Question

Question 2: 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 =0.0103 – 0.4Q2 +3Q (a) What can you say about the fixed costs of this firm? (b What can you say about the variable costs of this firm? (c) Find the (non-zero) output for which average cost is equal to marginal cost, and explain the significance of this value. (d Find the output which maximises profit and use second order derivative to confirm that the profit is maximized at one of the two quantities (Q). 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

TC= 0.01Q^3 - 0.4Q^2 + 3Q

Answer a) There are no fixed costs because in the total cost function there is no constant , the entire Total cost is a function of Q and there is no independent number.

Answer b) The total cost function is itself the variable cost function . Variable cost is that cost which depends on the level of output Q. In this case the entire Total cost function is dependent on Q so it represents variable costs of the firm

Date: Page No. क TC = 0.010* -0.400* +34 A(= IC 0 Als 0.0102-0.49 +3 IMC = OTC MC = 0.030 - 0.89 +3 AL=MC 0.010-0 444$ = 0.030-0.80 +7 0.020² -0.40 =0 910029 -0.4) = 0 Oto 0.020-0.4=0 - 10=20 d) P = 43-0.39 At profit maxinailation MR=MC MR = OTR TR= (43 -0.399 00 TR = PXQ IMR = 43 -0.60 IMC 0.030² -0.80 +3 .

Page No MR=MC 43-0,60 = 0.03 0–0-80 +3 → 0.034-0.20-40 = 0 (940) (0+33.33) = 0 Q +33.330=40 P= 43-0-39 = 32 Profit= TR-FC T = PXQ - TC (40) A:- 34x40-F2-011400-4(40)°+3(40)] Masticity at Q=40 l P=31 ed = P x AO ф де AQ AP FP-43-0.30 = Q=43 Q] 0.3 03 - 2.58 40 ed - 3181 0.3 Demand is elastic sinu ed>1 f it is luxury

Answer d (continued) Second order condition for profit maximisation is that slope of MC> Slope of MR

MC= 0.03Q^2- 0.8Q +3

slope of MC =∆MC/∆Q= 0.06Q-0.8

MR= 43-0.6Q

Slope of MR= ∆MR/∆Q= -0.6

at profit maximisation Quantity, Q= 40

Slope of MC= 0.06Q- 0.8 = 1.6

Slope of MR= -0.6

slope of MC> Slope of MR , so profits are maximised.

Answer f) Since the price elasticity of demand is greater than 1 according to total revenue approach there exist an inverse relationship between price and total revenue when elasticity is greater than 1 . So, if price goes down Revenue goes up