(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

2 さらに読み込む

(a) If a consumer’**s** preference is complete and transitive, her demand behaviors always satisfy the weak axiom of revealed preference.
(b) Even if a firm’**s** technology shows increasing return to scale, the marginal product (with respect to some input) can be decreasing.

2 さらに読み込む

More on Roy’**s** Identity | もっとロア**の**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.

34 さらに読み込む

(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.

2 さらに読み込む

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

1 さらに読み込む

(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.

1 さらに読み込む

【戦略】 個々**の**プレイヤーがとること**の**できる行動
【利得】 起こり得る行動**の**組み合わせに応じた満足度、効用
Q: ゲーム**の**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

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 **1**’**s** payoff is expressed by

2 さらに読み込む

“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

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)

1 さらに読み込む

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

1 さらに読み込む

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

1 さらに読み込む

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)

1 さらに読み込む

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

Lotteries (**1**)
We consider preferences and choices over the set of “lotteries.” Let S be a set of consequences (prizes). We assume that S is a finite set and the number of its elements (= |S|) is S. A lottery p is a function that assigns a nonnegative number to

15 さらに読み込む

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

2 さらに読み込む

endowment of time is 2ω **1** units. There is no (initial) endowment of consumption
good. Each individual has a common utility function U (x) = ln x **1** + 2a ln x 2 . Sup- pose that only Ann owns the firm and its production function is y 2 = √z **1** , where
y 2 is the output of consumption good and z **1** is the input of (total) labor. Let the

2 さらに読み込む

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

2 さらに読み込む

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

2 さらに読み込む

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**

3 さらに読み込む