Production. Costs
Problem 6 on p.194.
Output
FC
0
10,000
VC
TC
AFC
AVC
ATC
---
100
200
200
125
300
133.3
400
150
500
200
600
250
MC
Production. Costs
Problem 6 on p.194.
Output
FC
VC
TC
AFC
AVC
ATC
0
10,000
---
100
10,000
200
200
10,000
125
300
10,000
133.3
400
10,000
150
500
10,000
200
600
10,000
250
MC
Production. Costs
Problem 6 on p.194.
Output
FC
VC
TC
AFC
AVC
ATC
0
10,000
100
10,000
200
10,000
125
300
10,000
133.3
400
10,000
150
500
10,000
200
600
10,000
250
--20,000
200
MC
Production. Costs
Problem 6 on p.194.
Output
FC
VC
TC
AFC
AVC
ATC
0
10,000
100
10,000
20,000
200
200
10,000
25,000
125
300
10,000
40,000
133.3
400
10,000
60,000
150
500
10,000
100,000
200
600
10,000
150,000
250
---
MC
Production. Costs
Problem 6 on p.194.
Output
FC
0
10,000
VC
TC
AFC
AVC
ATC
---
100
10,000 10,000
20,000
200
200
10,000 15,000
25,000
125
300
10,000 30,000
40,000
133.3
400
10,000 50,000
60,000
150
500
10,000 90,000 100,000
200
600
10,000 140,000 150,000
250
MC
Production. Costs
Problem 6 on p.194.
Output
FC
VC
0
10,000
0
TC
AFC
AVC
ATC
---
100
10,000 10,000
20,000
200
200
10,000 15,000
25,000
125
300
10,000 30,000
40,000
133.3
400
10,000 50,000
60,000
150
500
10,000 90,000 100,000
200
600
10,000 140,000 150,000
250
MC
Production. Costs
Problem 6 on p.194.
Output
FC
VC
TC
AFC
AVC
ATC
0
10,000
0
10,000
---
100
10,000 10,000
20,000
200
200
10,000 15,000
25,000
125
300
10,000 30,000
40,000
133.3
400
10,000 50,000
60,000
150
500
10,000 90,000 100,000
200
600
10,000 140,000 150,000
250
MC
Production. Costs
Problem 6 on p.194.
Output
FC
VC
TC
AFC
AVC
0
10,000
0
10,000
---
---
ATC
---
100
10,000 10,000
20,000
100
200
200
10,000 15,000
25,000
50
125
300
10,000 30,000
40,000
33.3
133.3
400
10,000 50,000
60,000
25
150
500
10,000 90,000 100,000
20
200
600
10,000 140,000 150,000
16.7
250
MC
Production. Costs
Problem 6 on p.194.
Output
FC
VC
TC
AFC
AVC
ATC
0
10,000
0
10,000
---
---
---
100
10,000 10,000
20,000
100
100
200
200
10,000 15,000
25,000
50
75
125
300
10,000 30,000
40,000
33.3
100
133.3
400
10,000 50,000
60,000
25
125
150
500
10,000 90,000 100,000
20
180
200
600
10,000 140,000 150,000
16.7
233.3
250
MC
Production. Costs
Problem 6 on p.194.
MC = cost of making an extra unit
Output
FC
VC
TC
AFC
AVC
ATC
0
10,000
0
10,000
---
---
---
100
10,000 10,000
20,000
100
100
200
200
10,000 15,000
25,000
50
75
125
300
10,000 30,000
40,000
33.3
100
133.3
400
10,000 50,000
60,000
25
125
150
500
10,000 90,000 100,000
20
180
200
600
10,000 140,000 150,000
16.7
233.3
250
MC
Production. Costs
Problem 6 on p.194.
MC 
TC
Q
Output
FC
VC
TC
AFC
AVC
ATC
0
10,000
0
10,000
---
---
---
100
10,000 10,000
20,000
100
100
200
200
10,000 15,000
25,000
50
75
125
300
10,000 30,000
40,000
33.3
100
133.3
400
10,000 50,000
60,000
25
125
150
500
10,000 90,000 100,000
20
180
200
600
10,000 140,000 150,000
16.7
233.3
250
MC
Production. Costs
Problem 6 on p.194.
MC 
TC VC

Q
Q
Output
FC
VC
TC
AFC
AVC
ATC
0
10,000
0
10,000
---
---
---
100
10,000 10,000
20,000
100
100
200
200
10,000 15,000
25,000
50
75
125
300
10,000 30,000
40,000
33.3
100
133.3
400
10,000 50,000
60,000
25
125
150
500
10,000 90,000 100,000
20
180
200
600
10,000 140,000 150,000
16.7
233.3
250
MC
Production. Costs
Problem 6 on p.194.
MC 
TC VC

Q
Q
Output
FC
VC
TC
AFC
AVC
ATC
0
10,000
0
10,000
---
---
---
100
10,000 10,000
20,000
100
100
200
200
10,000 15,000
25,000
50
75
125
300
10,000 30,000
40,000
33.3
100
133.3
400
10,000 50,000
60,000
25
125
150
500
10,000 90,000 100,000
20
180
200
600
10,000 140,000 150,000
16.7
233.3
250
MC
100
Production. Costs
Problem 6 on p.194.
MC 
TC VC

Q
Q
Output
FC
VC
TC
AFC
AVC
ATC
0
10,000
0
10,000
---
---
---
MC
100
10,000 10,000
20,000
100
100
200
100
200
10,000 15,000
25,000
50
75
125
50
300
10,000 30,000
40,000
33.3
100
133.3
400
10,000 50,000
60,000
25
125
150
500
10,000 90,000 100,000
20
180
200
600
10,000 140,000 150,000
16.7
233.3
250
Production. Costs
Problem 6 on p.194.
MC 
Output
FC
VC
TC
AFC
AVC
0
10,000
0
10,000
---
TC VC

Q
Q
ATC
MC
---
---
---
100
10,000 10,000
20,000
100
100
200
100
200
10,000 15,000
25,000
50
75
125
50
300
10,000 30,000
40,000
33.3
100
133.3
150
400
10,000 50,000
60,000
25
125
150
200
500
10,000 90,000 100,000
20
180
200
400
600
10,000 140,000 150,000
16.7
233.3
250
500
If cost is given as a function of Q, then
For example:
TC = 10,000 + 200 Q + 150 Q2
MC = ?
MC 
d (TC )
dQ
Profit is believed to be the ultimate goal of any firm.
If the production unit described in the problem
above can sell as many units as it wants for P=$360,
what is the best quantity to produce (and sell)?
Profit is believed to be the ultimate goal of any firm.
If the production unit described in the problem
above can sell as many units as it wants for P=$360,
what is the best quantity to produce (and sell)?
Output
FC
VC
TC
AFC
AVC
ATC
MC
0
10,000
0
10,000
---
---
---
---
100
10,000 10,000
20,000
100
100
200
100
200
10,000 15,000
25,000
50
75
125
50
300
10,000 30,000
40,000
33.3
100
133.3
150
400
10,000 50,000
60,000
25
125
150
200
500
10,000 90,000 100,000
20
180
200
400
600
10,000 140,000 150,000
16.7
233.3
250
500
Doing it the “aggregate” way,
by actually calculating the profit:
Output
FC
VC
TC
0
10,000
0
10,000
100
10,000
10,000
20,000
200
10,000
15,000
25,000
300
10,000
30,000
40,000
400
10,000
50,000
60,000
500
10,000
90,000
100,000
600
10,000
140,000
150,000
Doing it the “aggregate” way,
by actually calculating the profit:
P=$360
Output
FC
VC
TC
0
10,000
0
10,000
100
10,000
10,000
20,000
200
10,000
15,000
25,000
300
10,000
30,000
40,000
400
10,000
50,000
60,000
500
10,000
90,000
100,000
600
10,000
140,000
150,000
TR
Doing it the “aggregate” way,
by actually calculating the profit:
P=$360
Output
FC
VC
TC
TR
0
10,000
0
10,000
0
100
10,000
10,000
20,000
36,000
200
10,000
15,000
25,000
72,000
300
10,000
30,000
40,000
108,000
400
10,000
50,000
60,000
144,000
500
10,000
90,000
100,000 180,000
600
10,000
140,000
150,000 216,000
Doing it the “aggregate” way,
by actually calculating the profit:
P=$360
Output
FC
VC
TC
TR
0
10,000
0
10,000
0
100
10,000
10,000
20,000
36,000
200
10,000
15,000
25,000
72,000
300
10,000
30,000
40,000
108,000
400
10,000
50,000
60,000
144,000
500
10,000
90,000
100,000 180,000
600
10,000
140,000
150,000 216,000
Profit
Doing it the “aggregate” way,
by actually calculating the profit:
P=$360
Output
FC
VC
TC
TR
Profit
0
10,000
0
10,000
0
–10,000
100
10,000
10,000
20,000
36,000
16,000
200
10,000
15,000
25,000
72,000
47,000
300
10,000
30,000
40,000
108,000
68,000
400
10,000
50,000
60,000
144,000
84,000
500
10,000
90,000
100,000 180,000
80,000
600
10,000
140,000
150,000 216,000
66,000
Doing it the “aggregate” way,
by actually calculating the profit:
P=$360
Output
FC
VC
TC
TR
Profit
0
10,000
0
10,000
0
–10,000
100
10,000
10,000
20,000
36,000
16,000
200
10,000
15,000
25,000
72,000
47,000
300
10,000
30,000
40,000
108,000
68,000
400
10,000
50,000
60,000
144,000
84,000
500
10,000
90,000
100,000 180,000
80,000
600
10,000
140,000
150,000 216,000
66,000
Alternative: The Marginal Approach
The firm should produce only units that are worth
producing, that is, those for which the selling price
exceeds the cost of making them.
Output
FC
VC
TC
AFC
AVC
ATC
MC
0
10,000
0
10,000
---
---
---
---
100
10,000 10,000
20,000
100
100
200
100 < 360
200
10,000 15,000
25,000
50
75
125
50
300
10,000 30,000
40,000
33.3
100
133.3
150
400
10,000 50,000
60,000
25
125
150
200
500
10,000 90,000 100,000
20
180
200
400 > 360
600
10,000 140,000 150,000
16.7
233.3
250
500
Principle (Marginal approach to profit maximization):
If data is provided in discrete (tabular) form, then
profit is maximized by producing all the units for
which
and stopping right before the unit for which
Principle (Marginal approach to profit maximization):
If data is provided in discrete (tabular) form, then
profit is maximized by producing all the units for
which MR > MC
and stopping right before the unit for which MR < MC
In our case, price of output stays constant throughout
therefore MR = P
(an extra unit increases TR by the amount it sells for)
If costs are continuous functions of QOUTPUT, then profit
is maximized where
Principle (Marginal approach to profit maximization):
If data is provided in discrete (tabular) form, then
profit is maximized by producing all the units for
which MR > MC
and stopping right before the unit for which MR < MC
In our case, price of output stays constant throughout
therefore MR = P
(an extra unit increases TR by the amount it sells for)
If costs are continuous functions of QOUTPUT, then profit
is maximized where MR=MC
What if FC is $100,000 instead of $10,000? How does the
profit maximization point change?
Output
FC
VC
TC
TR
Profit
0
10,000
0
10,000
0
–10,000
100
10,000
10,000
20,000
36,000
16,000
200
10,000
15,000
25,000
72,000
47,000
300
10,000
30,000
40,000
108,000
68,000
400
10,000
50,000
60,000
144,000
84,000
500
10,000
90,000
100,000 180,000
80,000
600
10,000
140,000
150,000 216,000
66,000
What if FC is $100,000 instead of $10,000? How does the
profit maximization point change?
Output
FC
VC
TC
TR
Profit
0
100,000
0
10,000
0
–10,000
100
100,000
10,000
20,000
36,000
16,000
200
100,000
15,000
25,000
72,000
47,000
300
100,000
30,000
40,000
108,000
68,000
400
100,000
50,000
60,000
144,000
84,000
500
100,000
90,000
100,000 180,000
80,000
600
100,000 140,000
150,000 216,000
66,000
What if FC is $100,000 instead of $10,000? How does the
profit maximization point change?
Output
FC
VC
TC
TR
Profit
0
100,000
0
100,000
0
–10,000
100
100,000
10,000
110,000
36,000
16,000
200
100,000
15,000
115,000
72,000
47,000
300
100,000
30,000
130,000 108,000
68,000
400
100,000
50,000
150,000 144,000
84,000
500
100,000
90,000
190,000 180,000
80,000
600
100,000 140,000
240,000 216,000
66,000
What if FC is $100,000 instead of $10,000? How does the
profit maximization point change?
Output
FC
VC
TC
TR
Profit
0
100,000
0
100,000
0
–100,000
100
100,000
10,000
110,000
36,000
–74,000
200
100,000
15,000
115,000
72,000
–43,000
300
100,000
30,000
130,000 108,000 –22,000
400
100,000
50,000
150,000 144,000
500
100,000
90,000
190,000 180,000 –10,000
600
100,000 140,000
240,000 216,000 –24,000
–6,000
What if FC is $100,000 instead of $10,000? How does the
profit maximization point change?
Output
FC
VC
TC
TR
Profit
0
100,000
0
100,000
0
–100,000
100
100,000
10,000
110,000
36,000
–74,000
200
100,000
15,000
115,000
72,000
–43,000
300
100,000
30,000
130,000 108,000 –22,000
400
100,000
50,000
150,000 144,000
500
100,000
90,000
190,000 180,000 –10,000
600
100,000 140,000
240,000 216,000 –24,000
–6,000
Principle:
Fixed cost does not affect the firm’s optimal shortterm output decision and can be ignored while
deciding how much to produce today.
Consistently low profits may induce the firm to close down
eventually (in the long run) but not any sooner than your fixed
inputs become variable
( your building lease expires,
your equipment wears out and new equipment needs to be purchased,
you are facing the decision of whether or not to take out a new loan,
etc.)
Sometimes, it is more convenient to formulate a problem not
through costs as a function of output but through output
(product) as a function of inputs used.
Problem 2 on p.194.
“Diminishing returns” – what are they?
In the short run, every company has some inputs fixed
and some variable. As the variable input is added,
every extra unit of that input increases the total output
by a certain amount; this additional amount is called
“marginal product”.
The term, diminishing returns, refers to the situation
when the marginal product of the variable input starts
to decrease (even though the total output may still
keep going up!)
Total output, or Total Product, TP
Amount of input used
Marginal product, MP
Range of diminishing
returns
Amount of input used
Calculating the marginal product (of capital)
for the data in Problem 2:
K
0
1
2
3
4
5
6
L
20
20
20
20
20
20
20
Q
0
50
150
300
400
450
475
MPK
Calculating the marginal product (of capital)
for the data in Problem 2:
K
0
1
2
3
4
5
6
L
20
20
20
20
20
20
20
Q
0
50
150
300
400
450
475
MPK
--50
Calculating the marginal product (of capital)
for the data in Problem 2:
K
0
1
2
3
4
5
6
L
20
20
20
20
20
20
20
Q
0
50
150
300
400
450
475
MPK
--50
100
150
100
50
25
In other words, we know we are in the range of
diminishing returns when the marginal product of the
variable input starts falling, or, the rate of increase in
total output slows down.
(Ex: An extra worker is not as useful as the one before him)
Implications for the marginal cost relationship:
Worker #10 costs $8/hr, makes 10 units. MCunit =
In other words, we know we are in the range of
diminishing returns when the marginal product of the
variable input starts falling, or, the rate of increase in
total output slows down.
(Ex: An extra worker is not as useful as the one before him)
Implications for the marginal cost relationship:
Worker #10 costs $8/hr, makes 10 units. MCunit = $0.80
Worker #11 costs $8/hr, makes …
In other words, we know we are in the range of
diminishing returns when the marginal product of the
variable input starts falling, or, the rate of increase in
total output slows down.
(Ex: An extra worker is not as useful as the one before him)
Implications for the marginal cost relationship:
Worker #10 costs $8/hr, makes 10 units. MCunit = $0.80
Worker #11 costs $8/hr, makes 8 units. MCunit =
In other words, we know we are in the range of
diminishing returns when the marginal product of the
variable input starts falling, or, the rate of increase in
total output slows down.
(Ex: An extra worker is not as useful as the one before him)
Implications for the marginal cost relationship:
Worker #10 costs $8/hr, makes 10 units. MCunit = $0.80
Worker #11 costs $8/hr, makes 8 units. MCunit = $1
In the range of diminishing returns, MP of input is falling
and MC of output is increasing
Marginal cost, MC
Amount of output
Marginal product, MP
This amount of output
corresponds to
this amount of input
Amount of input used
When MP of input is decreasing, MC of
output is increasing and vice versa.
Therefore the range of diminishing
returns can be identified by looking at
either of the two graphs.
(Diminishing marginal returns set in at
the max of the MP graph, or at the min
of the MC graph)
Back to problem 2, p.194.
To find the profit maximizing amount of input (part d), we will
once again use the marginal approach, which compares the
marginal benefit from a change to the marginal cost of than
change.
More specifically, we compare VMPK, the value of marginal
product of capital, to the price of capital, or the “rental rate”, r.
K
0
1
2
3
4
5
6
L
20
20
20
20
20
20
20
Q
0
50
150
300
400
450
475
MPK
--50
100
150
100
50
25
VMPK
r
Back to problem 2, p.194.
To find the profit maximizing amount of input (part d), we will
once again use the marginal approach, which compares the
marginal benefit from a change to the marginal cost of than
change.
More specifically, we compare VMPK, the value of marginal
product of capital, to the price of capital, or the “rental rate”, r.
K
0
1
2
3
4
5
6
L
20
20
20
20
20
20
20
Q
0
50
150
300
400
450
475
MPK
--50
100
150
100
50
25
VMPK
--100
200
300
200
100
50
r
Back to problem 2, p.194.
To find the profit maximizing amount of input (part d), we will
once again use the marginal approach, which compares the
marginal benefit from a change to the marginal cost of than
change.
More specifically, we compare VMPK, the value of marginal
product of capital, to the price of capital, or the “rental rate”, r.
K
0
1
2
3
4
5
6
L
20
20
20
20
20
20
20
Q
0
50
150
300
400
450
475
MPK
--50
100
150
100
50
25
VMPK
--100
200
300
200
100
50
r
>
>
>
>
>
<
75
75
75
75
75
75
STOP
Back to problem 2, p.194.
To find the profit maximizing amount of input (part d), we will
once again use the marginal approach, which compares the
marginal benefit from a change to the marginal cost of than
change.
More specifically, we compare VMPK, the value of marginal
product of capital, to the price of capital, or the “rental rate”, r.
K
0
1
2
3
4
5
6
L
20
20
20
20
20
20
20
Q
0
50
150
300
400
450
475
MPK
--50
100
150
100
50
25
VMPK
--100
200
300
200
100
50
r
>
>
>
>
>
<
75
75
75
75
75
75
STOP
Why would we ever want to be in the range of
diminishing returns?
Consider the simplest case when the price of output
doesn’t depend on how much we produce.
Until we get to the DMR range, every next worker is
more valuable than the previous one, therefore we
should keep hiring them.
Only after we get to the DMR range and the MP starts
falling, we should consider stopping.
Therefore, the profit maximizing point is always in the
diminishing marginal returns range!
Surprised?