを分析  各プレイヤーは独立かつ同時に戦略を決定  相手決定を知らずに自分戦略を決めるような状況  決定タイミングは文字通り“同時”である必要は無い！

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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 1s payoff is expressed by ### PS1 最近の更新履歴 yyasuda's website

(a) Show that the above data satisfy the Weak Axiom of revealed preference. (b) Show that this consumer’s behavior cannot be fully rationalized. Hint: Assume there is some preference relation % that fully rationalizes the above data, and verify that % fails to satisfy transitivity. ### PQ1 最近の更新履歴 yyasuda's website

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. ### Micro1 最近の更新履歴 yyasuda's website

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]

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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) ### PQ1 最近の更新履歴 yyasuda's website

Solve the following problems in Snyder and Nicholson (11th):. 1.[r] ### EX1 最近の更新履歴 yyasuda's website

Solve the following problems in Snyder and Nicholson (11th):. 1.[r] ### 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) ### 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]

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2 α ◦ x ⊕ (1 − α) ◦ y ∼ (1 − α) ◦ y ⊕ α ◦ x: The consumer does not care about the order in which the lottery is described. 3 β ◦ (α ◦ x ⊕ (1 − α) ◦ y) ⊕ (1 − β) ◦ y ∼ (βα) ◦ x ⊕ (1 − βα) ◦ y: A consumer’s perception of a lottery depends only on the net probabilities of receiving the various prizes.

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6. General Equilibrium (30 points) Consider a production economy with two individuals, Ann (A) and Bob (B), and two goods, leisure x 1 and a consumption good x 2 . Ann and Bob have equal en- dowments of time (= ω 1 ) to be allocated between leisure and work, so the total ### Midterm1 14 最近の更新履歴 yyasuda's website

(a) Suppose % is represented by utility function u(·). Then, u(·) is quasi-concave IF AND ONLY IF % is convex. (b) Marshallian demand function is ALWAYS weakly decreasing in its own price. (c) Lagrange’s method ALWAYS derives optimal solutions for any optimization ### Final1 14 最近の更新履歴 yyasuda's website

is increasing in x 1 , the marginal product of x 2 must be negative. (c) Let (x, p) be a competitive equilibrium. Suppose u i (y i ) > u i (x i ) for some bundle y i . Then show that p · y i > p · x i . Does this depend on whether utility ### Lec1 最近の更新履歴 yyasuda's website

Consider the case that M ≻ m. By I and C, there must be a single number v(s) ∈ [0, 1] such that v(s) ◦ M ⊕ (1 − v(s)) ◦ m ∼ [s] where [s] is a certain lottery with prize s, i.e., [s] = 1s. In particular, v(M ) = 1 and v(m) = 0. I implies that

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