Answer to Question #291733 in Microeconomics for jay

Question

You are the manager of a firm that receives revenues of $40,000 per year from product X and $90,000 per year from product Y. The own price elasticity of demand for product X is -1.5, and the cross-price elasticity of demand between product Y and X is -1.8. How much will your firm’s total revenues (revenues from both products) change if you increase the price of good X by 2 percent? b. An individual consumes three goods, Q1, Q2, and Q3. The proportions of total Income devoted to the consumption of Q1 and Q2 are 75 and 15%, respectively. The income elasticities for Q1 and Q2 are 𝜀1,𝑀 = 0.75 and 𝜀2,𝑀 = −1.5, respectively. How would you classify the three goods? (5mks) c. Suppose that a firm’s marginal cost of production is constant at shs.25. Suppose further that the price elasticity of demand ( 𝜀𝑃 ) for the firm’s product is -5.0. i) Using optimal price formula what price should the firm charge for its product. ii) Suppose that 𝜀𝑃 = −0.5.What price should the firm charge for its product? Comment on this price.

Answer 1

R=$40000 from X

R=$90000 from Y

$E_{px}=-1.5$

$E_{px-py}=-1.8$

2% increase in X =40800

Since the good is an inelastic good, when price increases for inelastic good, the demand for that good remains the same hence an increase in the total revenue. Therefore, there will an increase in the revenue obtained from good X.

b)$Q1=75\%, Q2=15\% , Q3=10\%$

$E_1=0.75, E_2=-1.5, E_3=0.1$

From the information above, one can classify the goods as

$Q1-$ Normal good

$Q2-$ Inelastic good

$Q3-$ Normal good

c)Marginal cost,$C$ = shs.$25$

$E_P=-5.0, P=?$ , it is highly elastic hence the optimal price will approach the marginal cost of production.

Optimal price, $P=\frac{C}{dQ/dP}$

$=\frac{0.25}{-5}=-0.05$

ii)$if E_p=-0.5, P=\frac{0.25}{-0.5}=-0.5$

since it is inelastic, the price should be set higher than the marginal cost of production.