Economic Principles Solutions to Problem Set 2
Question 1. Given the conditions, Bob' budget constraint is equal to: s (x1 i.e., 2x1 + 2x2 = 100 if x1 10 x1 + 2x2 = 90 if x1 > 10 Graphically, the budg
Economic Principles Solutions to Problem Set 5
Question 1 f (= (minf x1 ; x2 g) Since f (kx1 ; kx2 ) = (minf kx1 ; kx2 g) = k minf x1 ; x2 g = k f (x1 ; x2 ), we have that:
< 1 =) f (kx1 ; kx2 ) < kf
Game Theory Problem Set 6
1. (Mixed and behavioral strategies) Consider the following extensive-form game.
1 A 2 L M 1 l r l r R B
(a) Let 1 denote player 1' mixed strategy in which she plays (B; r) w
Economic Principles Problem Set 2
1. Bob consumes ice creams (x1 ) and hamburgers (x2 ) : His utility function is u (x1 ; x2 ) = (x1 ) 2 (x2 ) 2 : Bob' income is $ 100. The price of each hamburger is
Economic Principles Solutions to Problem Set 3
Question 1 The WARP requires that, if a bundle x0 is chosen when another bundle x1 is available, then when this new bundle x1 is itself chosen, x0 must n
Economic Principles Problem Set 11
1. A monopolist faces a market demand curve given by q (p) = 70 p:
(a) If the monopolist can produce at constant average and marginal costs of AC = M C = 6; what out
Economic Principles Problem Set 8
1. Consider the following Robinson Crusoe economy. Robinson the consumer is endowed with zero units of coconuts, x; and 24 hours of time, h; so that e = (0; 24) : His
Economic Principles Problem Set 10
1. Consider an economy with two consumers. The utility function of consumer i = 1; 2 is equal to u(xi ; li ; xj ) = log(xi + xj ) + li ; where li denotes i' (leisure
Economic Principles Problem Set 3
1. (JR 2.8). The consumer buys bundle xi at price pi ; i = 0; 1: Separately for parts (a) to (d), state whether these indicated choices satisfy WARP: (a) p0 = (1; 3);
Economic Principles Problem Set 9
1. Consider a two-consumer, two-good exchange economy. Utility functions and endowments are: uA (x1 ; x2 ) = (x1 x2 )2 and eA = (15; 6) ; B u (x1 ; x2 ) = ln (x1 ) +
Economic Principles Problem Set 1
1. Let < be represented by u : Rn ! R. Prove that u (x) is strictly quasiconcave if and + only if < is strictly convex. p 2. Consider the following utility functions:
Economic Principles Problem Set 5
1. Suppose a production function has the form y = (min f x1 ; x2 g) ; where > 0; > 0; > 0: Carefully sketch the isoquant map for this technology. Discuss returns to s
Economic Principles, Spring 2013 Midterm Solutions
You have two hours to complete this exam. Please answer the following three questions. Be sure to allocate your time in proportion to the points. Alw
Economic Principles Solutions to Problem Set 4
Question 1 The investor' problem is s max
n X i=1 i u(w
2[0;1]
(1
) r+w
xi )
Let wi = w (1 ) r+w xi . For simplicity, let' assume that we have an interio
Economic Principles, Spring 2013 Final Exam Solutions You have two hours to complete this exam. Please answer the following four questions. Be sure to allocate your time in proportion to the points. A
Economic Principles Solutions to Problem Set 6
Question 1 We know that in the long run equilibrium, price will be equal to the minimum of the AC of the production for a representative .rm, and it is e
Economic Principles Solutions to Problem Set 9
Question 1 (a) The Pareto-e cient allocations solve to the following problem (where we took the square root of uA and take the logarithm, both monotonic
Economic Principles Solutions to Problem Set 8
Question 1 Let p denote the price of the coconuts and w denote the price of Robinson' time. s Normalize p = 1. p Given the production function, the produ
Economic Principles Solutions to Problem Set 11
Question 1 (a) The maximization problem of the monopolist is: max
q
(70
q)q
6q
The F.O.C. is 70 2q = 6 =) q = 32 Also, the monopolistic price and pro.ts
Economic Principles Solutions to Problem Set 10
Question 1 (a) In this economy there are two goods, labor h and the public good x. By Walras'law we can set the price of labor w = 1:By constant return
Economic Principles Solutions to Problem Set 1
Question 1. Let < be represented by u : Rn ! R. Prove that u (x) is strictly quasiconcave if and only if + < is strictly convex. "If"part: ( "strict conv
Economic Principles, Spring 2013 Midterm Exam Dino Gerardi April 8th You have two hours to complete this exam. Please answer the following three questions. Be sure to allocate your time in proportion
Economic Principles Problem Set 4
1. Consider an investor who has initial wealth w and has to decide how to invest it. There is a riskless asset with rate of return r: The risky asset can have any of
Game Theory Solutions to Problem Set 2
1
(a)
Find all NE
L 3; 4 0; 3 R 2; 6 5; 1
U D
First, note that pure strategy D is strictly dominated by U )we can eliminate D. Then pure strategy L is strictly d
Game Theory Problem Set 9
1. Suppose there are n .rms in a Cournot oligopoly. Inverse demand is given by: P (q1 ; : : : ; qn ) = a (q1 + : : : + qn ) :
For simplicity, assume that there are no product
Game Theory Problem Set 10
1. In the following game, nature .rst chooses one of two types of player 1 (in the .gure, the two types are denoted t1 and t2 ). Each type is chosen with equal probability.
Game Theory Problem Set 7
1. (The centipede game) In class we showed that in the unique subgame perfect equilibrium of the centipede game (see the .gure below) both players exit in every information s
Game Theory, Spring 2013 Midterm Exam Dino Gerardi April 9th You have two hours to complete this exam. Please answer the following three questions. Be sure to allocate your time in proportion to the p
Game Theory Problem Set 2
1. Find all Nash equilibria of the following normal-form games. a) L U 3; 4 D 0; 3 b) L R U 4; 5 3; 1 D 4; 0 0; 6 c) L C R U 6; 6 1; 2 3; 3 M 2; 1 4; 7 4; 3 D 3; 4 2; 5 3; 9