Question

Q3. The general linear demand for good X is estimated to be Q = 25,000 - 80P-0.25M + 72P (6 Pts) where P is the price of good X, M is average income of consumers who buy good X, and P, is the price of related good R. The values of P, M, and P, are expected to be $100, $35,000, and $60, respectively. Use these values at this point on demand to make the following computations. a. Compute the quantity of good X demanded for the given values of P, M, and P. b. For the quantity in part a, calculate the point price elasticity of demand. At this point on the demand, is demand elastic, inelastic, or unitary elastic? How would decreasing the price of X affect total revenue? Explain. c. Calculate the income elasticity of demand EM. Is good X normal or inferior? Explain how a 3.5 percent decrease in income would affect demand for X, all other factors affecting the demand for X remaining the same. d. Calculate the cross-price elasticity EXR. Are the goods X and R substitutes or complements? Explain how a 6 percent increase in the price of related good R would affect demand for X, all other factors affecting the demand for X remaining the same? e. Find the equations for demand, inverse demand and marginal revenue for the given values of P, M, and PR. At the point on demand in parts a and b, is marginal revenue positive, negative or zero? Is this as you expected? Explain why or why not.

Answer 1

A)Qd=25,000-80p+0.25M+72Pr

Qd=25,000-80*100+0.25*35,000+72*60=30,070

B) price Elasticity={∆Qd/∆p)*p/Q=(-80)*(100/30,070)=-0.266

Demand is inelastic. So Decrease in price will increase in Quantity demanded lower percentage than Decrease in price . So as a result total revenue will decrease.

C) Income Elasticity=(∆Qd/∆M)*M/Qd=0.25*35,000/30,070=0.29

Positive income tells that good is normal

a 3.5% decrease in income will decrease demand=3.5*0.29=1.015%

D) cross Elasticity={∆Qd/∆pr)*pr/Qd=72*60/30,070=0.143

Positive cross elasticity tells that goods are substitues

6% Increase in price of pr will increase demand=6*0.143=0.858%