Chapter 8/Output, Price, and Prot: The Importance of Marginal Analysis
CHAPTER 8
OUTPUT, PRICE, AND PROFIT: THE
IMPORTANCE OF MARGINAL ANALYSIS
This chapter analyzes the output and price decisions of firms, using the concepts of marginal cost
CHAPTER OUTLINE
PRICE AND QUANTITY: ONE DECISION, NOT TWO
Firms face a demand curve that determines the relationship and pairings of price and quantity
demanded.
They can choose either price or quantity, but not both.
TOTAL PROFIT: KEEP YOUR EYE ON THE GOAL
Maximum total profit is the goal.
ECONOMIC PROFIT AND OPTIMAL DECISION MAKING
If economic profit is zero, the firm’s results are still satisfactory because price and output yield as
much profit as the best alternative.
Total, Average, and Marginal Revenue
TR = P × Q
Total, Average, and Marginal Cost
These were derived in Chapter 7.
Maximization of Total Profit
The central question is: What combination of output and price will yield the largest total
profit?
Chapter 8/Output, Price, and Prot: The Importance of Marginal Analysis
Profit Maximization: A Graphical Interpretation
Profits typically increase with output, then fall.
MARGINAL ANALYSIS AND MAXIMIZATION OF TOTAL PROFIT
Marginal profit is the slope of the total profit curve.
Profit is at a maximum when the marginal profit is zero.
Marginal Revenue and Marginal Cost: Guides to Optimization
Profit is at a maximum at the output level where marginal revenue is (approximately) equal
to marginal cost.
Finding the Optimal Price from Optimal Output
GENERALIZATION: THE LOGIC OF MARGINAL ANALYSIS AND
MAXIMIZATION
We have seen enough examples of marginal analysis to be able to generalize: when a
decision maker wishes to maximize net benefit (total benefit minus total cost), she should set
marginal benefit equal to marginal cost.
Application: Fixed Cost and the Profit-Maximizing Price
An increase in the fixed cost of a profit-maximizing producer does not change the optimal
Puzzle Resolved: Using Marginal Analysis to Unravel the Case of the “Unprofitable”
Calculator
The example from the text regarding a company losing money on each calculator sold can be
cleared up by using marginal analysis. Although the average cost of the calculator was
CONCLUSION: THE FUNDAMENTAL ROLE OF MARGINAL ANALYSIS
Any problem involving optimization can be illuminated with marginal analysis.
Chapter 8/Output, Price, and Prot: The Importance of Marginal Analysis
THEORY AND REALITY: A WORD OF CAUTION
Real business people seldom use the techniques described in the last four chapters, but these
theories can be used as models to understand and predict behavior.
APPENDIX: THE RELATIONSHIPS AMONG TOTAL, AVERAGE, AND
MARGINAL DATA
The three concepts are logically related:
Rule (1a) Average equals total divided by the number of units.
Rule (1b) Total equals average times the number of units.
Graphical Representation of Marginal and Average Curves
The aforementioned rules can be readily illustrated by graphing these curves on the same set
of axes.
MARGIN DEFINITIONS
Optimal Decision: a decision, which, among all the decisions that are actually possible, is best
for the decision maker.
Total Profit: total revenue − total cost.
Economic Profit: net earnings, in the accountant’s sense, minus the opportunity costs of capital
and of any other inputs supplied by the firm’s owners.
MAJOR IDEAS
1. A firm cannot simultaneously select both price and output.
2. The goal of a firm is to maximize profits.
Chapter 8/Output, Price, and Prot: The Importance of Marginal Analysis
ON TEACHING THE CHAPTER
In contrast to the authors of some other introductory texts, Baumol and Blinder fully discuss the
decision-making process of firms before they deal with different market structures. The
principles of profit-maximizing decisions are quite general: In the succeeding chapters they will
be applied to perfect competition and other market types.
A trap that students can fall into with this material is to treat MR = MC as a simple,
There is no substitute for working out problems of all types: verbal, graphical, and numerical.
This is a nonmathematical text, but if the students have had just a little calculus, it is
revealing to show them that the MR = MC criterion can be derived in just two lines of math. If Z
is profit, then Z = R – C. To maximize Z with respect to output, Q, set its first derivative equal to
zero:
PROBLEMS
1. Consider the total cost and total revenue schedules of two firms:
Gulp and Devour Shady Enterprise
Output TC TR TC TR
1 100 135 50 160
2 200 260 125 300
3 300 375 225 420
a) For each firm, and each level of output, calculate marginal cost, average cost,
marginal revenue, price, profit, and marginal profit.
Chapter 8/Output, Price, and Prot: The Importance of Marginal Analysis
b) On graph paper, plot all the variables in part a).
c) What is the profit-maximizing output in each case? Show that three criteria are
equivalent: marginal cost equals marginal revenue, maximum profit, and marginal
profit equals zero.
d) For each firm, describe the relationship between marginal cost and average cost, and
between marginal revenue and price. How do you explain those relationships?
Solution:
a)
Gulp and Devour
Output TC TR MC AC MR Price Profit MP
1 100 135 100 100 135 135 35 35
2 200 260 100 100 125 130 60 25
Shady Enterprise
Output TC TR MC AC MR Price Profit MP
1 50 160 50 50 160 160 110 110
2 125 300 75 62.5 140 150 175 65
b)
Chapter 8/Output, Price, and Prot: The Importance of Marginal Analysis
2. If output comes in indivisible chunks, it may not be possible to pick an output level such
that marginal revenue exactly equals marginal cost. In this case, what rule should a
profit-maximizing firm follow? Should it get as close as possible to MC = MR, without
worrying which is greater and which smaller? Should it always stop production while
MR still exceeds MC? Should it always proceed past the point of equality, to the first
level at which MC exceeds MR? Consider your answer to Problem 1 in answering this.
Solution: Profit can be maximized only at an output level at which marginal revenue is
Chapter 8/Output, Price, and Prot: The Importance of Marginal Analysis
3. Leopold Bus Company runs daily service between Bigcity and Tinytown. It calculates
that the average cost per trip (wages, gas, insurance, payments on loans, etc.) is $140.
Leopold sells the bus tickets for $5 each. The buses hold 40 people, but are usually just
three-quarters full. Leopold is considering offering half-rate tickets to students, on a
standby basis.
a) Will the sales of the standby tickets cover the average costs of the extra passengers?
b) Will the sales of the standby tickets cover the marginal costs of the extra passengers?
c) Should Leopold proceed with the plan? Why?
d) Can you think of circumstances under which it would be unwise to offer the standby
tickets?
Solution:
a) No, the half-rate tickets would cost $2.50. If the buses are full, the average cost would
be $3.50 ($140 ÷ 40).
4. Artsy T-Shirts sells 100,000 shirts a year, priced at $14 each. The company can produce
any number of shirts at a constant cost of $10 each. It is considering expanding its sales
by lowering the price of shirts to $12. What minimum increase in sales would be
necessary in order to justify this expansion?
DISCUSSION QUESTIONS
1. What, if anything, do these institutions maximize?
a) A consumer-owned, cooperative grocery store
b) The Department of Defense of the federal government
c) The Red Cross
d) The economics department of your college
e) The local public radio station
f) The household in which you grew up
Suggested Answer: This question is intended to make the students discuss the different
2. Think of a decision-making situation in which each of the institutions in Question 1 is
attempting to optimize or maximize. What in this institution corresponds to the
comparison of marginal cost and marginal revenue in a profit-maximizing firm?
3. Firms that are successful sometimes take their profitability as a signal that they should
expand. Why does this expansion sometimes get them in serious trouble?
Chapter 8/Output, Price, and Prot: The Importance of Marginal Analysis
Suggested Answer: If the marginal profit from increasing output by one unit is positive,
then output should be increased. If the marginal profit from increasing output by one unit
4. The decision-making analysis presented in this chapter rests heavily on the proposition
that firms equate marginal cost and marginal revenue. But accountants find it very
difficult if not impossible to calculate marginal cost and marginal revenue. Does this
mean that this kind of analysis is not very useful?
Suggested Answer: If one wants to make optimal decisions, marginal analysis should be
used in the planning calculations. This is true whether the decision applies to a business
5. How should a profit-maximizing retail firm think about how much money it should spend
on advertising?
Suggested Answer: The firm should apply marginal analysis in decision making.