1. Walter Nicholson Christopher Snyder
Amherst College
Christopher Snyder
Dartmouth College
PowerPoint Slide Presentation | Philip Heap, James Madison University
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

2. Profit Maximization and Supply
CHAPTER 8
Profit Maximization and Supply
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

3. Chapter Preview In the last two chapters:
Production: relationship between inputs and output.
Costs: relationship between output and costs.
In this chapter, we want to study a firm’s output decision.
How much should the firm produce to maximize profits?
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

4. The Nature of the Firm Why do firms exist?
If they did not, how would goods be produced?
The role of transaction costs.
Contracts within Firms
Formal vs. informal contracts
Contract Incentives
Relationship between incentives and efficiency
Firms’ Goals and Profit Maximization
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

5. Profit Maximization
Economic profit is the difference between revenue and economic cost.
Economic cost includes all relevant opportunity costs.
Owner’s return on her investment and normal rate of return.
Economic profit (loss) and entry (exit).
Marginalism
How much profit can I make from making one more car or hiring one more worker?
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

6. Profit Maximization The Output Decision π(q) = R(q) – TC(q)
The firm chooses the level of output that generates the largest profit.
The firm choose the level of output for which the difference between revenue and costs is the largest.
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

7. Profit Maximization: Graphical Approach
Costs (TC)
Costs,
Revenue
Revenues (R)
Output per week
Profits
Output per week q1 q* q2
Profits
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

8. Profit Maximization: Golden Rule
At q* what condition must hold?
Marginal Revenue = Marginal Cost
Why?
If at the current level of output, MR > MC, the firm should . . .
If at the current level of output, MR < MC, the firm should . . .
Therefore, if MR = MC, the firms maximizes profits.
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

9. Profit Maximization: Graphical Approach
Costs (TC)
Costs,
Revenue
Revenues (R)
slope = MR
slope = MC
Output per week
Profits
Output per week q1 q* q2
Profits
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

10. Profit Maximization: Calculus
π(q) = R(q) – TC(q)
To maximize a function set the first derivative equal to zero
dπ(q)/dq = dR(q)/dq – dTC(q)/dq = 0
MR(q) – MC(q) = 0
MR(q) = MC(q)
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

11. Profit Maximization: Calculus
π(q) = 20q – ( q + 0.1q2)
dπ(q)/dq = ?
20 – ( q) = 0
q* = 50
20 – ( q)
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

12. Marginal Revenue
Marginal revenue is the additional revenue from selling one more unit.
What happens to marginal revenue as the firm sells more or less output?
Price taker is a firm whose decisions have no effect on the prevailing market price of a good.
For a price taking firm MR = P.
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

13. Marginal Revenue
What about for a firm that faces a downward sloping demand curve?
To sell one more unit the firm would have to cut the price for all units sold, not just the last one.
Revenue from the last unit = new price – revenue lost from selling the other units at a lower price
MR < P
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

14. A Numerical Example: q = 10 - P
What happens to TR and MR as output increases?
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

15. Marginal Revenue Price Loss in revenue from cutting price by $1 = $3$7 $6
Gain in revenue from selling one more unit = $6
Marginal revenue = $3
Demand
Quantity 3 4
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

16. Marginal Revenue and Elasticity
The price elasticity of demand in a market:
The price elasticity of demand for a firm:
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

17. Marginal Revenue and Elasticity
What is the relationship between elasticity and marginal revenue?
When demand is elastic, eq,P < -1, MR > 0
When demand is unit elastic, eq,P = 1, MR = 0
When demand is inelastic, eq, P > -1, MR < 0
In general, can show that: MR = (1 + 1/eq,P)
If eq,P = -2 (elastic), MR = (1 + 1/-2) = 1/2 > 0
If eq,P = -0.5 (inelastic), MR = (1 + 1/-0.5) = -1 < 0
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

18. Marginal Revenue and Elasticity
The firm can use elasticity information to see what happens to revenue if it sells one more unit?
Suppose eq,P = -2 and the current price is $10.
MR = $10 x (1 + 1/-2) = $5
The firm will sell one more unit as long as MC < $5
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

19. Marginal Revenue Curve
A marginal revenue curve shows the relation between the quantity a firm sells and the revenue yielded by the last unit sold.
The marginal revenue curve will lie below the demand curve or the average revenue curve.
Price P1
Demand (average revenue)
Quantity q1
Marginal revenue
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

20. Marginal Revenue Curve for Linear Demand Curves
Derive the marginal revenue curve for q = 10 – P.
Solve for P so P = 10 – q
MR = 10 – 2q
For a linear demand curve, the marginal revenue curve has the same intercept but twice the slope.
If P = a – bQ, MR = a – 2bQ
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

21. Marginal Revenue Curve
Price 10
MR = 10 – 2q
Demand: q=10-P or P = 10-q 5 10
Quantity
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

22. Supply Decision for a Price Taking Firm
When does it make sense to assume that firms are price takers?
Suppose the market demand for corn is:
Q = 16,000,000,000 – 2,000,000,000P
P = 8 – Q/2,000,000,000
Assume there are 1 million corn farmers who each produce 10,000 bushels per year
P = $3 and Q = 1 billion bushels
What if one farmer decides to stop growing corn?
Q = 9,999,990,000 and P = $
If one farmer doubles output, P = $
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

23. Supply Decision for a Price Taking Firm
If there are many suppliers in the market, each producing a small percentage of total output, their decisions will have no impact on the market price.
Short Run Profit Maximization
A price taking firm will maximize profits by producing a level of output where ....?
P* = MC
The profit maximizing condition is still MR = MC.
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

24. Supply Decision for a Price Taking Firm
SMC
SAC
P*=MR q*
Quantity
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

25. Profits for a Price Taking Firm
Profit = π = Total Revenue – Total Cost = P*q* - STC(q*)
Profit = π = q*(P* - STC/q*) = q*[P* - SAC(q*)]
If P* > SAC(q*), then profit > 0
If P* = SAC(q*), then profit = 0
If P* < SAC(q*), then profit < 0

26. Economic Profit: P* > SAC
Price
SMC
SAC
P*=MR q*
Quantity
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

27. Economic Loss: P* < SAC
Price
SMC
SAC
P*=MR q*
Quantity
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

28. The Price Taking Firm’s Supply Curve
SMC
P**
SAC
P*=MR
P***
q*** q*
q**
Quantity

29. The Shut Down Decision
If profits are negative, the firm must compare losses from producing some output to how much it would lose if it shut down: q = 0.
If it shuts down it only loses its fixed costs.
Therefore, a firm will stay open as long as it can cover its VC.
P x q ≥ SVC or P ≥ SVC/q = AVC
To stay open price must be greater than or equal to short run average variable cost.

30. The Price Taking Firm’s Supply Curve
SMC
P**
SAC
P*=MR
P***
PSD
qSD
q*** q*
q**
Quantity

31. Summary Any firm maximizes profits by producing where MR=MC.
If a firm faces a downward sloping demand curve, MR < P and the marginal revenue curve will lie below the demand curve.
With many firms in the market one firm’s actions will not affect the market price. Therefore, P = MR.
A price taking firm will maximize profits where P = MC, and the firm’s supply curve is its short-run marginal cost curve.
If price is less than average variable cost, the firm will shut down and only incur its fixed costs.
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.