Answers to Odd-Numbered Problems 11- a. We are given that MC $20,000, and from the price equation, we
derive MR 30,000 .2Q. Setting MR MC implies Q 50,000,
confirming that GM’s current output level is profit maximizing.
b. The outside sales option means that GM faces an opportunity cost.
Every engine sold to the SUV manufacturer generates additional
contribution of $2,000. GM should not only employ the unused
capacity to produce engines for external sale, it should also cut back
somewhat its production of light trucks. The effective MC per truck is
now $20,000 $2,000 (where the latter is the opportunity cost per
engine.) The shift upward in MC implies a lower optimal output level
(40,000 engines to be exact).
c. Fixed costs should not be mixed with variable costs in determining
output and price decisions. Removing the allocated fixed cost means
taking out 160,000,000/40,000 $4,000 per unit. Thus, the true
marginal cost per unit is $22,000 $4,000 $18,000. Note that the
actual MC in the West Coast factory is lowerthan the MC in the
Michigan plants. Thus, GM should expand its West Coast output (to
60,000 units to be exact). - a. C 500 5Q^2. Minimum average cost occurs at the quantity Q such
that MC AC. We know that MC 10Q and AC 500/Q 5Q.
Setting these equal implies 10Q 500/Q 5Q. Collecting terms, we
find that 5Q^2 500 or Qmin10. At this output, minimum average
cost equals $100.
b. Setting MR MC implies 600 10Q 10Q. Therefore, Q 30; in
turn, P 600 (5)(30) $450, and 13,500 5,000 $8,500.
c. If either MC differed from MR, the firm could increase its profit by
redirecting output. Setting MRMC 1 MC 2 implies 600 10Q
10(Q/2). Therefore, Q 40. Each plant produces 20 units at a cost
of $2,500 (from the original cost function). Finally, we find P $400,
and 16,000 5,000 $11,000.
d. If the firm can use as many plants as it likes, it enjoys constant returns
to scale. It should set the number of plants so that each is producing
10 units (where MC min AC $100). In short, $100 is the relevant
long-run marginal cost. Setting MR MC implies 600 10Q 100.
Therefore, Q 50. In turn, P $350 and (350 100)(50)
$12,500. The number of plants is 50/10 5.
Chapter 7
- a. According to the “law” of supply and demand, the existence of a large
body of Picasso’s artwork will tend to lower the value of any individual
piece of work.
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