Question

^{Suppose a perfectly competitive firm has the following total cost function for the short run (STC):}        

^{STC = 5,000 + 150Q – 12Q2 + (1/3)Q3.}

^{a.   Determine its profit-maximizing or loss-minimizing output for the short run, given that the market price of its product is $330 per unit.}

^{b.   What will be the firm’s short-run profit or loss?}

^{c.   Now disregard the preceding cost function, and suppose its long-run total cost (LTC) is}        

^{LTC = 660Q – 9Q2 + 0.05Q3}

^{i.   Write an equation for long-run average cost.}

^{ii.   Indicate the firm’s long-run price, quantity sold, and profit, assuming the industry is in long-run equilibrium.}

Answer 1

A. Given

Short run total cost=5000+150Q-12Q²+Q³/3

Price is given at 330.

Now, we know that profit will be maximized where Marginal Cost=Marginal Revenue.

Marginal Revenue is 330 as per extra output will bring revenue equal to its price.

MC can be calculated by differentiating the given total cost curve. So,

MC=150-24Q+Q²

Equating MC and MR

330=150-24Q+Q²

Solving for Q, we get

Q=30. This is the profit maximizing output.

B. At this output, the firm's total revenue is

30*330=9900.

Total cost is 5000+150*30-12*30²+30³/3=7700

Total profit=Revenue-Total cost

Total profit=9900-7700=2200

C. The new long run cost function is 660Q-9Q²+.05Q³

Since Average Cost=Total Cost/Quantity

So,

average cost=(660Q-9Q²+.05Q³)/Q

=660-9Q+.05Q²

In the long run, the average total cost is minimized. And average total cost will be minimized when its derivative will be zero. So,

-9+.1Q=0

Q=90 is the long run quantity.

The price in the long run equals average cost. So,

P=660-9*90+.05*90²

P=255 is the long run price.

Since price is equal to average cost, there will be no profit.