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CHAPTER 8
Profit Maximization and Supply
A. Summary
Chapter 8 examines models of firms’ output decisions. Primary emphasis is
placed on the consequences of the profit-maximization hypothesis. The
chapter begins by analyzing the marginal decisions that accompany the prof-
it-maximization hypothesis. It is at this point that marginal revenue is intro-
B. Lecture and Discussion Suggestions
Some students have difficulty with the marginal revenue concept and there-
fore that concept should be featured in lectures on Chapter 8. One way to ap-
proach the subject is to repeat that the demand curve is an “average revenue”
curve with the MR curve “marginal” to it. This approach creates an analogy
between revenue and cost curves that may otherwise escape many students.
Repeating the numerical example based on a linear demand curve can be es-
pecially helpful in this regard.
Empirical material might again be appropriate for filling out lectures on
Chapter 8. “Incremental” thinking on the part of firm managers could be
C. Glossary Entries in the Chapter
• Firm’s Short-run Supply Curve
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SOLUTIONS TO CHAPTER 8 PROBLEMS
8.1 a. Set P = MC, 20 = .2q + 10. q = 50.
b. Maximum Profits = TR – TC = (50 20) –
[.1(50)2 + 10(50) + 50] = 1000 – 800 = 200.
c.
8.2 a. This charge is a fixed cost of $100 per week. Will lower profits to $100, but
will not affect output.
d. Net revenue per acre is now 18.
P = MC yields 18 = .2q + 10
8.3
a. Assume that the demand curve has the linear form
P c dQ=−
. Then mar-
b. Total spending is maximized when MR = 0.
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c. If demand were inelastic raising price would increase spending, if demand were
8.4 a. The graph shows that the demand curve has a convex shape, whereas the MC
curve is linear.
Here the demand curve has a constant elasticity of –2. Hence
This is also shown in the graph. For profit-maximization need to show MR in
terms of q, not P.
Setting MR=MC yields
8.5 a. Let
AC MC c==
and suppose demand is given by
.Q a bP=−
The firm
should now charge
Pc=
and total quantity sold will be
Q a bc=−
.
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d. It should sell just one unit. Price would be
1a
b
−
and unit profits would be
8.6 a.
1 0.2 5 5P SMC q q P= = + = −
b. Variable costs are
2
0.1qq+
Average variable costs are
1 0.1q+
. Hence SMC is always greater than aver-
age variable cost. There is no shutdown price.
8.7 a. Beth’s supply function is q = 5P – 50.
If P = 15, q = 25.
d.
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Since high profits are associated with the high P, q combination, it’s more
profitable to let price fluctuate.
8.8 a. With a flat grant of $200 per week, Beth will end up with a total of $400 per
week. The grant itself will not change the profit maximizing choice from Prob-
lem 9.1.
With a subsidy of $4 per acre, net price rises to $24 per acre. Now profit max-
b. With q = 70, at $4 per acre, the subsidy will cost the government $280 per
8.9 a. STC = vK + wL
b. Use P = MC.
20 = .1q so q = 200.
L = q2/100 so L = 400.
c. If P = 15, P = MC implies 15 = .1q or q = 150, L = 225.
d. Cost will be 175 to reduce L from 400 to 225. With q = 150,
8.10 a. Using the profit-maximizing condition that P = MC yields q = 5 on Wednes-
days and q = 10 on Saturdays.
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c. With P = 15, She should produce 7.5 each day. Profits on each day will be