The demand for a commodity is given by Q = β0 + β1P + u, where Q denotes quantity, P denotes price, and u denotes factors other than price that determine demand. Supply for the commodity is given by Q = g0 + g1P + v, where v denotes factors other than price that determine supply. Suppose u and v both have a mean of 0, have standard deviations su and sv, respectively, and are mutually uncorrelated. a) Solve the two simultaneous equations to show how Q and P depend on u and v. b) Derive the means of P and Q. c) Derive the variance of P, the variance of Q, and the covariance between Q and P.
The demand for a commodity is given by Q = β0 + β1P + u, where Q denotes quantity, P denotes price, and u denotes factors other than price that determine demand. Supply for the commodity is given by Q = g0 + g1P + v, where v denotes factors other than price that determine supply. Suppose u and v both have a mean of 0, have standard deviations su and sv, respectively, and are mutually uncorrelated. a) Solve the two simultaneous equations to show how Q and P depend on u and v. b) Derive the means of P and Q. c) Derive the variance of P, the variance of Q, and the covariance between Q and P.
Managerial Economics: A Problem Solving Approach
5th Edition
ISBN:9781337106665
Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Publisher:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Chapter17: Making Decisions With Uncertainty
Section: Chapter Questions
Problem 6MC
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Part 1. The demand for a commodity is given by Q = β0 + β1P + u, where Q denotes quantity, P denotes price, and u denotes factors other than price that determine demand. Supply for the commodity is given by Q = g0 + g1P + v, where v denotes factors other than price that determine supply. Suppose u and v both have a mean of 0, have standard deviations su and sv, respectively, and are mutually uncorrelated.
a) Solve the two simultaneous equations to show how Q and P depend on u and v.
b) Derive the means of P and Q.
c) Derive the variance of P, the variance of Q, and the covariance between Q and P.
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