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1. Course Description    This  is  an  advanced  course  in  microeconomics,  emphasizing  the  applications  of  mathematical tools and models to the study of individual economic decisions and their  aggregate  consequences.  We  begin  with  a  parsimonious  set  of  hypotheses  about  human behavior and the ways in which individual choices interact, and then examine  the  implications  for  markets.  This  entails  treatments  and  applications  of  consumer  theory and theory of the firm, under the ideal conditions implied by our hypotheses.
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This  is  an  advanced  course  in  microeconomics,  emphasizing  the  applications  of  mathematical tools and models to the study of individual economic decisions and their  aggregate [r] ### syllabus micro1 最近の更新履歴 yyasuda's website

1. Course Description    This  is  an  advanced  course  in  microeconomics,  emphasizing  the  applications  of  mathematical tools and models to the study of individual economic decisions and their  aggregate  consequences.  We  begin  with  a  parsimonious  set  of  hypotheses  about  human behavior and the ways in which individual choices interact, and then examine  the  implications  for  markets.  This  entails  treatments  and  applications  of  consumer  theory and theory of the firm, under the ideal conditions implied by our hypotheses.
さらに見せる ### syllabus micro1 最近の更新履歴 yyasuda's website

1. Course Description    This  is  an  advanced  course  in  microeconomics,  emphasizing  the  applications  of  mathematical tools and models to the study of individual economic decisions and their  aggregate  consequences.  We  begin  with  a  parsimonious  set  of  hypotheses  about  human behavior and the ways in which individual choices interact, and then examine  the  implications  for  markets.  This  entails  treatments  and  applications  of  consumer  theory and theory of the firm, under the ideal conditions implied by our hypotheses.
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where x is a vector of choice variables, and a := (a 1 , ..., a m ) is a vector of parameters ( パラメータ ) that may enter the objective function and constraint. Suppose that for each vector a, the solution is unique and denoted by x(a). ◮ A maximum-value function, denoted by M (a), is defined as follows:

34 さらに読み込む ### 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…

22 さらに読み込む ### 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

“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 ### 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) ### 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) ### PQ1 最近の更新履歴 yyasuda's website

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

(1) Write the payoff functions π 1 and π 2 (as a function of p 1 and p 2 ). (2) Derive the best response function for each player. (3) Find the pure-strategy Nash equilibrium of this game. (4) Derive the prices (p 1 , p 2 ) that maximize joint-profit, i.e., π 1 + π 2 . ### 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

Suppose % is a preference relation on X. Then, show the followings. (a) Re‡exive: For any x 2 X, x x. (b) Transitive 1: For any x; y; z 2 X, if x y and y z, then x z. (c) Transitive 2: For any x; y; z 2 X, if x y and y z, then x z. (d) Transitive 3:For any x; y; z 2 X, if x y and y % z, then x % z. where and are de…ned as follows: ### 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. ### 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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