Question

The general linear demand for good X is estimated to be
Q = 190,000 - 500P +0.8M - 200PR
where P is the price of good X, M is average income of consumers who buy good X, and PR is the price of related good R. The values of P, M and PR are expected to be $200, $50,000, and $250, respectively. Use these values at this point on demand to make the following computations.
18. What is the quantity good X demanded for the given value of P, M, and PR? A. 50,000 B. 80,000 C. 10,000 D. 12,000

19. What is the price elasticity of demand? A. 0.5 B. -0.625 C. 0.8 D. -1.25
20. What is the income elasticity of demand? A. 0.5 B. -0.625 C. 0.8 D. -1.25
21. Which of the following statements is correct? A. Goods X and R are complements. B. Good X is an inferior good. C. If good R’s price becomes lower, the demand for good X will be lower. D. If the consumer income increases, the demand for good X will decrease.

22. Consider that the price of related good R decreases by 5 percent. How it would affect the demand for X, all other factors affecting the demand for X remaining the same? A. The demand for X would decrease by 0.125 percent. B. The demand for X would increase by 0.625 percent. C. The demand for X would decrease by 0.625 percent. D. The demand for X would increase by 3.125 percent.

Answer 1

(18) (B)

Q = 190,000 - (500 x 200) + (0.8 x 50,000) - (200 x 250)

Q = 190,000 - 100,000 + 40,000 - 50,000

Q = 80,000

(19) (D)

Price Elasticity of demand = (Q/P) x (P/Q) = -500 x (200 / 80,000) = -1.25

(20) (A)

Income elasticity = (Q/M) x (M/Q) = 0.8 x (50,000 / 80,000) = 0.5

(21) (A)

Since coefficient of PR is negative, a fall (rise) in price of related good will increase (decrease) the demand for the good in question, so these are complements.

(22) (D)

Cross-price elasticity = (Q/PR) x (PR/Q) = -200 x (250 / 80,000) = -0.625

So, 1% decrease in PR will increase demand by 0.625%, therefore 5% decrease in PR will increase demand by (5 x 0.625%) = 3.125%.