Output, Profit, Fixed Costs and Perfect Competition

1. Consider a firm operating in a perfectly competitive market.
a. How much output will this firm produce ?
b. How much profit (or loss) is this firm making in the short run ?
c. What is the value of average fixed cost at this profit-maximizing output?
d. At what output will average variable cost be minimized?
e. What is the value of average variable cost at its minimum point?
f. If price falls to $5, how much out put will this firm produce?

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...h output will this firm produce?
b. What will the firm's price be at this output?
c. What will the firm's revenue be at this output?
d. Is the firm's price equal to its long-run average cost at this output?

Solution:

1. P = $10
STC=0.5q3 - 3q2 + 10q + 6 .....................(1)
SMC= 1.5q2 - 6q + 10 .....................(2)

a) The short-run profit-maximizing condition in the Perfectly Competitive Market,
P = SMC = SMR
So, we follow, 10 = 1.5q2 - 6q +10
 1.5q2 - 6q = 10 - 10 = 0
 1.5q(q - 4)= 0
 either 1.5q = 0 or (q - 4) =0
Here, as 1.5q or q cannot be equal to 0, we take (q - 4) = 0 or q = 4.
So, at P=10, in equilibrium, the firm will produce 4 units of output.

b) As we know that profit Π = STR - STC
STR = P X q = 10 X 4 = 40
And, putting q=4 in equation (1), STC = (0.5)(4)3 - 3(4)2 + 10(4) +6 = 30

So, the short-run profit = 40 - 30 =10.

c) As we know that STC = SVC + SFC,
So, in equation (1), the SFC = 6 , because FC is independent of q
So, at this profit-maximizing output level, the AFC =6/4 = 1.5

d) As we know that MC cuts VC at its minimum point. That means, the AVC will be minimized at which MC = AVC. And, here, in equilibrium, P = MC = 10
From equation (1), SVC = STC - SFC = 0.5q3 - 3q2 + 10q
And, AVC = SVC/q ...