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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(a) The intersection of any pair of open sets is an open set.
(b) The union of any (possibly infinite) collection of open sets is open.
(c) The intersection of any (possibly infinite) collection of closed sets is closed. (You can use (b) and De Morgan’**s** Law without proofs.)

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Problem Set **2**: Due on May 10
Advanced Microeconomics I (Spring, **1**st, 2012) **1**. Question **1** (**2** points)
Suppose the production function f satisfies (i) f (0) = 0, (ii) increasing, (iii) con- tinuous, (iv) quasi-concave, and (v) constant returns to scale. Then, show that f must be a concave function of x.

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A good is called normal (resp. inferior) if consumption of it increases (resp. declines) as income increases, holding prices constant.. Show the following claims.[r]

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that a plea bargain is allowed):
If both confess, each receives 3 years imprisonment.
If neither confesses, both receive **1** year.
If one confesses and the other one does not, the former will be set free immediately ( 0 payoff) and

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e z . The prices of the three goods are given by (p, q, **1**) and the consumer’**s** wealth is given by ω.
(a) Formulate the utility maximization problem of this consumer.
(b) Note that this consumer’**s** preference can be expressed in the form of U (x, y, z) = V (x, y) + z. Derive V (x, y).

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Combination of dominant strategies is Nash equilibrium. There are many games where no dominant strategy exists[r]

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

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Problem Set **2**: Due on May 14
Advanced Microeconomics I (Spring, **1**st, 2013)
**1**. Question **1** (6 points)
(a) Suppose the utility function is continuous and strictly increasing. Then, show that the associated indirect utility function v(p, ω) is quasi-convex in (p, ω). (b) Show that the (minimum) expenditure function e(p, u) is concave in p.

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◮ A lottery p is a function that assigns a nonnegative number to
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

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(a) The intersection of any pair of open sets is an open set.
(b) The union of any (possibly infinite) collection of open sets is open.
(c) The intersection of any (possibly infinite) collection of closed sets is closed. (You can use (b) and De Morgan’**s** Law without proofs.)

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

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

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(a) The intersection of any pair of open sets is an open set.
(b) The union of any (possibly infinite) collection of open sets is open.
(c) The intersection of any (possibly infinite) collection of closed sets is closed. (You can use (b) and De Morgan’**s** Law without proofs.)

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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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Problem Set **2**: Posted on November 18
Advanced Microeconomics I (Fall, **1**st, 2013)
**1**. Question **1** (7 points)
A real-valued function f (x) is called homothetic if f (x) = g(h(x)) where g : R → R is a strictly increasing function and h is a real-valued function which is homo- geneous of degree **1**. Suppose that preferences can be represented by a homothetic utility function. Then, prove the following statements.

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

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Problem Set **2**: Posted on November 4
Advanced Microeconomics I (Fall, **1**st, 2014)
**1**. Question **1** (7 points)
A real-valued function f (x) is called homothetic if f (x) = g(h(x)) where g : R → R is a strictly increasing function and h is a real-valued function which is homo- geneous of degree **1**. Suppose that preferences can be represented by a homothetic utility function. Then, prove the following statements.

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

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u **2** (x, y **2** ) = **2** ln x + y **2** .
u 3 (x, y 3 ) = 3 ln x + y 3 .
(a) Assume that the public good is purchased, privately and that person 3 is the first to go to the market and buy the public good. Assume he does not act strategically; he ignores persons **1** and **2** when he buys x, and thinks only of his own utility maximization problem. What is the outcome? How much of the public good does person 3 buy? How much do persons **1** and **2** buy? (b) Use the Samuelson optimality condition to find the Pareto optimal quantity

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