Suppose a firm produces its output in two different plants. Production costs at plant 1 are given by C1 = 4(Q1)2, where Q1 is the amount of production at plant 1. The production costs at plant 2 are given by C2 = 2(Q2)2, where Q2 is the amount of production at plant 2. The corresponding marginal costs at each plant are MC1 = 8Q1 and MC2 = 4Q2. If the firm produces a total of 24 units of output, how much output should it produce at each plant?
What will be an ideal response?
In order to minimize costs, the marginal costs must be the same at both plants. Since total output is 24 units, Q2 = 24 - Q1. Substituting this into the expression for MC2 and equating the marginal costs for both plants yields:
8Q1 = 96 - 4Q1
12Q1 = 96
Q1 = 8
So Q2 = 16.
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