Page 152 - DECO405_MANAGERIAL_ECONOMICS

Unit 9: Market Structure – Perfect Competition

Notes
Figure 9.7

The condition for the long run equilibrium of the firm is that the marginal cost be equal to
the price and to the long run average cost.
LMC = AC = P

At equilibrium the short run marginal cost is equal to the long run marginal cost and the short
run average cost is equal to the long run average cost. Thus, given the above equilibrium
condition, we have
SMC = LMC = LAC = SAC P = MR
This implies that at the minimum point of the LAC the corresponding (short run) plant is
worked at its optimal capacity so that minimum of LAC and SAC coincide. On the other point,
the LMC cuts the LAC at its minimum point and the SMC cuts the SAC at its minimum.

Example: For a firm operating in a perfectly competitive market, the following data are
available
Price P = AR = MR = 20/- unit
2
Total cost function is C = 8 + 17Q – 4Q + Q 3
Let us find out the profit maximising output and the maximum profit.
Marginal cost will be available if the first derivative of the total cost function is obtained. Thus,
d(C)
MC = = 17–8Q+3Q 2
dQ
Maximum profit will be earned when

MC and MR are equal:
20 = 17–8Q+3Q 2
Solving this equation gives two values for Q as –1/3 and 3. Obviously, negative output cannot be
produced; hence at Q = 3, the firm will maximise profits. Total revenue will be 60 and total cost
50. The maximum profit at the output of 3 units is 10.

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