トップPDF Midterm1 10 最近の更新履歴 yyasuda's website

Midterm1 10 最近の更新履歴  yyasuda's website

Midterm1 10 最近の更新履歴 yyasuda's website

1. True or False (9 points) Answer whether each of the following statements is true (T) or false (F). You do NOT need to explain the reason. (a) Suppose % is represented by utility function u( ). Then, u( ) is quasi-concave IF AND ONLY IF % is convex.

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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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PS1 最近の更新履歴  yyasuda's website

PS1 最近の更新履歴 yyasuda's website

6. Question 6 (10 points) We say that a preference relation % is homothetic if x % y implies x % y for all 0. Show that if a consumer has a homothetic preference relation, then her demand function is homogeneous of degree one in !. That is, x(p; !) = x(p; !) for any > 0. 7. Question 7 (20 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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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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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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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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Final1 10 最近の更新履歴  yyasuda's website

Final1 10 最近の更新履歴 yyasuda's website

where ; > 0. Let w 1 ; w 2 > 0 be the prices for inputs x 1 and x 2 respectively. Then, answer the following questions. (a) Sketch the isoquant for this technology. Hint: Isoquant is the combination of inputs that achieves a certain given level of output. (corresponds to “indi¤erence curve” in consumer theory.)

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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

where J (/ M ) is the number of hours per day spent studying for Japanese (/ Math- ematics). You only care about your GPA. Then, answer the following questions. (a) What is your optimal allocation of study time? (b) Suppose T = 10. If you follow this optimal strategy, what will be your GPA?

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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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Lec2 1 最近の更新履歴  yyasuda's website

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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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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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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Final 最近の更新履歴  yyasuda's website

Final 最近の更新履歴 yyasuda's website

3. Auction (14 points) Suppose that a seller auctions one object to two buyers, = 1, 2. The buyers submit bids simultaneously, and the buyer with higher bid receives the object. The loser pays nothing while the winner pays the average of the two bids b + b

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