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Unformatted text preview: Consumers Theory February 8, 2009 1 Problem Set 1: Solution Exercise 2.6 The data are P Q 4 30 4 . 5 27 5 24 Its pretty easy to see that these points lie above a line with slope equal to6: Q P = 27 30 4 . 5 4 = 6 = 24 27 5 4 . 5 In order to identify a line you need just 2 parameters: the slope and the vertical intercept. So, if the equation of a generic demand is Q = a bP and we already know that b = 6, then we can find a by just plugging in any one of the three points 30 = a 6(4) = a = 54 The direct demand is Q = 54 6 P , and the inverse demand is P = 9 1 / 6 Q Now, in order to find the elasticity we can use the formula for linear de mands D = b P Q so P Q 4 30 4 / 5 4 . 5 27 1 5 24 5 / 4 1 Exercise 2.7 The existence of a shortage implies that the official price, P is below the equilibrium one. At this price, therefore, the quantity de manded is greater than the quantity supplied. Black market tickets have a price above the official one: the scalping price cleans the market. Increasing penalties for scalping has the effect of increasing costs for black market traders: as a consequence their supply function shrinks. Their new prices are higher than before, thus reducing the amount of customers inter ested in the transaction. Exercise 2.16 The economic system is represented by the following equa tions Q d = 90 2 P 2 T Q s = 9 + 5 P 2 . 5 R Equilibrium is found at the intersection of demand and supply: Q d = Q s . Therefore Q * = 46 P * = 12 For the price elasticities, use the formulas = slope P * Q * . The slope of the demand function is 2 (the coefficient in front of P ), and the slope of the supply is +5. Therefore the elasticities are d = 2 12 46 = 12 23 s = 5 12 46 = 30 23 The cross price elasticity of gold balls with respect to the price of titanium is Q,T = Q T T Q = Q T T Q now, the first term of the expression is the partial derivative of Q with respect to T : 2 (since T enters linearly it is just the coefficient in front of T in the demand function). Therefore Q,T = 2 10 46 = 10 23 Exercise 2.26 1. January: the economic system is defined by Q s = 30 P 30 Q d = 120 2 P 2 Q P 6 120 D Ja n D M a r 7 P^D Jan = 6  Q/20 P^d Mar = 7  Q/20 P^s Jan = 1 + Q/30 1 2 P^s Feb = 2 + Q/30 A B C 48 60 Equating demand and supply we get P Jan = 3 Q Jan = 60 2. February: the economic system is defined by Q s = 30 P 60 Equating demand and supply we get P Feb = 18 5 Q Feb = 48 3. March: the economic system is defined by Q d = 140 20 P Equating demand and supply we get P Mar = 4 Q Mar = 60 2 Utility Functions Utility functions are representation of the level of satisfaction that a con sumer achieves by purchasing certain quantities of several items. They 3 are functions (possibly multivariate) that take as arguments quantities con sumed of different items. Lets consider the case of an economy with just 2 goods that we label x, y . The the utility for each individual is given by the function U ( x, y...
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This note was uploaded on 05/09/2009 for the course ECON 200 taught by Professor Junnie during the Spring '08 term at NYU.
 Spring '08
 JunNie

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