Consider a firm in a perfectly competitive market that can sell all units of output at a constant
price of $32. The firm has a fairly old plant, and the total fixed cost and total variable cost at
various units of output are given in columns (2) and (3) below. The firm has the chance to invest
in a new plant. If it does, the total cost of production at various levels of output is given in
column (5) below. However, if the firm scraps the old plant, the salvage value is likely to be
zero, or in, other words, the fixed costs of the old plant are sunk.
Given the data below, compute the optimal output and profits of the firm if a) it continues to use
the old plant and b) builds and produces in the new plant.
Use your answer to explain why it might or might not advisable for the firm to invest in and
build the new plant.
Cost Marginal Long Run
Cost Cost Total Cost
Quantity Old Plant Old Plant Old Plant New Plant
1 200 35 35 65
2 200 44 9 80
3 200 60 16 96
4 200 80 20 128
5 200 106 36 180
6 200 138 32 240
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Because the old plant is sunk, the optimal quantity output if the firm continue to use the old plant is when the marginal cost equals the marginal revenue which is a price under a perfectly competitive market. It follows that the firm will choose to produce Q=6 and make a total revenue of 6 × 32 = $192 and it costs $338 to produce Q=6 and makes -$146 profit. Although the firm makes a negative profit, it still covers the part of the fixed cost...