7
Production and Cost in the Firm
 How do economists calculate profit?
 What is a production function? What is
marginal product? How are they related?
 What are the various costs, and how are
they related to each other and to output?
 How are costs different in the short run vs.
the long run?
 What are “economies of scale”?
Total Revenue, Total Cost, Profit
 We assume that the firm’s goal is to maximize
profit.
Profit = Total revenue – Total cost
the amount a
firm receives
from the sale
of its output
the market
value of the
inputs a firm
uses in
production
Costs: Explicit vs. Implicit
 Explicit costs – actual cash payments for
resources, such as paying wages to workers
 Implicit costs – opportunity cost of using
owner-supplied resources, such as the
opportunity cost of the owner’s time
 Remember: The cost of something is the value
of the next best alternative.
 This is true whether the costs are implicit or
explicit. Both matter for a firm’s decisions.
Explicit vs. Implicit Costs: An Example
Suppose you need $100,000 to start your business.
The interest rate is 5%.
 Case 1: borrow $100,000
• explicit cost =
 Case 2: use $40,000 of your savings, borrow the
other $60,000
• explicit cost =
• implicit cost =
Economic Profit vs. Accounting Profit
 Accounting profit
= total revenue minus total explicit costs
 Economic profit
= total revenue minus total costs (including
BOTH explicit and implicit costs)
 Accounting profit ignores implicit costs,
so it will be greater than economic profit.
2:
Economic profit vs. accounting profit
ACTIVE LEARNING
The equilibrium rent on office space has just
increased by $500 per month.
Compare the effects on your firm’s accounting
profit and economic profit if
a. you rent your office space
b. you own your office space
5
Production in the Short Run
 Some resources are considered to be variable
and some are considered to be fixed.
• It depends on how quickly the level can be
altered to change the rate of output.
 In the short run, at least one resource is fixed.
 In the long run, all resources are variable.
The Production Function
 A production function shows the relationship
between the quantity of inputs used to produce a
good, and the quantity of output of that good.
 It can be represented by a table, equation, or
graph.
 Example 1:
• Farmer Jack grows wheat.
• He has 5 acres of land.
• He can hire as many workers as he wants.
EXAMPLE 1: Farmer Jack’s Production Function
Q
(# of
(bushels
workers) of wheat)
3,000
Quantity of output
L
2,500
0
0
1
1,000
2
1,800
3
2,400
500
4
2,800
0
5
3,000
2,000
1,500
1,000
0
1
2
3
# of workers
4
5
Marginal Product
 The marginal product of any input is the
increase in output arising from an additional unit
of that input, holding all other inputs constant.
 If Farmer Jack hires one more worker, his output
rises by the marginal product of labor.
 Marginal product of labor (MPL) = ∆Q
∆L
EXAMPLE 1: Total & Marginal Product
L
Q
(# of
(bushels
workers) of wheat)
∆L = 1
∆L = 1
∆L = 1
∆L = 1
∆L = 1
0
0
1
1,000
2
1,800
3
2,400
4
2,800
5
3,000
MPL
∆Q = 1,000
∆Q = 800
∆Q = 600
∆Q = 400
∆Q = 200
EXAMPLE 1: MPL = Slope of Prod. Function
Q
(# of
(bushels MPL
workers) of wheat)
0
0
1,000
1
1,000
800
2
1,800
600
3
4
5
2,400
2,800
3,000
400
200
MPL
3,000
Quantity of output
L
equals the
slope of the
2,500
production function.
2,000
Notice that
MPL diminishes
1,500
as L increases.
1,000
This explains why
500 production
the
function
gets flatter
0
as L0 increases.
1
2
3
4
No. of workers
5
Why MPL Is Important
 Recall from Chapter 1: Rational people choose
actions for which the expected marginal benefit
exceeds the expected marginal cost.
 When Farmer Jack hires an extra worker,
• his costs rise by the wage he pays the worker
• his output rises by MPL
 Comparing the wage and the change in his output
helps Jack decide whether he would benefit from
hiring the worker.
EXAMPLE 2: A “Fold-It” Factory
We are going to create
a factory that produces
a product known as a
“fold-it”
Resources:
• factory
• paper
• stapler
• staples
• labor
Why MPL Diminishes
 The Law of Diminishing Marginal Returns:
the marginal product of a variable resource
eventually falls as the quantity of the resource
used increases (other things equal)
 If we increases the # of workers but not the # of
staplers or the desk area, each add’l worker has
less to work with and will be less productive.
 In general, MPL diminishes as L rises
whether the fixed resource is land (as would be
the case with Jack the wheat farmer) or capital
(our desk and stapler).
EXAMPLE 1: Farmer Jack’s Costs
 Farmer Jack must pay $1,000 per month for the
land, regardless of how much wheat he grows.
 The market wage for a farm worker is $2,000 per
month.
 So Farmer Jack’s costs are related to how much
wheat he produces….
EXAMPLE 1: Farmer Jack’s Costs
L
Q
Cost of
(# of (bushels
land
workers) of wheat)
0
0
1
1,000
2
1,800
3
2,400
4
2,800
5
3,000
Cost of
labor
Total
Cost
EXAMPLE 1: Farmer Jack’s Total Cost Curve
$12,000
Total
Cost
0
$1,000
1,000
$3,000
1,800
$5,000
2,400
$7,000
2,800
$9,000
3,000
$11,000
$10,000
Total cost
Q
(bushels
of wheat)
$8,000
$6,000
$4,000
$2,000
$0
0
1000
2000
3000
Quantity of wheat
Marginal Cost
 Marginal Cost (MC)
is the increase in Total Cost from producing one
more unit:
∆TC
MC =
∆Q
EXAMPLE 1: Total and Marginal Cost
Q
(bushels
of wheat)
0
Total
Cost
$1,000
∆Q = 1000
1,000
$3,000
∆Q = 800
∆Q = 600
∆Q = 400
∆Q = 200
1,800
Marginal
Cost (MC)
$5,000
2,400
$7,000
2,800
$9,000
3,000 $11,000
∆TC = $2000
$2.00
∆TC = $2000
$2.50
∆TC = $2000
$3.33
∆TC = $2000
$5.00
∆TC = $2000
$10.00
EXAMPLE 1: The Marginal Cost Curve
0
TC
MC
$1,000
$2.00
1,000
$3,000
$2.50
1,800
$5,000
$3.33
2,400
$7,000
$10
Marginal Cost ($)
Q
(bushels
of wheat)
$12
$8
MC usually rises
as Q rises,
as in this example.
$6
$4
$2
$5.00
2,800
$9,000
3,000 $11,000
$10.00
$0
0
1,000
2,000
Q
3,000
Why MC Is Important
 Farmer Jack is rational and wants to maximize
his profit. To increase profit, should he produce
more wheat or less?
 To find the answer, Farmer Jack needs to “think at
the margin.”
 If the cost of an additional bushel of wheat (MC) is
less than the revenue he would get from selling it,
Jack’s profits rise if he produces more.
(In the next chapter, we will learn more about
how firms choose Q to maximize their profits.)
EXAMPLE 3
 Our third example is more general, and applies
to any type of firm producing any good with any
types of resources.
EXAMPLE 3: Costs
FC
VC
0 $100
$0
1
100
70
2
100 120
3
100 160
4
100 210
5
100 280
TC
FC
$700
VC
TC
$600
$500
Costs
Q
$800
$400
$300
$200
$100
6
7
100 380
100 520
$0
0
1
2
3
4
Q
5
6
7
EXAMPLE 3: Marginal Cost
TC
MC
0 $100
1
2
3
4
5
6
7
170
220
260
310
380
480
620
$70
50
40
50
70
100
140
$200 Marginal Cost (MC)
Recall,
is $175
the change in total cost from
producing
one more unit:
$150
∆TC
MC =
∆Q
$100
Usually,
MC rises as Q rises, due
$75
to diminishing marginal product.
Costs
Q
$125
$50
Sometimes (as here), MC falls
$25
before rising.
$0
(In other0 examples,
1 2 3 MC
4 may
5 6be 7
constant.)
Q
EXAMPLE 3: Average Fixed Cost
FC
0 $100
1
2
100
100
3
100
4
100
5
100
6
100
7
100
AFC
----
$200
Average
fixed cost (AFC)
is$175
fixed cost divided by the
quantity
of output:
$150
Costs
Q
AFC
$125
= FC/Q
$100
Notice
$75 that AFC falls as Q rises:
The firm is spreading its fixed
$50
costs over a larger and larger
$25
number
of units.
$0
0
1
2
3
4
Q
5
6
7
EXAMPLE 3: Average Variable Cost
VC
0
$0
1
70
2
120
3
160
4
210
5
280
6
380
7
520
AVC
----
$200
Average
variable cost (AVC)
is$175
variable cost divided by the
quantity of output:
$150
Costs
Q
AVC
$125
= VC/Q
$100
As$75
Q rises, AVC may fall initially.
In most cases, AVC will
$50
eventually rise as output rises.
$25
$0
0
1
2
3
4
Q
5
6
7
EXAMPLE 3: Average Total Cost
Q
TC
0 $100
ATC
AFC
AVC
----
----
1
170
$100
$70
2
220
50
60
3
260
33.33
53.33
4
310
25
52.50
5
380
20
56.00
6
480
16.67
63.33
7
620
14.29
74.29
Average total cost
(ATC) equals total
cost divided by the
quantity of output:
ATC = TC/Q
Also,
ATC = AFC + AVC
EXAMPLE 3: Average Total Cost
TC
0 $100
1
2
170
220
ATC
$200
Usually,
as in this example,
$175
the ATC curve is U-shaped.
----
$150
$170
110
Costs
Q
$125
$100
3
260 86.67
4
310 77.50
5
380
76
$25
6
480
80
$0
7
620 88.57
$75
$50
0
1
2
3
4
Q
5
6
7
EXAMPLE 3: The Cost Curves Together
$200
$175
ATC
AVC
AFC
MC
Costs
$150
$125
$100
$75
$50
$25
$0
0
1
2
3
4
Q
5
6
7
ACTIVE LEARNING
Costs
3:
Fill in the blank spaces of this table.
Q
VC
0
1
10
2
30
TC
AFC
AVC
ATC
$50
----
----
----
$10
$60.00
80
3
16.67
4
100
5
150
6
210
150
20
12.50
36.67
8.33
$10
30
37.50
30
260
MC
35
43.33
60
30
EXAMPLE 3: Why ATC Is Usually U-shaped
As Q rises:
$200
Initially,
falling AFC
pulls ATC down.
$175
Costs
Eventually,
rising AVC
pulls ATC up.
$150
$125
$100
$75
$50
$25
$0
0
1
2
3
4
Q
5
6
7
EXAMPLE 3: ATC and MC
When MC < ATC,
ATC is falling.
$175
$150
ATC is rising.
$125
Costs
When MC > ATC,
The MC curve
crosses the
ATC curve at
the ATC curve’s
minimum.
ATC
MC
$200
$100
$75
$50
$25
$0
0
1
2
3
4
Q
5
6
7
Costs in the Long Run
 Short run:
Some inputs are fixed
 Long run:
All inputs are variable (firms can build new
factories, or remodel or sell existing ones)
 In the long run, ATC at any Q is cost per unit
using the most efficient mix of inputs for that Q
(the factory size with the lowest ATC).
EXAMPLE 4: LRAC with 3 Factory Sizes
Firm can choose
from 3 factory
sizes: S, M, L.
Each size has its
own SRATC curve.
The firm can
change to a
different factory
size in the long
run, but not in the
short run.
Cost
($)
ATCS
ATCM
ATCL
Q
EXAMPLE 4: LRAC with 3 Factory Sizes
Cost
($)
ATCS
ATCM
ATCL
LRATC
QA
QB
Q
A Typical LRAC Curve
In the real world,
factories come in
many sizes,
each with its own
SRATC curve.
Cost
LRAC
So a typical LRAC
curve
looks like this:
Q
How LRAC Changes as
the Scale of Production Changes
Economies of
scale: LRAC falls
as Q increases.
Cost
LRAC
Constant returns
to scale: LRAC
stays the same
as Q increases.
Diseconomies of
scale: LRAC rises
as Q increases.
Q