KINH TẾ VI MÔ 2015 chapter 4 (part 2) micro 1 5 producers choice

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Part 2- Contents
1. Production in the Long-run

Chapter 4

2. Cost in the Long –run

MICROECONOMICS

Theories of Producer
Behavior
By Tran ThiKieu Minh, MSc.

2015, FTU Kieu Minh

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4.4. Production in the Long-run

2

Production:Two Variable Inputs

 Two Variable Inputs

 The information can be represented graphically

 Firm can produce output by combining

using isoquants

different amounts of labor and capital

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◦ Curves showing all possible combinations of inputs
that yield the same output

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Isoquant Map
Capital
per year

Production:Two Variable Inputs


E

5

4

3
A

B

C

2
q3 = 90

D

1

q2 = 75

 Amount by which the quantity of one input can be reduced when
one extra unit of another input is used, so that output remains
constant.

q1 = 55
1

2

3

4

5

Labor per year

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Substituting Among Inputs
◦ There is a trade-off between inputs allowing them to use
more of one input and less of another for the same level
of output.
◦ Slope of the isoquant shows how one input can be
substituted for the other and keep the level of output
the same.
◦ Positive slope is the marginal rate of technical
substitution (MRTS)

Ex: 55 units of output
can be produced with
3K & 1L (pt. A)
OR
1K & 3L (pt. D)

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Marginal Rate of
Technical Substitution

Production:Two Variable Inputs

Capital
per year

 The marginal rate of technical substitution

equals:

5

4

Changein Capital input
Changein Labor input
MRTS   K
(for a fixed level of q )
L
MRTS 

Slope measures MRTS
MRTS decreases as move down
the indifference curve

2

1

3

1
1

2

Q3 =90

2/3 1
1/3

1

Q2 =75
1

Q1 =55
1
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2

3

4

5

Labor per month
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MRTS and Isoquants

Isoquants: Special Cases

Diminishing MRTS occurs because of diminishing returns
and implies isoquants are convex.
 There is a relationship between MRTS and marginal
products of inputs. If we are holding output constant


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Two extreme cases show the possible range of
input substitution in production
1. Perfect substitutes


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B

C

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Q2

Q3

Extreme cases (cont.)

2. Perfect Complements
◦ Fixed proportions production function
◦ There is no substitution available between inputs
◦ The output can be made with only a specific
proportion of capital and labor
◦ Cannot increase output unless increase both
capital and labor in that specific proportion

Same output can be
reached with mostly
capital or mostly labor (A
or C) or with equal
amount of both (B)

Q1

Same output can be produced with a lot of capital
or a lot of labor or a balanced mix

Isoquants: Special Cases


A

MRTS is constant at all points on isoquant

◦

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Perfect Substitutes
Capital
per
month

◦

Labor
per month
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Fixed-Proportions
Production Function

4.5 Cost in the Long Run


Capital
per
month

Same output can only
be produced with one
set of inputs.





Q3

C

B

Q1
A
Labor
per month
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Assumptions

◦ Two Inputs: Labor (L) & capital (K)
◦ Price of labor: wage rate (w)
◦ The price of capital
 r = depreciation rate + interest rate
 Or rental rate if not purchasing
 These are equal in a competitive capital market

Q2

K1

In the long run a firm can change all of its inputs
In making cost minimizing choices, must look at the
cost of using capital and labor in production
decisions

L1
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Isocost Line

Cost in the Long Run

Capital
per
year

 Total cost of production

C = wL + rK

K2

or K = C/r - (w/r)L
 The Isocost Line

 r

◦ A line showing all combinations of L & K that can be
purchased for the same cost

Slope   w

◦ For each different level of cost, the equation shows
another isocost line

A
K1

K3
C0
L2

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L1

C1
L3

C2
Labor per year
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Producing a Given Output at
Minimum Cost

Choosing Inputs
 We will address how to minimize cost for a

Capital
per
year

given level of output by combining isocosts with
isoquants
 We choose the output we wish to produce and
then determine how to do that at minimum
cost

Q1 is an isoquant for output Q1.
There are three isocost lines, of
which 2 are possible choices in
which to produce Q1

K2

Isocost C2 shows quantity
Q1 can be produced with
combination K2L2 or K 3L3.
However, both of these
are higher cost combinations
than K 1L1.

A

◦ Isoquant is the quantity we wish to produce
◦ Isocost is the combination of K and L that gives a set
cost

K1

Q1

K3

C0
L2
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 The minimum cost combination can then be

written as:

production process?

L

 MPL

Slope of isocost line  K

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MPK

w

r

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Choosing Inputs

 How does the isocost line relate to the firm’s

MPL

Labor per year

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Choosing Inputs

MRTS  - K

C2

C1
L3

L1

MPL
MPK

L

 w

◦

r

w

 MPK

r

Minimum cost for a given output will occur when
each dollar of input added to the production process
will add an equivalent amount of output.

when firmminimizes cost

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Ex

Quiz
 If w = $10, r = $20, and MPL = MP K, which input

would be used more of?

MPL MPK

10 20

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A firm operates with the production function Q = K 2 L. The
manager has been given a production target: Produce 8,000
units per day. She knows that the daily rental price of capital is
$400 per unit. The wage rate paid to each worker is $200 day.
a) Currently the firm employs at 80 workers per day. What is the
firm’s daily total cost if it rents just enough capital to produce
at its target?
b) Compare the marginal product per dollar sent on K and on L
when the firm operates at the input choice in part (a). What
does this suggest about the way the firm might change its
choice of K and L if it wants to reduce the total cost in
meeting its target?
c) In the long run, how much K and L should the firm choose if it
wants to minimize the cost of producing 8,000 units of output
day? What will the total daily cost of production be?

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A Firm’s Expansion Path

Cost in the Long Run
 Cost minimization with Varying Output Levels

Capital
per
year

◦ For each level of output, there is an isocost curve
showing minimum cost for that output level
◦ A firm’s expansion path shows the minimum cost
combinations of labor and capital at each level of
output.

The expansion path illustrates
the least-cost combinations of
labor and capital that can be
used to produce each level of
output in the long-run.

150 $3000

Expansion Path
$200

100 0

C
75

◦ Slope equals K/L

B
50
300 Units

A

25
200 Units

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50

100

150

200

300

Labor per year
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A Firm’s Long-Run Total Cost
Curve

Expansion Path & Long-run Costs
 Firms expansion path has same information as

Cost/
Year

long-run total cost curve
 To move from expansion path to LR cost curve

Long Run Total Cost
F
3000

◦ Find tangency with isoquant and isocost

E

◦ Determine min cost of producing the output level
selected
◦ Graph output-cost combination

2000

D

1000

100
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Long-Run Versus
Short-Run Cost Curves


If input is doubled, output will double
AC cost is constant at all levels of output.

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Output, Units/yr
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2. Increasing Returns to Scale

Most important determinant of the shape of the

LR AC and MC curves is relationship between
scale of the firm’s operation and inputs required to
min cost

1. Constant Returns to Scale

◦
◦

300

Long-Run Versus Short-Run Cost
Curves

Long-Run Average Cost (LAC)
◦

200

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◦
◦

If input is doubled, output will more than double
AC decreases at all levels of output.

3. Decreasing Returns to Scale

◦

If input is doubled, output will less than double

◦

AC increases at all levels of output

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Long-Run Versus Short-Run Cost
Curves

Long-Run Versus Short-Run Cost
Curves

 In the long-run:
◦ Firms experience increasing and decreasing returns
to scale and therefore long-run average cost is “U”
shaped.
◦ Source of U-shape is due to returns to scale rather
than diminishing marginal returns to a factor of

production
◦ Long-run marginal cost curve measures the change in
long-run total costs as output is increased by 1 unit

 Long-run marginal cost leads long-run

average cost:
◦ If LMC < LAC, LAC will fall
◦ If LMC > LAC, LAC will rise
◦ Therefore, LMC = LAC at the minimum of
LAC
 In special case where LAC if constant,

LAC and LMC are equal
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Long-Run Average and Marginal
Cost

Long Run Costs


Cost
($ per unit
of output

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LMC

As output increases, firm’s AC of producing is
likely to decline to a point
1. On a larger scale, workers can better specialize
2. Scale can provide flexibility – managers can
organize production more effectively

LAC

A

3. Firm may be able to get inputs at lower cost if it
can get quantity discounts. Lower prices might
lead to different input mix
Output

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Long Run Costs


Long Run Costs

At some point, AC will begin to increase

 When input proportions change, the firm’s

1. Factory space and machinery may make it more
difficult for workers to do their job efficiently
2. Managing a larger firm may become more complex
and inefficient as the number of tasks increase
3. Bulk discounts can no longer be utilized. Limited
availability of inputs may cause price to rise

 Economies of scale reflects input proportions

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expansion path is no longer a straight line
◦ Concept of return to scale no longer applies

that change as the firm change its level of
production
 Unlike returns to scale, economies of scale
allows inputs proportions vary

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Economies and Diseconomies of
Scale

34

Quiz

 Economies of Scale
◦ Increase in output is greater than the increase in
inputs.
 Diseconomies of Scale
◦ Increase in output is less than the increase in inputs.
 U-shaped LAC shows economies of scale for

relatively low output levels and diseconomies of
scale for higher levels

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In the long run for Firm A, total cost is $105 when
output is 3 units and $120 when output is 4 units.
Does Firm A exhibit economies or diseconomies of
scale?
a. Diseconomies of scale, since total cost is rising as

output rises.
b. Diseconomies of scale, since average total cost is
falling as output rises.
c. Economies of scale, since total cost is rising as output
rises.
d. Economies of scale, since average total cost is falling
as output rises.
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Long-Run Versus Short-Run Cost
Curves

Average total cost in the short and long runs
Average
Total
Cost

 We will use short and long-run cost to

ATC in short ATC in short
run with
run with
small factory medium factory

ATC in short
run with
large factory

LAC

determine the optimal plant size
 We can show the short run average costs for 3

different plant sizes
 This decision is important because once built,

$12,000

the firm may not be able to change plant size
for a while

10,000
Economies
of scale

Constant returns to scale

Diseconomies
of scale

0
1,000 1,200
Quantity of Cars per Day

Because fixed costs are variable in the long run, the average-total-cost curve in the short run differs
from the average-total-cost curve in the long run.
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Average total cost in the short and long
runs
 Firm will always choose plant that minimizes the

average cost of production
 The long-run average cost curve envelopes the

short-run average cost curves
 The LAC curve exhibits economies of scale
initially but exhibits diseconomies at higher
output levels

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The firm experiences diseconomies of scale if it changes its
level of output
 a. from Q1 to Q2.
 b. from Q2 to Q3.
 c. from Q3 to Q4.
 d. from Q4 to Q5.



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