Question

The demand equation for a product sold by a competitive firm in UAE is given by the following equation and firms sell their product at 100 AED: Q = 500 – 10P The total cost equation of the firm is given by the following equation: TC = 80 + 20Q + 0.2Q2 a) Derive the inverse demand function. (1 Point) b) What is the firm’s MC function? (1/2 Point) c) What is the firm’s MR function? (1/2 Point) d) What is the firm’s profit maximizing level of output? (1 Point) e) What is the firm’s profit maximizing level of price? (1/2 Point) f) How much profit will the firm make? (1 Point) g) Is the firm in the short run or long run? (1/2 Point

Answer 1

Q)

(a) We have, Q = 500 - 10P

=> 10P = 500 - Q

=> P = 50 - Q/10

(b) MC = dTC/dQ

= 20 + 0.4Q

(c) MR = dTR/dQ

TR = PQ = (50-Q/10)*Q

=> MR = 50 - Q/5 = 50 - 0.2Q

(d) At profit max, we have, P = MC

=> 50 - 0.1Q = 20 + 0.4Q

=> 0.5Q = 30

=> Q = 30/0.5 = 60

(e) putting the value of Q=60 in the inverse demand function we get:

P = 50 - 60/10 = 50 - 6 = 44

(f) profits = 60*44 - 80 - 20*60 - 0.2*60*60 = 640

(g) Since a competitive firm can make profits only in the short run, the firm is currently in the short run.