1. Profit Maximization

2. Profit Maximization assuming:
Firm must charge every consumer the same price (i.e., no price discrimination)
No Strategic Interaction among Firms
We will consider three industry structures:
Price taking Firms
Monopoly
Monopolistic Competition

3. Price Taking Firm’s Short Run CostsQ FC VC TC
AFC
AVC
ATC MC
100 - 50 1
150 30 2 80
180 40 90 20 3
200
33.3
33.33
66.7 10 4
110
210 25
27.5
52.5 5
130
230 26 46

4. Price Taking Firm’s Short Run CostsQ FC VC TC
AFC
AVC
ATC MC 5
100
130
230 20 26 46 30 6
160
260
16.7
26.67
43.3 40 7
200
300
14.3
28.57
42.9 50 8
250
350
12.5
31.25
43.8 60 9
310
410
11.1
34.44
45.6 70 10
380
480 38 48

5. What output maximizes profits if the marginal revenue (MR) for each unit the firm sells is $55? What are these profits? 8
55* *8=90

6. What output maximizes profits if the marginal revenue for each unit the firm sells is $35? What are these profits? 6
35* *6=-50
Produce an output of 6 in short-run if fixed costs are sunk.

7. What output maximizes profits if the marginal revenue for each unit the firm sells is $25? What are these profits? 5?
25*5-46*5=-105
Better off producing 0 so profits=-FC=-100

8. Short-Run Profit Maximizing Rule
Produce at an Output where
Marginal Revenue = Marginal Cost
(MR) (MC)
if Total Revenue > Variable Cost
[When the firm cannot price discriminate, this is the same thing as saying as long as
Price > AVC (from P*Q > AVC*Q) ]

9. Monopoly Characteristics
There is a single seller
There are no close substitutes for the good
There are extremely high barriers to entry

10. Natural Monopoly (type of monopoly where there exists large economies of scale)
$/unit
when a single firm can supply a
good or service to an entire
market at a smaller cost than could
two or more firms.
Long Run
Average Total Cost
ATC1/2 big firm
ATCone big firm
Q1/2 big firm
Qbig firm
Quantity 60

11. Monopolist Marginal Revenue (with no price discrimination)Q TR MR 10 9 1 8 2 16 7 3 21 6 4 24 5 25 +9 +7 +5 +3 +1 -1 Q -3 -5 MR -7
Note that Marginal Revenue for a given unit is plotted at the midpoint of that unit. -9

12. Use Calculus to Obtain MR curve for Linear Demand Curve
P=a-bQ
Slope of D TR
= (a-bQ)Q
=aQ-bQ2 MR
=ΔTR/ ΔQ =∂TR/ ∂Q
=a-2bQ
[In prior graph, a=10 and b=1]
Slope of MR

13. Monopoly Elastic Inelastic
If the firm’s goal were to maximize total revenue, where would it produce?
P=$5; hD=-1; TR=$25
Inelastic
The elastic and inelastic portions of the demand curve are labeled. How do these relate to MR?
Elastic: MR>0
Inelastic: MR<0 Q
Will a monopolist ever produce on the inelastic portion of the demand curve? No. MR

14. Monopoly Maximizing Profits
If the monopolist maximizes profits, where would it produce?
At an output where MR=MC as long as P>AVC.
This is at an output of Q=4 so a price of P=6. Q MR

15. MATH BEHIND: Maximizing Profits being where MR=MC
MaxQ Profits = MaxQ TR(Q)-TC(Q)
so profits are maximized where
Or where,
Applies when Q>0

16. Monopoly Maximizing Profits
At Q=4 and P=6, what is Total Revenue?
TR=P*Q=6*4=24
At Q=4, what are Total Costs?
TC=ATC*Q=4.5*4=18
At Q=4 and P=6, what are Profits?
Profits=TR-TC=24-18=6 Or
Profits=P*Q-ATC*Q
=(P-ATC)*Q
=(6-4.5)*4=6 TR
Profits Q TC MR

17. Monopolist in Long Run
What should this monopolist do in the Long Run assuming that the monopolist thinks his costs will not change and neither will demand?
Keep producing Q=4 or change plant size depending if there is a plant size that would result in greater profits.
Profits Q MR

18. Short Run and Long Run ATCs

19. Monopolist in Long Run
Profits
What should this monopolist do in the Long Run assuming that the monopolist thinks his costs will not change and neither will demand?
Exit the industry or change plant size depending if there is a plant size that would result in positive profits given demand curve. MR

20. Monopolistic Competition Characteristics
There are many buyers and seller
Each firm in the industry produces a differentiated product
There is free entry into and exit from the industry
[Think bakery or coffee shop in big city.]

21. Bakery in a Monopolistically Competitive Industry Maximizing Profits in the Short Run
If bakery maximizes profits, where would it produce?
Where MR=MC which is at an output of Q=3.5 so a price of P=8.
What are the bakery’s profits?
TR-TC=P*Q-ATC*Q
=8* *3.5 = 6.12 MR

22. Bakery in a Monopolistically Competitive Industry Maximizing Profits in the Long Run
In long-run if the bakery is making positive economic profits, we would expect other bakeries to enter causing a reduction in demand.
What are maximum profits when demand is D’?
Q=3 so a price of P=6.67.
Profits=P*Q-ATC*Q
=6.67*3-6.67*3=0 D’ MR

23. Review of Profit Maximization (when setting a single price)

24. Marginal Revenue from 5th Unit is just the shaded area below
Marginal Revenue from 5th Unit is just the shaded area below. This area is $11.
When the MR curve is linear, the area under the MR curve can be obtained by just taking the MR at the midpoint of the quantities – in this case at 4.5.
The orange area is the same as the purple area. MR

25. Marginal Cost of 5th Unit is just the shaded area below
Marginal Cost of 5th Unit is just the shaded area below. This area is $9.
When the MC curve is linear, the area under the MC curve can be obtained by taking the MC at the midpoint of the quantities – in this case at 4.5.
The purple area is the same as the red area MR

26. Change in Profits associated with producing 5 Units rather than 4 units.
Yellow area is change in profits associated with producing 5 units rather than 4 units. This area is $2.
Subtract MC of 5th unit from MR of 5th unit– brown area from purple. MR

27. Review of Profit Maximization (when setting a single price)

28. PROFIT MAXIMIZATION
Profits are maximized at an output where MR=MC which is Q=5. Price is 15 and ATC is 11.2 at Q=5.
Profits are then 15*5-11.2*5=19 15
11.2 MR