Profit Maximization
Maximization
In
general, we characterize firms’
firms’
behavior as to maximize profits.
Total profit = Total Revenue – Total
Cost
TP = TR - TC
14. Firm’s output decision
Gene Chang
U of Toledo
Profit maximization
Table: Portion of the cost schedules of farmer Joe
Output of corn
(250 bushels per unit)
Price for each unit
(Marginal Revenue)
(250 bushels per
unit) ($)
…
Marginal
cost
($)
Total
revenue
($)
Total cost
($)
…
Total
Profit
($)
…
4 (1000 bushels)
400
-
1600
2000
-400
5 (1250 bushels)
400
300
2000
2300
-300
6 (1500 bushels)
400
250
2400
2550
-150
7 (1750 bushels)
400
200
2800
2750
50
8 (2000 bushels)
400
150
3200
2900
300
9 (2250 bushels)
400
250
3600
3150
450
10 (2500 bushels)
400
400
4000
3550
450
11 (2750 bushels)
400
750
4400
4300
100
Price
= 400 dollars a unit of corn
produced
This is the additional revenue for the
firm to produce one more unit of
good. (called marginal revenue)
The firm compares this marginal
revenue to the MC.
Profit maximization
MC
<P
– It pays to produce the additional unit of
the product
– expand the production
MC
>P
– It does not pay to produce the
additional unit of the product
– cut the production
Profit maximization
Rule
for profit maximization (when
price represents the marginal
revenue)
MC = P
Graphical illustration
Profit maximization
Total Revenue = P X Q
$
TC
Total profits
AT
Q*, the point where profit is
maximized
0
MC = P
– The vertical distance between TR and
TC is maximized
– The slope of TR equals the slope of TC
Q
MC
The
P
rule for profit maximization
MC = P
0
Q
Q*
Graphical illustration
At
$
MC
P
0
Q*
Q
Firm’
Firm’s supply curve
We
Profit maximization
need to refine the statement of
“MC is the supply curve”
curve”:
Actually, only a segment of the MC is
the supply curve of the firm.
price P, quantity supplied by the
firm is Q*.
As P changes, Q* would change as
well.
Thus, MC provides the information
about the quantity supplied by the
firm at each price.
MC is the supply curve.
Firm’
Firm’s supply curve
Reason:
Price must be at least as
high as the breakbreak-even level, so the
firm can make profits.
Graphical illustration
Total revenue, total cost and total
profit: graphical illustration
Total
MC
$
revenue = P X Q
P
– the rectangle area under P and Q*
Total
cost = ATC X Q
ATC
Total profit
(ATC = TC /
ATC
Q)
Total
Revenue
– The rectangle area under ATC and Q
Total
Total cost
profit = TR – TC
0
– is the difference between total revenue
and total cost areas
Firm’
Firm’s supply in the short run
Q*
P > ATC, still making profits
MC
$
What
happens if P falls?
Three situations:
Total profit
ATC
– Still making profits although the price is
down: TR > TC
– The breakbreak-even point: TR = TC (P is at
the minimum ATC curve)
– Loss: TR < TC
P
ATC
Total
Revenue
Total cost
0
Q*
Q
P < ATC Making a loss
P = ATC break-even point
MC
$
Q
MC
$
Total profit = 0
ATC
P = ATC
ATC
ATC
Total
Revenue
Total cost
Total loss
P
Total
Revenue
Total cost
0
Q*
Q
0
Q*
Q
Graphical illustration
Firm’
Firm’s supply curve
the firm’
firm’s (long run) supply curve
is the segment of MC that is above
the minimum ATC.
And the part of vertical axis that is
below the minimum ATC
MC
$
So
Long run supply curve
P
ATC
Minimum ATC
0
The shortshort-run case
Fixed
inputs and fixed costs
inputs and variable costs
LongLong-run
Variable
– Definition: In the long run, all inputs are
variable inputs, thus no fixed costs.
Q*
Q
The shortshort-run case
Fixed
cost is also called sunk cost
Sunk costs are costs that have
already been committed and cannot
be recovered.
ShortShort-run
– In the short run, at least some inputs
are fixed inputs therefore there is a
fixed cost.
Output decision in the shortshort-run
Only
AVC < P < ATC
requires that P > AVC
MC
ATC
ATC
AVC
A
P
B
AVC
0
Q*
Q
TC, TVC, TFC areas
AVC < P < ATC
TC
area
TVC area
Total
cost
– the rectangle area below the AVC line.
– VC = AVC X Q*
TFC
area
MC
ATC
ATC
AVC
P
AVC
– the area between TC and VC
– FC = TC – VC
0
Q*
Q
AVC < P < ATC
AVC < P < ATC
When
MC
ATC
ATC
AVC
d
l fi xe
T ota
P
costs
AVC
AVC < P < ATC
If stop production, total loss is TFC,
the sunk cost, which equals A + B
If continues production, total loss is
B
It pays to continue production
Total variable costs
0
Q*
Q
AVC < P < ATC
AVC < P < ATC
MC
ATC
ATC
MC
ATC
AVC
ATC
A
AVC
A
P
P
B
B
AVC
Total revenue
AVC
Total variable costs
0
Q*
Q
0
Q*
Q
A firm’
firm’s shortshort-run supply curve
In the short run, the firm still has to pay
the fixed cost FC = A + B, regardless the
amount of output. (sunk cost)
If the firm continues production at Q*, the
loss is A.
It pays for the firm to continue production,
since the loss is minimized.
In the short run, a firm continues its
production if P > AVC.
AVC < P < ATC
The
Minimum
AVC
Q
The market supply curve
is
shortshort-run supply curve is the
segment of MC above the AVC and
the part the vertical axis below
minimum AVC.
MC
AVC
0
The
Summary of a firm’
firm’s supply curve
as it takes price as given
P
ATC
A firm’
firm’s shortshort-run supply curve
the horizontal sum of the
individual supply curves.
supply curve of an individual
firm is its MC curve
above the AVC in the short run, and
above the ATC in the long run.