# トップPDF Lec1 10 最近の更新履歴 yyasuda's website ### Lec1 10 最近の更新履歴 yyasuda's website

When we analyze the demand for a single good (partial equilibrium study), it would be convenient to aggregate “all other goods”. A Consumer’s Problem (again)[r]

12 さらに読み込む ### 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.) ### Micro1 最近の更新履歴 yyasuda's website

◮ A set S in R n is called compact if it is closed ( 閉 ) and bounded. Thm A1.10 (Weierstrass) Existence of Extreme Values Let f : S → R be a continuous real-valued function where S is a non-empty compact subset of R n . Then f has its maximum and minimum values. That

34 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. ### 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. ### 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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“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) ### 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.

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

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 ### 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 ### 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 ### 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.

15 さらに読み込む ### 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 ### 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 ### 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