Question 3: Firm Supply Curve Suppose that the short-run cost function for a fir
ID: 1204817 • Letter: Q
Question
Question 3: Firm Supply Curve
Suppose that the short-run cost function for a firm is TC (q) = 0.1q3 2q2 + 15q + 10.
1. Calculate the average cost and marginal cost.
2. From the firm profit maximization behavior, solve the firm’s short run supply curve.
3. Now consider the long run equilibrium in a perfectly competitive market. What are the
conditions for the long run equilibrium to hold?
Explanation / Answer
1. Marginal Cost: It is the first derivative of the total cost with respect to the output. Average total cost: It is the total cost divided by the number of units produced. For the given monopolistically competitive firm the total cost is given by:
TC = 0.1q3 2q2+ 15q + 10.
AC = TC/q
0.1q2 2q + 15 + 10/q
MC = dTC/dq
= 0.3q2 4q + 15
2.) The rising portion of the marginal cost curve (MC) just as soon as it cuts the average cost AC from below is the firm’s short run supply curve. Find the individual firm’s supply curve by finding the minimum of AVC which is TVC/q:
Minimum of AVC can be find by setting its derivative equal to zero
dAVC/dq = 0
0.2q – 2 = 0
0.2q = 2
q = 10
At q = 10, AVC is 10 – 20 + 15 = 5
Hence, MC cuts AVC from below at q = 10
To check the validity of this point, check if MC is 5:
MC (at q = 10) = 30 – 40 + 15 = 5
Hence, the short run supply curve for a firm is:
P = 0.3q2 4q + 15, q>20
3) In the long run, a typical firm in perfectly competitive market operates at the minimum level of AC where LRAC = LRMC where there are no fixed costs.
This gives q = 10.45
Hence, in the long run, the profit maximizing quantity is 10.45 units
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