2015, FTU Kieu Minh Choosing Inputs 17 We will address how to minimize cost for a given level of output by combining isocosts with isoquants We choose the output we wish to produc
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Chapter 4
Theories of Producer
Behavior
MICROECONOMICS
1
By Tran ThiKieu Minh, MSc
2015, FTU Kieu Minh
Part 2- Contents
1 Production in the Long-run
2 Cost in the Long –run
2
2015, FTU Kieu Minh
4.4 Production in the Long-run
Two Variable Inputs
Firm can produce output by combining
different amounts of labor and capital
2015, FTU Kieu Minh
Production: Two Variable Inputs
The information can be represented graphically using isoquants
◦Curves showing all possible combinations of inputs that yield the same output
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Isoquant Map
5
Labor per year
1 2 3 4 5
Ex: 55 units of output can be produced with 3K & 1L (pt A)
OR 1K & 3L (pt D)
q 1 = 55
q 2 = 75
q 3 = 90
1
2
3
4
5
Capital
per year
D
E
A B C
2015, FTU Kieu Minh
Production: Two Variable Inputs
6
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)
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
2015, FTU Kieu Minh
Production: Two Variable Inputs
The marginal rate of technical substitution
equals:
) of level fixed a
L K
MRTS
input Labor in
Change
input Capital in
Change
MRTS
2015, FTU Kieu Minh
Marginal Rate of Technical Substitution
Labor per month
1
2
3
4
1 2 3 4 5
5 Capital per year
Slope measures MRTS MRTS decreases as move down the indifference curve
1
1
1
1
2
1
2/3 1/3
Q 1 =55
Q 2 =75
Q 3 =90
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MRTS and Isoquants
9
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
2015, FTU Kieu Minh
Isoquants: Special Cases
10
Two extreme cases show the possible range of input substitution in production
1 Perfect substitutes
◦ MRTS is constant at all points on isoquant
◦ Same output can be produced with a lot of capital
or a lot of labor or a balanced mix
2015, FTU Kieu Minh
Perfect Substitutes
Labor per month
Capital
per
month
Q 1 Q 2 Q 3
A
B
C
Same output can be reached with mostly capital or mostly labor (A
or C) or with equal amount of both (B)
2015, FTU Kieu Minh
Isoquants: Special Cases
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
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Fixed-Proportions
Production Function
13
Labor per month
Capital
per
month
L 1
A
Q 2
Q 3
B
C
Same output can only
be produced with one set of inputs
2015, FTU Kieu Minh
4.5 Cost in the Long Run
14
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
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
2015, FTU Kieu Minh
Cost in the Long Run
Total cost of production
C = wL + rK
or K = C/r - (w/r)L
The Isocost Line
◦A line showing all combinations of L & K that can be
purchased for the same cost
◦For each different level of cost, the equation shows
another isocost line
2015, FTU Kieu Minh
Isocost Line
Labor per year
Capital per year
C 0 C 1 C 2
A
K 1
L 1
K 3
L 3
K 2
L 2
w r
Slope
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Choosing Inputs
17
We will address how to minimize cost for a
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
◦Isoquant is the quantity we wish to produce
◦Isocost is the combination of K and L that gives a set
cost
2015, FTU Kieu Minh
Producing a Given Output at Minimum Cost
18 Labor per year
Capital per year
Isocost C 2 shows quantity
Q 1 can be produced with
combination K 2 L 2 or K 3 L 3
However, both of these are higher cost combinations
than K 1 L 1
Q 1
Q 1 is an isoquant for output Q 1
There are three isocost lines, of which 2 are possible choices in which to produce Q1
C 0 C 1 C 2
A
K 1
L 1
K 3
L 3
K 2
L 2
2015, FTU Kieu Minh
Choosing Inputs
How does the isocost line relate to the firm’s
production process?
K L MP MP
L K
r
w L
K
line isocost
of
Slope
cost minimizes firm
when
r w MP
MP
K
2015, FTU Kieu Minh
Choosing Inputs
The minimum cost combination can then be written as:
◦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
r
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Quiz
21
If w = $10, r = $20, and MPL = MPK, which input
would be used more of?
20 10
K
L MP MP
2015, FTU Kieu Minh
Ex
A firm operates with the production function Q = K2L 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?
22
2015, FTU Kieu Minh
Cost in the Long Run
Cost minimization with Varying Output Levels
◦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
◦Slope equals K/L
2015, FTU Kieu Minh
A Firm’s Expansion Path
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
Expansion Path
Capital per year
25
50
75
100
150
50 100 150 200 300 Labor per year
A
$200
0
200 Units
B
$3000
300 Units
C
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Expansion Path & Long-run Costs
25
Firms expansion path has same information as
long-run total cost curve
To move from expansion path to LR cost curve
◦Find tangency with isoquant and isocost
◦Determine min cost of producing the output level
selected
◦Graph output-cost combination
2015, FTU Kieu Minh
A Firm’s Long-Run Total Cost Curve
26
Long Run Total Cost
Output, Units/yr
100 200 300
Cost/
Year
1000
2000
3000
D
E
F
2015, FTU Kieu Minh
Long-Run Versus
Short-Run Cost Curves
Long-Run Average Cost (LAC)
◦ Most important determinant of the shape of the
LR AC and MC curves is relationship between
scale of the firm’s operation and inputs required to
min cost
1 Constant Returns to Scale
◦ If input is doubled, output will double
◦ AC cost is constant at all levels of output
2015, FTU Kieu Minh
Long-Run Versus Short-Run Cost Curves
2 Increasing Returns to Scale
◦ If input is doubled, output will more than double
◦ AC decreases at all levels of output
3 Decreasing Returns to Scale
◦ If input is doubled, output will less than double
◦ AC increases at all levels of output
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Long-Run Versus Short-Run Cost
Curves
29
In the long-run:
◦Firms experience increasing and decreasing returns
to scale and therefore long-run average cost is “U”
shaped
◦Source of U-shape is due to returns to scale rather
than diminishing marginal returns to a factor of
production
◦Long-run marginal cost curve measures the change in
long-run total costs as output is increased by 1 unit
2015, FTU Kieu Minh
Long-Run Versus Short-Run Cost Curves
30
Long-run marginal cost leads long-run average cost:
◦If LMC < LAC, LAC will fall
◦If LMC > LAC, LAC will rise
◦Therefore, LMC = LAC at the minimum of LAC
In special case where LAC if constant, LAC and LMC are equal
2015, FTU Kieu Minh
Long-Run Average and Marginal
Cost
Output
Cost
($ per unit
of output
LAC LMC
A
2015, FTU Kieu Minh
Long Run Costs
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
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
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Long Run Costs
33
At some point, AC will begin to increase
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
2015, FTU Kieu Minh
Long Run Costs
34
When input proportions change, the firm’s expansion path is no longer a straight line
◦Concept of return to scale no longer applies
Economies of scale reflects input proportions that change as the firm change its level of production
Unlike returns to scale, economies of scale allows inputs proportions vary
2015, FTU Kieu Minh
Economies and Diseconomies of
Scale
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
2015, FTU Kieu Minh
Quiz
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
37
We will use short and long-run cost to
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,
the firm may not be able to change plant size
for a while
2015, FTU Kieu Minh
Average total cost in the short and long runs
38
Average Total
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
Quantity of Cars per Day
0
ATC in short run with small factory
ATC in short run with medium factory
ATC in short run with large factory
LAC
10,000
$12,000
1,000 1,200
Economies
of scale Constant returns to scale Diseconomies of scale
2015, FTU Kieu Minh
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
2015, FTU Kieu Minh
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