1. Output, Price, and Profit: The Importance of Marginal Analysis6
Output, Price, and Profit: The Importance of Marginal Analysis

2. Outline Price and Quantity: One Decision, Not Two
Total Profit: Keep your Eye on the Goal
Marginal Analysis and Maximization of Total Profit
Generalization: The Logic of Marginal Analysis and Maximization
Copyright © 2006 South-Western/Thomson Learning. All rights reserved.

3. Puzzle: Making Profit by Selling Below Cost
Legal battle between Co. A and B who make calculators.
B accused A of selling 10M for $12 each, which A knew was below cost.
B claimed A was trying to drive B out of business.
When A’s cost records were shown in court, looked like B was right.
Direct costs of materials, L, and ads = $10.30/unit
Indirect costs of admin. and R& D = $4.25 /unit
So P of $12 did not cover $14.55 cost/unit.

4. Puzzle: Making Profit by Selling Below Cost
Economists defending A showed that its calculator sales were profitable, so it wasn’t just trying to destroy B.
After discussing profit-max output decisions, you’ll see why A was profitable.

5. Price and Quantity: One Decision, Not Two
Critical decision -when Apple decides how many ipods to produce and P it will charge.
P affects how consumers respond and Q affects K and L costs.
When firms chose P and Q to max profits → they can pick only one –P or Q.
Chose P → customers decide Q
Chose Q → market determines P at which this Q can be sold

6. FIGURE 1. Demand Curve for Flo’s Poultry Meat
Flo faces a local D curve.
If she picks P = $19 → Qd = 1.
If she picks Q = 9 → P = $11 to find required # of customers. A
$19
Price per package B
$11 D 1 9
Quantity of Chicken (20 lb-packages per week)

7. Price and Quantity: One Decision, Not Two
Each pt on D curve corresponds to a (P,Q) pair. A firm can pick 1 pair, but it can never pick P from 1 pt on D and a different Q from another pt on D.
Economists assume that firms pick (P,Q) pair that maximizes profits.

8. Total Profit: Keep Your Eye on the Goal
Total profit (or economic profit) = TR – TC (including opportunity cost)
Opportunity costs include any K or L supplied by the firm’s owners.
Economic profit = Accounting profit – opportunity cost.
E.g., if a talented attorney, gives up her salary of $120,000 to start her own law firm and earns $150,000 after paying for all operating costs → accounting profit = $150,000 but economic profit = $30,000
E.g., if you start a business and earn 6% on money you invested but could have earned 4% in T-Bills → economic profit = 2%.

9. Total Profit: Keep Your Eye on the Goal
Total, Average, and Marginal Revenue:
Total Revenue (TR) = P  Q
Calculated from D curve
Average Revenue (AR) = TR/Q = (P  Q)/Q = P
AR curve = D curve
Marginal Revenue (MR) =  TR when ↑output by 1 unit.
Slope of TR curve

10. TABLE 1. Schedule of Flo’s Total, Average, and Marginal Revenue
Chicken
(20 lb-pack)
Price (or AR)
($ per package)
Total Revenue
(P x Q)
Marginal Revenue
----- 1
$19 2 18 36 17 3 51 15 4 16 64 13 5 75 11 6 14 84 9 7 91 8 12 96 99 10
100

11. FIGURE 2. Flo’s Total Revenue Curve

12. Total Profit: Keep Your Eye on the Goal
Total, Average, and Marginal Cost:
TC = P inputs x Q inputs
AC = TC/Q output
Per unit costs
MC = ∆TC when ↑output by 1 unit.
Slope of TC curve

13. TABLE 2. Flo’s Total, Average, and Marginal Cost
Chicken
(20 lb-pack)
Total Cost
Marginal Cost
Average Cost
$0.0
----- 1
17.0
$17.0 2
26.0
9.0
13.0 3
33.0
7.0
11.0 4
40.0
10.0 5
48.0
8.0
9.6 6
57.0
9.5 7
67.2
10.2 8
80.0
12.8 9
99.0
19.0 10
125.0
12.5

14. FIGURE 3(a). Flo’s Total Cost Curve

15. FIGURE 3(b). Flo’s Average and Marginal Cost Curves

16. Total Profit: Keep Your Eye on the Goal
Maximization of Total Profits:
Profits typically increase with output, then fall.
Some intermediate level of output generates max profit.

17. TABLE 3. TR, TC, and Profit for Flo
Chicken
(20 lb-pack)
Total Revenue
(P x Q)
Total Cost
Total Profit $0
$0.0 1 19
17.0
2.0 2 36
26.0
10.0 3 51
33.0
18.0 4 64
40.0
24.0 5 75
48.0
27.0 6 84
57.0 7 91
67.2
23.8 8 96
80.0
16.0 9 99
99.0
0.0 10
100
125.0
-25.0

18. Total Profit: Keep Your Eye on the Goal
In our example:
Total profit (Π) is max at 5 or 6 packages, where farm earns its highest profits of $27 per week.
Any other Q level → ↓Π
E.g., if Q = 3 → Π = $18 or if Q = 8 → Π = $16

19. Marginal Analysis and Maximization of Total Profit
Use marginal analysis to find Q that max profits.
Marginal profit = ∆ total profit when ↑Q by 1 unit.
Slope of total profit curve
Rule: if marginal Π > 0 → ↑Q
if marginal Π < 0 → ↓Q
Profit-max Q is reached when marginal Π = 0.
Graphically, only reach top of total profit “hill” when marginal profit (its slope) = 0.

20. FIGURE 4(a). Profit Maximization
Total Profit “hill” 27 20
Total Profit per week ($) 2 3 4 5 6 7 8 9 10 1
–20
–30
Output, Packages per week
Total profit has a “hill” shape. At Q = 0, Π = 0. At larger Q levels, firm floods the market, and ↓Π. Only at intermediate Q levels is Π > 0.

21. Marginal Analysis and Maximization of Total Profit
Like marginal Π, MR and MC can guide us to Q output where total profit is maximized.
MR = slope of TR and MC = slope of TC
Total profit is max when TR and TC are farthest apart.
Occurs when their slopes are equal, so they are not growing closer together (Π↓) or growing further apart (Π↑).
Rule: if MR > MC → Q
if MR < MC → Q
Profit maximizing Q is where MR = MC.

22. FIGURE 4(b). Profit Maximization
Total Π = vertical distance between TR and TC curves TC
125 TR 99 84
Total Revenue, Total Cost per week ($)
Profit 57 20
$27 1 2 3 4 5 6 7 8 9 10
Output, packages per week

23. TABLE 4. Maximization of Flo’s Total Profits
Output
(packages)
Marginal Revenue
Marginal Cost
Marginal Profit
Total Profit
-----
$0.0 1
$19
$17.0
$2.0
2.0 2 17
9.0
8.0
10.0 3 15
7.0
18.0 4 13
6.0
24.0 5 11
3.0
27.0 6 9
0.0 7
10.2
-3.2
23.8 8
12.8
-7.8
16.0
19.0
-16.0 10
26.0
-25.0

24. Marginal Analysis and Maximization of Total Profit
Finding the Optimal P from Optimal Q:
Optimal Q is where MR = MC (and marg. Π = 0).
E.g., at Q = 6; MR = MC = $9.
Producer picks Q then demand curve  P buyers will pay to purchase that level of output.
E.g., at Q = 6 → P = $14 –only P at which this Q is purchased by consumers.

25. Logic of Marginal Analysis & Maximization
Decision makers constantly faced with problem of choosing the magnitude of some variable.
E.g., how many cars to produce; how many workers to hire, or how many pints of ice cream to buy.
Generally, larger the number selected → higher the total benefit. However, costs ↑ as number chosen ↑.
Optimally, decision makers chose Q of some variable where difference between total benefit and total cost is greatest.

26. Logic of Marginal Analysis & Maximization
Decide about Q of some variable, then max net benefit = total benefit – total cost by choosing the Q where marginal benefit = marginal cost.
Rule is true regardless of who the decision maker is.
Decision maker
Marginal benefit
Marginal
cost
Choice variable
Objective
consumer MU
P good
Q of good
Max CS
firm
MRP input
P input
Q of 1 input
Max Π
MR output
MC output
Q of output

27. Logic of Marginal Analysis & Maximization
Application: Fixed Cost and Profit-max P
Suppose firm’s TFC ↑. How does this affect Π-max (P,Q) pair?
E.g., If Flo’s rent doubles should she ↑P to cover ↑costs or ↑Q which will ↓P? She should do nothing!
When a firm’s ↑TFC, it’s Π-max (P,Q) pair remain unchanged; assuming it pays to stay in business.
TFC remain constant with ∆Q → so Flo’s TFC is the same if she produces 2 or 200 packages.

28. TABLE 5. Rise in Fixed Cost: Total Profits Before and After
Output
(packages)
Total Profit
with TFC = 0
Total Fixed Cost
Total Profit with TFC = 5
$0.0 $5
-$5.0 1
2.0 5
-3.0 2
10.0
5.0 3
18.0
13.0 4
24.0
19.0
27.0
22.0 6 7
23.8
18.8 8
16.0
11.0 9
0.0
-5.0 10
-25.0
-30.0

29. FIGURE 5. Fixed Cost Does Not Affect Profit-Maximizing Output
Inward shift of total profit by $5 27 22
Total Profit per week ($) 2 3 4 5 6 7 8 9 10 1
–20
–30
Output, Packages per week
↓∏ by $5 at every Q → whatever Q was most profitable before ↑TFC must still be the most profitable.

30. Puzzle: Making Profit by Selling Below Cost
The “unprofitable” calculator:
Firm B accused A of trying to drive it out of business.
Firm A charged $12 per unit when its AC = $14.55.
AC = $14.55 = $10.30 (direct costs) + $4.25 (indirect costs)
Economist (for A) argued if calculators were really unprofitable, then firm A would be better off with Q = 0.
If Q = 0 (rather than 10M), lose annual sales of $120M = $12 x 10M. And it would only save direct costs of the calculators ($10.30 x 10M) = $103M.

31. Puzzle: Making Profit by Selling Below Cost
Indirect costs (of $4.25) –largely admin. overhead, would not be saved if A stopped making calculators.
Thus, Q = 0 saves $103M and costs $120M, so A’s profits would fall by $17M.
Marginal profit = MR – MC = $12 - $10.30 = $1.7
Total profit = $17M = marginal profit x Q
Lesson: pay attention to MC and not AC when deciding on Q of output.