Question

Assume a firm with the following

Demand Curve:         P = 10,004 – Q
Total Cost Curve:       TC = 15,000,000 + 4Q + Q2

   •   What is the Profit-Maximizing Price and Quantity this firm will use? Show work
   •   Is the firm making a profit or a loss? Explain why
   •   Should the firm stay in business or quit immediately? Explain why

Answer 1

P = 10004 - Q

TR = PQ  

TR = (10004 - Q)Q

TR = 10004Q - Q²  

dTR/dQ = MR = 10004 - 2Q

MR = 10004 - 2Q

TC = 15,000,000 + 4Q + Q²

dTC/dQ = 4 + 2Q

MC = 4 + 2Q

Profit maximising condition

MR = MC

10004 - 2Q = 4 + 2Q

10004 - 4 = 2Q + 2Q

10000 = 4Q

Q = 10000/4  

Q = 2500

P = 10004 - Q

P = 10004 - 2500

P = 7504

Thus, profit maximising quantity is Q = 2500 and price is P = 7504

profit   = PQ - TC

= PQ - 15,000,000 - 4Q - Q²

= 7504(2500) - 15,000,000 - 4(2500) - (2500)²

= 18,760,000 - 15,000,000 - 10,000 - 6,250,000

= 18,760,000 - 21,260,000

= - 2,500,000

Therefore the firm is making a loss of 2,500,000

TC =  15,000,000 +  4Q + Q²

TVC = 4Q + Q²

AVC = TVC/Q

AVC = (4Q + Q² )/Q

AVC = 4 + Q

At profit maximising quantity Q = 2500 average variale cost is

AVC = 4 + 2500  

AVC = 2504

Since P > AVC which means  the firm is able to cover all its variale costs and have some revenue left over for paying a proportion of its fixed costs.Hence the firm will continue or stay in business.