In: Economics
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
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.