The demand for a commodity is given by Q = B₁ + B₁P+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=% + v, where v denotes factors other than price that determine supply. Suppose that u and u both have a mean of zero, have variances o2 and 2, and are mutually uncorrelated. Solve the two simultaneous equations to show how Q and P depend on u and v.
The demand for a commodity is given by Q = B₁ + B₁P+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=% + v, where v denotes factors other than price that determine supply. Suppose that u and u both have a mean of zero, have variances o2 and 2, and are mutually uncorrelated. Solve the two simultaneous equations to show how Q and P depend on u and v.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:(a) The demand for a commodity is given by Q = Bo + B₁P+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 = % + v, where v denotes factors other than price that determine
supply. Suppose that u and u both have a mean of zero, have variances
o and o2, and are mutually uncorrelated.
Solve the two simultaneous equations to show how Q and P depend on
u and v.
(b) Derive the covariances between P and u in part (b). Is the least squares
estimator of slope coefficient 3₁ in the demand equation unbiased and
consistent?
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