Question

A monopolistic firm produces goods in a market where the demand function is P​ = 43​ − 0.3Q and the corresponding total cost function is TC=0.01Q^3-0.4Q^2+3Q

e) Calculate the price elasticity of demand at the profit maximizing Q​ (use ​ Q>0). Comment​ (elastic, inelastic or unit​ elastic?) on the calculated price elasitity of demand. Is the good is necssary or​ luxary?

​f) What would happen to the revenue of the firm if price goes​ down? [Use the vlaue of price elasticity of demand you obtained in part e to exlain​ this]

Answer 1

P = 43 - 0.3Q or Q = 143.33 - 3.33P

TC = 0.01Q^³ - 0.4Q^² + 3Q

TR = P * Q = 43Q - 0.3Q^²

MR (first derivative of TR with respect to Q) = 43 - 0.6Q

MC (first derivative of TR with respect to Q) = 0.03Q^² - 0.8Q + 3

E) Firm maximize their profit when MR = MC

43 - 0.6Q = 0.03Q^² - 0.8Q + 3

0.03Q^² - 0.2Q - 40 = 0

Q = 40

At Q = 40, P = 31

Elasticity of demand: (dQ / dP) * (P / Q)

(dQ / dP) = -3.33

Elasticity of demand = -3.33 * (31 / 40) = -2.58

As price and demand have negative relationship with each other, we can ignore the negative sign. Thus, elasticity of demand = 2.58. As elasticity of demand is more than 1, demand is elastic.

Good with elastic demand are luxury good.

F) If price goes down, consumer will raise their demand of the good more than fall in price which result in increase in net revenue.