Question

The market research Department of Paradox Enterprises has determined that the demand for fingolds is 𝑄 = 1,000 − 5𝑃 + 0.05𝑀 − 50𝑃𝑧 where P is the price of glibdips, M is income, and 𝑃𝑧 is the price of ballzacks. Suppose that P = $5, M = $20,000, and 𝑃𝑧 = $15. a. Calculate the price elasticity of demand for fingolds (3mks) b. Is the firm maximizing its total revenue at P = $5. If not, what price should it charge? (3mks) c. At P = $5, compute the income elasticity of demand for fingolds(3mks) d. At P = $5, cross-price elasticity of demand for fingolds. 

Answer 1

$Q=1000-5P+0.05M-50P_z$

$P$ =$5

$M$ =$20000

$P_z=$ $15

$1000-5(5)+0.05(20000)-50(15)$

$1000-25+1000-750=1225$

a)$E_p=\frac{\Delta Q}{\Delta P} \times \frac{P}{Q}$

$-5\times\frac{5}{1225}=-0.02$ , inelastic.

b) $R=Q\times P=1225\times 5=6125$

Yes, the firm is maximizing its total revenue at this price.

c)$E_i=\frac{dQ}{dI}\times\frac{I}{X}=0.05\times\frac{20000}{5}=200$

d)$E_cp=\frac{dQ}{dP}\times \frac{P}{Q}=-50\times\frac{5}{1225}=-0.2$ , inelastic.