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Unformatted text preview: INTERMEDIATE MICROECONOMICS ECON 3101, SECTION 005 MIDTERM EXAMINATION 2 - ANSWER KEY JACEK ROTHERT Please answer 4 out of 5 questions. Question 1. Market Demand [25 points] This question is about market demand and elasticities. (a) Let q ( p ) denote the market demand function, where p denotes the price of the good. Define price elasticity of demand in calculus form. What does it mean for the demand to be inelastic? (b) Suppose that an economy consists of 300 individuals. There are two goods in the economy: gasoline and dollars. Letting x denote gasoline and y denote dollars, each individual has the same utility over consumption of x and y given by: u ( x,y ) = 10 x 1 / 2 y 1 / 2 . Assuming that average income in the economy is 5, find the market demand function for good x (i.e. find a formula for the function q x = q x ( p x )). (c) Is the demand for gasoline (as calculated in part (b)) elastic or inelastic? Why? (d) Using your answer to part (b) derive an inverse demand function (i.e. rewrite your answer so that p is a function if q ). (e) Consider a single supplier of gasoline who faces the inverse demand function derived above. Write down the formula for that suppliers revenue as a function of quantity supplied. What is that suppliers marginal revenue? Answer (a) P p q q ( p ). Demand is inelastic if | P | < 1. (b) Powers in the utility add up to 1, so p x x = 1 2 m , m = 5 is income. So individual demand for x is then x = 5 2 p x . Market demand is the sum of individual demands, i.e. q x ( p x ) = 750 p x (c) Elasticity is =- 1, so demand is unit-elastic. (d) Inverse demand function is P ( q ) = 750 q (e) R ( q ) = qP ( q ) = q 750 q = 750, which is a constant. So marginal revenue is 0. 1 ECON 3101, Section 005 Midterm 2 Question 2. Technology [25 points] This question is about firms technology - production functions, marginal products and returns to scale....
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This note was uploaded on 02/07/2010 for the course ECON 101 taught by Professor Garton during the Spring '10 term at Edison College.
- Spring '10