Theme

   7  

Profit  Maximiza1on  

Indre Deksnyte
 Theme  Objec1ves  
•  Marginal  Revenue  
•  Profit  maximiza1on  and  loss  minimiza1on  
•  The  short-­‐run  supply  curve  
•  The  long-­‐run  supply  curve  
•  The  shut-­‐down  and  break-­‐even  points  
 PERFECTLY COMPETITIVE MARKETS

The model of perfect competition rests on three basic

assumptions:
(1) price taking,
(2) product homogeneity, and
(3) free entry and exit.

Price  Taking  
Because   each   individual   firm   sells   a   sufficiently   small  
propor5on   of   total   market   output,   its   decisions   have   no   impact  
on  market  price.  
● price taker Firm that has no influence over
market price and thus takes the price as given.

Product  Homogeneity  
When the products of all of the firms in a market are perfectly
substitutable with one another—that is, when they are homogeneous—
no firm can raise the price of its product above the price of other firms
without losing most or all of its business.
What  are  the  main  goals  for  
business?  
 MARGINAL REVENUE, MARGINAL COST,
AND PROFIT MAXIMIZATION

● profit Difference between total revenue and total cost.

π(q) = R(q) − C(q)
● marginal revenue Change in revenue resulting from a
one-unit increase in output.
Figure 8.1

Profit Maximization in the Short Run

A firm chooses output q*, so that

profit, the difference AB between
revenue R and cost C, is
maximized.
At that output, marginal revenue
(the slope of the revenue curve)
is equal to marginal cost (the
slope of the cost curve).

Δπ/Δq = ΔR/Δq − ΔC/Δq = 0

MR(q) = MC(q)
Graphing  Demand  &  Marginal  Revenue  
Total Revenue is price X output
Marginal revenue is the increase in total revenue when
output sold goes up by one unit
Output Price Total Revenue Marginal
Revenue
1 $5 $ 5 $5
2 5 10 5
3 5 15 5
4 5 20 5
5 5 25 5
6 5 30 5
 Graphing  Demand  &  Marginal  Revenue  

Output Price Total Revenue Marginal Revenue

1 $5 $ 5 $5 6

2 5 10 5 5 D,MR

3 5 15 5 4

4 5 20 5 3

5 5 25 5 2

6 5 30 5 1

0
0 1 2 3 4 5 6
Output
 Profit Maximization and Loss
Minimization
Output Price TR MR TC ATC MC Total Profits
1 1 $200 $200 $200 $500 $500 $100 - $300
1 2 200 400 200 550 275 50 - 150
1 3 200 600 200 610 203 60 - 10
1 4 200 800 200 700 175 90 100
1 5 200 1000 200 830 166 130 170
1 6 200 1200 200 1000 167 170 200
1 7 200 1400 200 1205 172 205 195

Profit Maximization Point: MC = MR

 Profit Maximization and Loss Minimization
Output Price TR MR TC ATC MC Total Profits
1 1 $200 $200 $200 $500 $500 $100 - $300
1 2 200 400 200 550 275 50 - 150
1 3 200 600 200 610 203 60 - 10
1 4 200 800 200 700 175 90 100
1 5 200 1000 200 830 166 130 170
1 6 200 1200 200 1000 167 170 200
1 7 200 1400 200 1205 172 205 195

Profit Maximization Point: MC = MR

This occurs somewhere between 6 and 7 units.

We are assuming output can be produced in tenths of a unit
 Profit Maximization and Loss Minimization

Output MR MC 500

1 $200 $100
400
2 200 50
3 200 60 300

4 200 90
5 200 130 200
D,MR MC

6 200 170 ATC

7 200 205 100

Profit Maximization Point: MC = MR

0
0 1 2 3 4 5 6 7
Output

The most profitable output is where the MC curve crosses the D, MR curve. This
occurs at an output of 6.7 units
 Profit Maximization and Loss Minimization
Total Profit=(Price-ATC) X Output
TP=Total Profit; P=Price

500
TP=(P-ATC) X Output
TP=$200-$170) X 6.7
400
TP=$30 X 6.7
TP=$201
300

D,MR
Price is $200
MC
200
ATC

ATC is $170
100

Profit Maximization Point: MC = MR

0
0 1 2 3 4 5 6 7
Output

The most profitable output is where the MC curve crosses the D, MR curve. This
occurs at an output of 6.7 units
Making Sure We Are Maximizing Profit
Output Profit
6.0. . . . . . . . . . . . . $200
If you calculated the total profit at
6.1
every level of output (6.1 through 6.9)
6.2 you would find that the output level of
6.3 6.7 units would provide you with the
6.4 greatest level of profit.
6.5 This is the output level where
6.6 MC=MR
6.7 . . . . . . . . . . . . . . 201 <------ Best that we can do!
6.8
6.9
7.0 . . . . . . . . . . . . . . 195
 Profit Maximization and Loss Minimization
1,500

TP = (P-ATC) X Output 1,400

TP = $450-$533) X 5.2 1,300

TP = -$83 X 5.2 1,200

TP = -$431.60
1,100

In this particular instance, losses 1,000

were minimized 900

Profit Maximization Point: MC = MR

800

MC
700

600 ATC

ATC is $533 500

Price is $450 D,MR

400

The most profitable output is where the 300

MC curve crosses the D, MR curve. This

200
occurs at an output of about 5.2 units
100

0
0 1 2 3 4 5 6 7
Output
Making Sure We Are Minimizing Losses
Output Profit
5.0 - $450.00
5.1
5.2 - 431.60 <----Best we can do!
5.3
If you calculated the total profit at every level
5.4 of output (5.1 through 5.9) you would find that
5.5 the output level of 5.2 units would provide you
with the smallest possible loss.
5.6
5.7 This is the output level where MC=MR
5.8
5.9

6.0 - 700.00
 Producing  Exactly  at  the  Output  Level  Where  
MC  =  MR    Enables  Us  to  Maximize  Total  Profits  (or  
Minimize  Total  Losses)  
•  MR  is  the  addi1onal  revenue  from  selling  one  
more  unit  of  output  
•  MC  is  the  addi1onal  cost  of  producing  one  more  
unit  of  output  
•  We  keep  adding  to  output  as  long  as  MR  exceeds  
MC  
–  If  we  stop  short  of  this  point,  we  would  not  maximize  
our  profit  
•  We  stop  adding  to  output  when  MR  =  MC  
–  If  we  con1nued  to  add  output  MC  would  exceed  MR  
and  this  would  diminish  our  profits  

Shut-­‐Down  Rule:  The  firm  should  shut  down  if  the  price  of  
the  product  is  less  than  the  average  variable  cost  of  
produc;on  at  the  profit-­‐maximizing  output.  
 The  Short-­‐Run  and  Long-­‐Run  Supply  Curves  
The Short-Run Supply Curve
A firm will always produce where MC equals MR
A firm will operate in the short-run if sales (TR) are greater than
variable cost (VC) [ Remember TR = Price X Output]
A firm will shut down if variable cost (VC) are greater than sales
(TR) [Remember, sales and TR are the same]

Therefore, a firm will shut down if VC is greater TR or if VC are

greater than Price X Output
A firm will shut down if VC > TR or if VC > Price X Output

A firm will shut down if

VC > Price X Output

Let’s divide both side of the above equation by Output

VC > Price X Output

Output Output
A firm will shut down if VC > TR or if VC > Price X Output

A firm will shut down if

VC > Price X Output

Let’s divide both side of the above equation by Output

VC > Price X Output

Output Output

AVC > Price

A firm will shut down if VC > TR or if VC > Price X Output

A firm will shut down if

VC > Price X Output

Let’s divide both sides of the above equation by Output

VC > Price X Output

Output Output

AVC > Price

In the short-run a firm will shut down if the
AVC is greater than the price

Alternatively

In the short-run a firm will operate if the

price is greater than the AVC
 Cost  Curves  
•  At  any  given  ;me,  a  business  firm  will  have  a  certain  
set  of  cost  curves:  AVC,  ATC,  and  MC.  
–  These  curves  are  determined  mainly  by  the  firm’s  capital  
stock  –  its  plant  and  equipment  
•  Over  ;me  these  curves  can  change,  but  at  any  given  
;me  they’re  fixed  
•  At  any  given  ;me,  we  can  assume  the  MC  curve  
doesn’t  change  
 Review  
•  MC  must  equal  MR  
•  MC  stays  the  same  
•  MR  can  change  to  any  value  because  
whenever  price  changes  we  have  an  new  MR  
line  
•  When  the  price  changes  MR  changes  and  will  
equal  MC  at  some  other  point  on  the  MC  
curve  
 Derivation of a Firm’s Short-Run & Long-
Run Supply Curve
The firm’s short-run supply
60
MC
55
curve begins at the shut-
50
down point and runs all the 45
way up the MC curve 40

The firm’s long-run supply 35

curve begins at the break- 30

even point and runs all the 25 ATC

way up the MC curve 20 Break-­‐e ven  point

AVC

15

Minimum point on the ATC 10

5 Shut-­‐down  point

0
0 1 2 3 4 5 6 7 8 9 10 11
Minimum point on the AVC Output
 Four  Rules  
•  In  the  short  run  
–  If  the  price  is  below  the  shut-­‐down  point,  the  firm  will  
shut  down  
–  If  the  price  is  above  the  shut-­‐down  point,  the  firm  will  
operate  
•  In  the  long  run  
–  If  the  price  is  below  the  break-­‐even  point,  the  firm  will  go  
out  of  business  
–  If  the  price  is  above  the  break-­‐even  point,  the  firm  will  
stay  in  business    
 The Shut-Down and Break-Even Points
200

What is the lowest price the

firm will accept in the long 180

run? 160
MC

Answer: $125.50
140 Break-­‐e ven
point ATC

D,MR
120
Output AVC ATC Total Profits AVC

1 $150 $250 -$120

100
2 120 170 - 80 Shut-­‐down  point

3 106.67 140 - 30
80
4 102.50 127.50 + 10 0 1 2 3 4 5 6 7
Output
5 106 126 + 20
6 116.67 133.33 - 20
 The Shut-Down and Break-Even Points
200
Calculate Total Profit
TP = (P – ATC) X Output 180

TP = ($130 – $126) X 5.25 MC

TP = 4 X 5.25 160

TP = $21 140 Break-­‐e ven

point ATC

Price is 130 D,MR

120
AVC
ATC is 126
100
Shut-­‐down  point

80
0 1 2 3 4 5 6 7
Output

Output is 5.25
 The Shut-Down and Break-Even Points
200

How much will the firm’s

output be in the short run and 180

D, MR
the long run if the price is MC
160
$170?
140 Break-­‐e ven

The firm will maximize profits point ATC

D,MR
at an output of 6 120
AVC

100
In both the short run and the Shut-­‐down  point

long run the output will be six 80

0 1 2 3 4 5 6 7
because that is where MC = MR Output
 The Shut-Down and Break-Even Points
200

How much will the firm’s

output be in the short run and 180

the long run if the price is MC

160
$115?
The firm will maximize profits 140 Break-­‐e ven
point ATC

at an output of 4.85 D,MR

120
AVC D, MR
The output in the shot run will
be 4.85 because the price is 100
Shut-­‐down  point
above the shut-down point. The
output in the long run will be 80
0 1 2 3 4 5 6 7
Output
zero because the price is below
the break-even point.
 The Most Efficient Output

How much is the firm’s most

efficient output? MC ATC

This occurs at an output of 10, 80

AVC

which is the minimum point on 70

the ATC (which is the break- 60

D,MR

even point) 50

40

How much is the most profitable 30

output? 20

10

This occurs at an output of 11 0 2 4 6 8 10 12 14 16 18

which is where MC=MR O utput