トップPDF Final1 13 最近の更新履歴 yyasuda's website

Final1 13 最近の更新履歴  yyasuda's website

Final1 13 最近の更新履歴 yyasuda's website

(a) If a consumer’s preference satisfies completeness and transitivity, her prefer- ence can be ALWAYS represented by some utility function. (b) It is POSSIBLE that an expenditure function is a convex function of prices. (c) If the utility function is quasi-linear, the compensating variation is ALWAYS

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Midterm 最近の更新履歴  yyasuda's website

Midterm 最近の更新履歴 yyasuda's website

Ann and Bob are in an Italian restaurant, and the owner offers them a free 3- slice pizza under the following condition. Ann and Bob must simultaneously and independently announce how many slice(s) she/he would like: Let a and b be the amount of pizza requested by Ann and Bob, respectively (you can assume that a and b are integer numbers between 1 and 3). If a + b ≤ 3, then each player gets her/his requested demands (and the owner eats any leftover slices). If a + b > 3, then both players get nothing. Assume that each players payoff is equal to the number of slices of pizza; that is, the more the better.
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PS1 最近の更新履歴  yyasuda's website

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.

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PQ1 最近の更新履歴  yyasuda's website

PQ1 最近の更新履歴 yyasuda's website

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

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PS1 最近の更新履歴  yyasuda's website

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.

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Lec1 最近の更新履歴  yyasuda's website

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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Micro1 最近の更新履歴  yyasuda's website

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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Lec1 最近の更新履歴  yyasuda's website

Lec1 最近の更新履歴 yyasuda's website

“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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PS1 最近の更新履歴  yyasuda's website

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)

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PQ1 最近の更新履歴  yyasuda's website

PQ1 最近の更新履歴 yyasuda's website

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

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EX1 最近の更新履歴  yyasuda's website

EX1 最近の更新履歴 yyasuda's website

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

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PS1 最近の更新履歴  yyasuda's website

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)

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Lec1 最近の更新履歴  yyasuda's website

Lec1 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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Lec2 1 最近の更新履歴  yyasuda's website

Lec2 1 最近の更新履歴 yyasuda's website

each prize s, where P s∈S p(s) = 1 (here p(s) is the objective probability of obtaining the prize s given the lottery p). Let α ◦ x ⊕ (1 − α) ◦ y denote the lottery in which the prize x is realized with probability α and the prize y with 1 − α. Denote by L(S) the (infinite) space containing all lotteries

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Final1 12 最近の更新履歴  yyasuda's website

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

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Midterm1 14 最近の更新履歴  yyasuda's website

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

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Final1 14 最近の更新履歴  yyasuda's website

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

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PS2 1 最近の更新履歴  yyasuda's website

PS2 1 最近の更新履歴 yyasuda's website

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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PracticeM 最近の更新履歴  yyasuda's website

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

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PracticeF 最近の更新履歴  yyasuda's website

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

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