Question

Long-Run Firm Supply. The retail market for unleaded gasoline is fiercely price competitive. Consider the situation faced by a typical gasoline retailer when the local market price for unleaded gasoline is $1.80 per gallon and total cost (TC) and marginal cost (MC) relations are TC = $40,000 + $1.64Q + $0.0000001 Q2 MC = ƏTC/2Q = $1.64 + $0.0000002Q and Q is gallons of gasoline. Total costs include a normal profit. A. Using the firm's marginal cost curve, calculate the profit-maximizing long-run supply curve for a typical retailer. B. Calculate the average total cost curve for a typical gasoline retailer, and verify that average total costs are less than price at the optimal activity level.

Answer 1

A. Long run profit maximizing equilibrium condition for perfectly competitive firm is P=MC given than P>ATC

P= MC

1.80= 1.64- 0.0000002Q

0.16/0.0000002=Q

Q= 800000

Q*= Equilibrium Quantity supplied= 8,00000

The long run supply curve is the part of MC above the price level of $1.80 .

Long run Supply curve=P= $1.64+0.0000002Q for P≥ 1.80

b. ATC=TC/Q= ($40,000 + $1.64Q + $0.0000001Q2)/Q

= $40,000/Q + $1.64 + $0.0000001Q

When Q= 800000

ATC=$40,000/800000 + $1.64+ $0.0000001(800000)

ATC= $1.77

Price= $1.80

Therefore at the optimal level of 800000, ATC is less than Price .