Download Lecture 2--Production, Economics Costs, Economic Profit

Lecture 2
Production, Costs, Profits
1
Overview
Production functions
– Short run vs. Long run
– Returns to a factor
– Returns to scale
Costs
– Types of costs
– Cost curves
Choice of Inputs
– Minimum efficient scale
2
Production Function
The Production Function indicates the
highest output that a firm can produce for
every specified combination of inputs
given the state of technology.
Shows what is technically feasible when
the firm operates efficiently.
Want the production function general
enough to describe what Boeing does as
well as what Microsoft does.
3
Production Function
The production function for two inputs:
Q = F(K,L)
Q = Output, K = Capital, L = Labor
For a given technology.
– Change technology and get a different F().
Just a way of expressing how inputs are
combined to make outputs.
4
Production Function
Examples
Q=2K+5L
Q=1/2(K*L)
Suppose production function for bagels is:
– Q=3L*4D, where L=number of workers
D=pounds of dough
– With 3 workers an 2 pounds of dough we get
72 bagels
5
Production Function
Example of different technology
– Use a standard drill to extract oil from the
ground or extract oil using hydraulic fracturing
Different technology but the output is the
same—oil
6
Production Function
Observations:
1) For any level of K, output increases
with more L.
2) For any level of L, output increases
with more K.
3) Various combinations of inputs
produce the same output.
7
Isoquant
Draw a curve showing all the possible
combinations of inputs that produce the
same output.
– Call this curve an isoquant.
Consider the following table showing how
many tons of steel we get from various
amounts of capital and labor.
8
Production of Steel
Labor Input
Capital Input 1
2
3
4
5
1
20
40
55
65
75
2
40
60
75
85
90
3
55
75
90
100
105
4
65
85
100
110
115
5
75
90
105
115
120
9
Production with Two Variable Inputs (L,K)
Capital
per year
The Isoquant Map
E
5
4
3
A
B
The isoquants are derived
from the production
function for output
of 55, 75, and 90.
C
2
Q3 = 90
D
1
Q2 = 75
Q1 = 55
1
2
3
4
5
Labor per year
10
Isoquants
 The isoquants emphasize how different input
combinations can be used to produce the same
output.
 This information allows the producer to respond
efficiently to changes in the markets for inputs.
 An isoquant is drawn assuming both factors can
be changed.
– It may take longer to vary some inputs
11
Short Run vs. Long Run

Short-Run is the period of time in which
quantities of one or more factors of
production cannot be changed.

These inputs are called fixed inputs.

Long-Run is the amount of time needed to
make all production inputs variable.
12
Short Run vs. Long Run
Not a set time period. Varies from firm to
firm and depends on the production
function.
Example
– Takes a bank a relatively short period of time
to replace all of their desk-top computers.
Short-run.
– Takes General Motors a long time to re-tool
all of their assembly lines. Long-run.
13
Consider production in the short-run with
one variable input (Labor)
Amount
of Labor (L)
Amount
Total
of Capital (K) Output (Q)
Average
Product
Marginal
Product
0
10
0
---
---
1
10
10
10
10
2
10
30
15
20
3
10
60
20
30
4
10
80
20
20
5
10
95
19
15
6
10
108
18
13
7
10
112
16
4
8
10
112
14
0
9
10
108
12
-4
10
10
100
10
-814
Production with one variable input (Labor)
With additional workers output (Q) initially
increases, reaches a maximum, and then
decreases.
The average product of labor (AP), or
output per worker, increases and then
decreases.
Output
Q
AP =
=
Labor Input L
15
Production with one variable input (Labor)
The marginal product of labor (MP), or
output of the additional worker, increases
rapidly initially and then decreases and
becomes negative.
∆Output
∆Q
MPL =
=
∆Labor Input ∆L
16
Production with one variable input (Labor)
Output
per
Month
D
112
Total Product
C
60
A: slope of tangent = MP (20)
B: slope of 0B = AP (20)
C: slope of 0C= MP & AP
B
A
0 1
2 3
4
5 6
7 8
9
10 Labor per Month
17
Production with one variable input (Labor)
Output
per
Month
Observations:
Left of E: MP > AP & AP is increasing
Right of E: MP < AP & AP is decreasing
E: MP = AP & AP is at its maximum
30
Marginal Product
E
20
Average Product
10
0 1
2 3
4
5 6
7 8
9
10 Labor per Month
18
Production with one variable input (Labor)
When MP = 0, TP is at its maximum
 When MP > AP, AP is increasing
 When MP < AP, AP is decreasing
 When MP = AP, AP is at its maximum

19
Production with one variable input (Labor)
As the use of an input increases in equal
increments, a point will be reached at
which the resulting additions to output
decreases (i.e. MP declines).
Known as the Law of Diminishing Marginal
Returns.
20
Law of Diminishing Marginal Returns
When the labor input is small, MP
increases due to specialization.
When the labor input is large, MP
decreases due to inefficiencies.
21
Production with one variable input (Labor)
Assumes the quality of the variable input is
constant.
Explains a declining MP, not necessarily a
negative one
Assumes a constant technology
22
The Effect of Technological Improvement
Output
per
time
period
Labor productivity
can increase if there
are improvements in
technology, even though
any given production
process exhibits
diminishing returns to
labor.
C
100
B
O3
A
O2
50
O1
0 1
2 3
4
5 6
7 8
9
10
Labor per
time period
23
Production with Two Variable Inputs
Back to the world where we have two
inputs into production, K & L, and we can
vary each factor.
Isoquants allow us to analyze and
compare the different combinations of K &
L and output
Also can see that we have diminishing
marginal returns for both inputs.
24
The Shape of Isoquants
Capital
per year
F
5
4
3
A
B
In the long run both
labor and capital are
variable and both
experience diminishing
returns.
C
E
2
Q3 = 90
D
1
Q2 = 75
Q1 = 55
1
2
3
4
5
Labor per year
25
Production with Two Variable Inputs
Assume capital is 3 and labor increases
from 0 to 1 to 2 to 3 (A→B→C).
–
Notice output increases at a decreasing rate
(55, 20, 15) illustrating diminishing returns
from labor in the short-run and long-run.
Assume labor is 3 and capital increases
from 0 to 1 to 2 to 3 (D→E→C).
–
Output also increases at a decreasing rate
(55, 20, 15) due to diminishing returns from
capital.
26
The Shape of Isoquants

The slope of each isoquant shows the
trade-off between two inputs while keeping
output constant.
–

Similar to the slope of the indifference curve.
Call the slope of the isoquant the marginal
rate of technical substitution (MRTS).
27
Marginal Rate of Technical Substitution

The marginal rate of technical substitution
equals:
MRTS = - Change in capital/Change in labor input
MRTS = − ∆K
∆L
(for a fixed level of Q)
28
Returns to Scale
One of the things we need to consider
when determining how much to produce is
the most efficient scale of operation
Suppose we have a hospital treating 100
patients a day with L=20 and K=30.
Further suppose that they can double L &
K to L=40 and K=60 and treat 250 patients
a day.
More efficient to operate at the higher level
of output.
29
Returns to scale
 Returns to Scale measures the
relationship between the scale or size of
a firm and output.
 3 possibilities.
30
Returns to Scale
1. Increasing returns to scale: output more
than doubles when all inputs are doubled
•
Larger output associated with lower cost (autos)
•
One firm is more efficient than many (utilities)
2. Constant returns to scale: output doubles
when all inputs are doubled
•
Size does not affect productivity
•
May have a large number of producers
31
Returns to Scale
3. Decreasing returns to scale: output less than
doubles when all inputs are doubled
•
Decreasing efficiency with large size
•
Reduction of managerial abilities
32
Returns to Scale
Important to note that decreasing returns
to scale is not the same as the law of
diminishing returns.
– The law of diminishing returns is a short-run
concept and tells us that marginal output will
fall as we add more of one input holding the
other input fixed.
– Decreasing returns to scale is a long-run
concept and says that output goes up by less
than twice as much when we double all
inputs.
33
Returns to Scale—Example
 Suppose we are operating a firm with the
following production function:
Q = 100 K
1
2
1
L
2
34
Returns to Scale—Example
L
K
Q
1
1
100
2
2
200
4
4
400
8
8
800
35
Returns to Scale—Example
 Now consider the following production
function:
1
Q = 100 K L
2
36
Returns to Scale—Example
L
K
Q
1
1
100
2
2
282.8
4
4
800
8
8
2262.7
37
Measuring Costs: Which Costs Matter?
 Start by considering the following costs
1. Accounting Cost
–
Actual expenses plus depreciation charges
for capital equipment
2. Economic Cost
–
Cost to a firm of utilizing economic
resources in production, including
opportunity cost
38
Opportunity Cost
Opportunity Cost is the value of a resource
when the resource is employed in it’s best
alternative use.
39
Opportunity Cost—Example
Consider a bank which owns the building
where it’s headquarters is located.
When figuring it’s costs of doing business,
should the bank say that it pays zero rent?
– No, they could sell the building to another firm
and then pay that other firm a rent.
– If this alternative way of doing business is
cheaper, then that is what the bank should do.
40
Opportunity Costs
Whenever we talk about costs in this class
we will talk about the cost including the
opportunity cost.
This includes the cost of labor.
– what the workers could earn working
somewhere else.
As well as the cost of capital.
– The return the capital could earn invested
somewhere else.
41
Accounting and Economic Profits
 Accounting profit = Sales – Accounting cost
 Economic profit = Sales – Economic cost
 Economic profit = Accounting profit – (Economic
cost – Accounting cost)
 Ignoring opportunity costs may overstate the
profitability of a firm
42
Sunk Cost
Another type of economic cost is Sunk
Cost.
Sunk Cost
–
–
Expenditure that has been made and cannot
be recovered.
Should not influence a firm’s decisions.
43
Sunk Cost—An Example
Consider the recent decision of UK to sell
a pharmaceutical lab for $30M
UK invested $47M to set up the lab;
should this matter?
No. That money is sunk and UK has no
way of recovering it. Only consider the
revenue that is generate from selling the
lab vs. the revenue from continuing to
operate the lab
44
Sunk Cost—An Example
Need to consider the potential return on
investment and riskiness of the venture
prior to making the original investments
when costs aren’t sunk.
45
Measuring Costs: Which Costs Matter?
Next, consider fixed costs and variable
costs.
Total output is a function of variable inputs
and fixed inputs.
Therefore, the total cost of production
equals the fixed cost (the cost of the fixed
inputs) plus the variable cost (the cost of
the variable inputs), or…
TC = FC + VC
46
Measuring Costs: Which Costs Matter?
Fixed Cost (FC)
– Does not vary with the level of output
Variable Cost (VC)
– Cost that varies as output varies
47
Measuring Costs: Which Costs Matter?
It is important to understand the distinction
between fixed costs and sunk costs.
Fixed Cost
– Cost paid by a firm that is in business
regardless of the level of output. Short run
concept
Sunk Cost
– Cost that has been incurred and cannot be
recovered
48
Fixed Costs
Examples of Fixed Costs Include:
– Rent—A dentist must pay the rent on his
office regardless of the number of patients
she sees
– Insurance
– Licenses fee—Dentist must also pay a yearly
fee for her license which does not vary with
the number of patients
– Interest on debt
49
Variable Costs
Costs that vary with the amount of output
you produce include:
– Wages
– Electricity
– Fuel
In general, anything we need more of to
produce more output
50
Costs in the Short Run
Marginal Cost (MC) is the cost of
expanding output by one unit. Since fixed
cost has no impact on marginal cost, it can
be written as:
∆VC ∆TC
MC =
=
∆Q
∆Q
51
Costs in the Short Run
Average Total Cost (ATC) is the cost per
unit of output, or average fixed cost (AFC)
plus average variable cost (AVC). This
can be written as:
TFC TVC
ATC =
+
Q
Q
52
Cost Curves for a Firm
Total cost
is the vertical
sum of FC
and VC.
Cost 400
($ per
year)
TC
VC
Variable cost
increases with
production and
the rate varies with
increasing &
decreasing returns.
300
200
Fixed cost does not
vary with output
100
FC
50
0
1
2
3
4
5
6
7
8
9
10
11
12
13
Output
53
Cost Curves for a Firm
Cost
($ per
unit)
100
MC
75
50
ATC
AVC
25
AFC
0
1
2
3
4
5
6
7
8
9
10
11
Output (units/yr.)
54
Relationship between short-run costs
and productivity
So we have:
w
MC =
MPL
… and a low marginal product (MP) leads
to a high marginal cost (MC) and vice
versa
55
Relationship between short-run costs
and productivity
 Using similar logic we can derive the following
relationship:
w
AVC =
APL
 These equations imply that MC is at a minimum
when MPL is at a maximum and AVC is at a
minimum when APL is at a maximum.
56
Costs in the Long Run
Consider costs in the long run where we
can vary all of our inputs.
– No fixed costs
How does a firm select the inputs needed
to produce a given level of output at a
minimum cost?
– Assume firms want to produce in a way that
minimizes costs.
57
Costs in the Long Run
Assume a firm uses two inputs into
production, capital (K) and labor (L).
Price of labor is w, the wage rate.
Price of capital is r, the user cost of capital
per dollar of capital.
58
Cost Minimizing Input Choice
Define the Isocost line:
–
C = wL + rK
–
Isocost: A line showing all combinations of L
& K that can be purchased for the same cost
59
The Isocost Line
 Rewriting C as linear:
–
–
K = C/r - (w/r)L
Slope of the isocost:
∆K
∆L
( r)
=−w
• is the ratio of the wage rate to rental cost of
capital.
• This shows the rate at which capital can be
substituted for labor with no change in cost.
60
The Isocost Line
Capital
per year
C/r
Slope=-(w/r)
C/w
Labor per year
61
The Isocost Line
Suppose, w=$36,000/year and
r=$18,000/year.
What does the budget line look like when
C=$180,000/year?
62
The Isocost Line
Capital
per year
180,000/18,000=10
Slope=-(36,000/18,000)=-2
180,000/36,000=5
Labor per year
63
Cost Minimizing Input Choice
In order to choose the cost minimizing
input choice we combined the isocost line
with the isoquant.
64
Producing a Given Output at Minimum
Cost
Capital
per
year
Q1 is an isoquant
for output Q1.
Isocost curve C0 shows
all combinations of K and L
that cost C0.
K2
Isocost C2 shows quantity
Q1 can be produced with
combination K2L2 or K3L3.
However, both of these
are higher cost combinations
than K1L1.
CO C1 C2 are
three
isocost lines
A
K1
Q1
K3
C0
L2
L1
C1
L3
C2
Labor per year
65
Costs in the Long Run
Relationship between Isoquants and
Isocosts and the Production Function
MPL
∆
K
MRTS =
−
=
−
∆L
MPK
Slope of isocost line =
− ∆K
=
−w
∆L
r
MPL
MPK
=w
r
66
Costs in the Long Run
The minimum cost combination can then
be written as:
MPL
w
= MPK
r
MPL gives us the additional output we get
from hiring one more unit of labor.
 w tells us the cost of hiring one more unit
of labor

67
Costs in the Long Run
MPL/w tells us how much additional output
we get from spending one more dollar on
labor.
MPK/r tells us how much additional output
we get from spending one more dollar on
capital.
By setting them equal this says that at the
cost minimizing point I get the same
increase in output from a dollar spent on
either capital or labor.
68
Input Substitution When an Input
Price Changes
Consider what happens when we change
prices.
w is now higher so the isocost curve is
steeper.
Assume we want to keep producing same
level of output.
69
Input Substitution When an Input
Price Changes
Capital
per
year
If the price of labor
changes, the isocost curve
becomes steeper due to
the change in the slope -(w/r).
This yields a new combination
of K and L to produce Q1.
Combination B is used in place
of combination A.
The new combination represents
the higher cost of labor relative
to capital and therefore capital
is substituted for labor.
B
K2
A
K1
Q1
C2
L2
L1
C1
Labor per year
70
Long-Run Cost Curves
 Long-Run total costs (LTC) shows how costs
change with output when we vary all inputs
 Long-Run Average Cost (LAC) is given by:
LTC
LAC =
Q
 Long-Run Marginal Cost is given by:
∆LTC
LMC =
∆Q
71
Long-Run Cost Curves
The shape of these curves depends on
whether the production function exhibits
increasing, constant, or decreasing returns
to scale.
72
Long-Run Average Cost (LAC)

Constant Returns to Scale
– If input is doubled, output will double and
average cost is constant at all levels of output.
– LAC curve will be a flat line.

Increasing Returns to Scale
– If input is doubled, output will more than
double and average cost decreases at all
levels of output.
– LAC curve is downward sloping.
73
Long-Run Average Cost (LAC)

Decreasing Returns to Scale
– If input is doubled, the increase in output is
less than twice as large and average cost
increases with output.
– LAC curve is upward sloping.
74
Long-Run Average Cost (LAC)

In the long-run, firms initially experience
increasing returns to scale at low output
and then decreasing returns to scale at
higher output and therefore long-run
average cost is “U” shaped
–
Evidence suggests that it may “L” be shaped
75
Long-Run Average Cost and Long-Run
Marginal Cost
Cost
($ per unit
of output
LMC
LAC
Minimum efficient size
is the firm size where
long-run average cost
is at a minimum
A
At Q* firm is operating
at the minimum
efficient size
Quantity of Output
Q*
76
Minimum Efficient Scale
Q’ = minimum efficient scale
77
Minimum Efficient Scale
Number of firms in an industry is
determined by the minimum efficient scale
of production and the market demand for
the product.
78
Summary
A production function describes the
maximum output a firm can produce for
each specified combination of inputs.
An isoquant is a curve that shows all
combinations of inputs that yield a given
level of output.
79
Summary
Average product of labor measures the
productivity of the average worker,
whereas marginal product of labor
measures the productivity of the last
worker added.
The law of diminishing returns explains
that the marginal product of an input
eventually diminishes as its quantity is
increased.
80
Summary
Managers must take into account the
opportunity cost associated with the use of
the firm’s resources.
Firms are faced with both fixed and
variable costs in the short-run.
81
Summary
When there is a single variable input, as in
the short run, the presence of diminishing
returns determines the shape of the cost
curves.
In the long run, all inputs to the production
process are variable.
A firm enjoys economies of scale when it
can double its output at less than twice the
cost.
82
Summary
In long-run analysis, we focus on the firm’s
choice of its scale or size of operation.
83