The general linear demand function for good X is estimated to be Q=250,000-500P-

Question

The general linear demand function for good X is estimated to be Q=250,000-500P-1.5M-240Pr

Where Q = the quantity demanded of good X, P = the price of good X, M = the average income of consumers, and Pr is the price of a related good R. Suppose that P=200 M = 60,000 and Pr=100

(a) Obtain the demand function (Q as a function of P) for good X and the quantity demanded of good X.

(b) Calculate the point elasticity of demand of good X. Is the demand elastic, unitary elastic or inelastic? How would increasing P affect total revenue?

(c) Calculate the income elasticity of demand of good X. Is good X a normal good or an inferior good?

(d) Calculate the cross-price elasticity of demand of good X. Are good X and R substitutes or complements?

Explanation / Answer

Q = 250,000 - 500P - 1.5M - 240PR

Plugging in given values,

Q = 250,000 - (500 x 200) - (1.5 x 60,000) - (240 x 100) = 250,000 - 100,000 - 90,000 - 24,000 = 36,000

(a)

Q = 250,000 - 500P - 1.5M - 240PR

Q = 250,000 - 500P- (1.5 x 60,000) - (240 x 100) = 250,000 - 500P - 90,000 - 24,000

Q = 136,000 - 500P [Demand function]

(b)

Elasticity of demand = (dQ/dP) x (P/Q) = - 500 x (200/36,000) = - 2.78

Since absolute value of elasticity is higher than 1, demand is elastic.

(c)

Income elasticity = (dQ/dM) x (M/Q) = - 1.5 x (60,000/36,000) = - 2.5

Since income elasticity is negative, this is an inferior good.

(d)

Cross-price elasticity = (dQ/dPR) x (PR/Q) = - 240 x (100/36,000) = - 0.67

Since cross price elasticity is negative, X and R are complements.

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