19/09/16 Outline Chapter 4
1.  Introduc-on 2.  The Technology of Produc-on 3.  Produc-on with One Variable Input (Labor) Produc-on 4.  Produc-on with Two Variable Inputs 5.  Returns to Scale 2
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1. Introduc-on 1. Introduc-on Produc-on decisions of a firm: •  Our study of consumer behavior was broken down into 3 steps: –  Describing consumer preferences –  Consumers face budget constraints –  Consumers maximize u-lityà demand •  Produc-on decisions of a firm are similar to consumer decisions –  Technology of produc-on –  Input cost constraint (Chap 5) –  Choice of Inputs à supply (Chap 6) 3
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1.  Produc-on Technology l  Describe how inputs (land, labor, capital and raw materials) can be transformed into outputs (cars, desks, books, etc) l  Firms can produce different amounts of outputs using different combina-ons of inputs 2.  Cost Constraints l  Firms must consider prices of labor, capital and other inputs l  Firms want to minimize total produc-on costs partly determined by input prices 3.  Input Choices l  Min Cost / Max Profit : Given input prices and produc-on technology, the firm must choose how much of each input to use in producing output 4
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2. The Technology of Produc-on 2. The Technology of Produc-on •  Produc-on Func-on (techno of the firm) •  The produc-on func-on for two inputs: q = F(K,L) –  Indicates the highest output (q) that a firm can produce for every specified combina-on of inputs –  For simplicity, we will consider only labor (L) and capital (K) –  Shows what is technically feasible when the firm operates efficiently –  Output (q) is a func-on of capital (K) and labor (L) –  The produc-on func-on is valid for a given technology. –  If technology increases, more output can be produced for a given level of inputs à Produc-on func-on should be adapted. 5
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2. The Technology of Produc-on Short term versus Long term •  Short Run –  Period of -me in which quan--es of one or more produc-on factors cannot be changed –  These inputs are called fixed inputs •  Long Run –  Amount of -me needed to make all produc-on inputs variable •  Short run and long run are not -me specific 9
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3. Produc-on: One Variable Input 3. Produc-on: One Variable Input •  We will begin looking at the short run when only one input can be varied •  We assume capital is fixed and labor is variable –  Output can only be increased by increasing labor –  Must know how output changes as the amount of labor is changed 11
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2 19/09/16 3. Produc-on: One Variable Input 3. Produc-on: One Variable Input •  Average product of Labor : how much, on average, each worker can produce Output
q
=
Labor Input L
APL =
•  Marginal Product of Labor – addi-onal output produced when labor increases €
by one unit ΔOutput
Δq
=
ΔLabor Input ΔL
MPL =
13
14
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€
3. Produc-on: One Variable Input Output
per
Month
3. Produc-on: One Variable Input Output
per
Month
D
112
• Left of E: MP > AP & AP is increasing
• Right of E: MP < AP & AP is decreasing
• At E: MP = AP & AP is at its maximum
• At 8 units, MP is zero and output is at max
30
Marginal Product (MP)
Total Product (TP)
C
60
20
At point D, output is
maximized.
B
2 3
4
5 6
7 8
9
10 Labor per Month
0 1
15
4
5 6
7 8
9
10 Labor per Month
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Product Curves q
Product Curves AP is the slope of the line
from origin to a point on
TP curve
q/L
112
TP C
q
q
TP 30
AP 10
Labor
0 1 2 3 4 5 6 7 8 9 10
15
60
30
10
A
MP 0 1 2 3 4 5 6 7 8 9 10
MP is the slope of the line
tangent to corresponding point
on TP curve
112
30
20
B
0 1 2 3 4 5 6 7 8 9 10
Labor
Labor
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2 3
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Average Product (AP)
10
A
0 1
E
AP MP 0 1 2 3 4 5 6 7 8 9 10
Labor
18
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3 19/09/16 Marginal and Average Product •  When marginal product is greater than the average product, the average product is increasing •  When marginal product is less than the average product, the average product is decreasing •  Marginal product crosses average product at its maximum •  When marginal product is zero, total product (output) is at its maximum Law of Diminishing Marginal Returns •  As the use of an input increases with other inputs fixed, the resul-ng addi-ons to output will eventually decrease –  When the use of labor input is small and capital is fixed, output increases considerably since workers can begin to specialize and MP of labor increases –  When the use of labor input is large, some workers become less efficient and MP of labor decreases 19
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Law of Diminishing Marginal Returns Malthus and the Food Crisis •  Malthus predicted mass hunger and starva-on as diminishing returns limited agricultural output and the popula-on con-nued to grow •  Why did Malthus’ predic-on fail? •  Typically applies only for the short run when one variable input is fixed •  Can be used for long-­‐run decisions to evaluate the trade-­‐offs of different plant configura-ons •  Assumes the quality of the variable input is constant •  A declining marginal product, does not necessarily mean a nega-ve one •  Assumes a constant technology, changes in technology will cause shi`s in the total product curve –  Did not take into account changes in technology –  Although he was right about diminishing marginal returns to labor 21
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4. Produc-on: Two Variable Inputs 4. Produc-on: Two Variable Inputs In the long run: •  Firm can produce an output by combining different amounts of labor and capital, because they are both variable •  We can look at the output we can achieve with different combina-ons of capital and labor 23
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4 19/09/16 4. Produc-on: Two Variable Inputs Isoquant Map E
Capital 5
per year
•  Isoquants –  Curves showing all possible combina-ons of inputs that yield the same output –  Slope of the isoquant shows how one input can be subs-tuted for the other and keep the level of output the same Ex: 55 units of output
can be produced with
3K & 1L (pt. A)
OR
1K & 3L (pt. D)
4
3
A
B
C
2
q3 = 90
D
1
q2 = 75
q1 = 55
1
25
2
3
4
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Capital 5
per year
Increasing labor holding
capital constant (A, B, C)
OR
Increasing capital holding
labor constant (E, D, C)
4
3
A
B
Marginal Rate of Technical Subs-tu-on Capital
per year
5
4
Negative Slope measures MRTS;
MRTS decreases as move down
the indifference curve
2
1
3
C
1
D
2
1
2
q3 = 90
E
1
2/3
q2 = 75
Q3 =90
1
1/3
1
1
q1 = 55
1
2
3
4
5
Labor per year
1
27
2
3
4
Q2 =75
Q1 =55
5
Labor per month
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Marginal Rate of Technical Subs-tu-on MRTS and Isoquants •  Slope of Isoquant = Marginal rate of technical subs4tu4on (MRTS) : Amount by which the quan-ty of one input can be reduced when one extra unit of another input is used, so that output remains constant MRTS = -
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Labor per year
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Diminishing Returns €
5
26
•  We assume there is diminishing MRTS •  Diminishing MRTS occurs because of diminishing returns and implies isoquants are convex •  As labor increases to replace capital –  Labor becomes rela-vely less produc-ve –  Capital becomes rela-vely more produc-ve –  Need less capital to keep output constant ΔK
(for a fixed level of q)
ΔL
29
30
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5 19/09/16 Isoquants: Perfect Subs-tutes MRTS and Marginal Products •  We know that q=F(K,L), along an isoquant, we have •  Two extreme cases show the possible range of input subs-tu-on in produc-on 1.  Perfect subs-tutes MPL ( ΔL) + MPK ( ΔK ) = 0
•  Rearranging equa-on, we can see the rela-onship between MRTS and MPs €
–  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 MPL
ΔK
=−
= MRTS
MPK
ΔL
31
32
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€
Isoquants: Perfect Subs-tutes Capital
per
month
A
Isoquants: Perfect Complements 2.  Perfect Complements Same output can be
reached with mostly
capital or mostly labor (A
or C) or with equal
amount of both (B)
B
–  Fixed propor-ons produc-on func-on –  There is no subs-tu-on available between inputs –  The output can be made with only a specific propor-on of capital and labor –  Cannot increase output unless increase both capital and labor in that specific propor-on C
Q1
Q2
Q3
Labor
per month
33
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Isoquants: Perfect Complements Capital
per
month
•  In addi-on to discussing the tradeoff between inputs to keep produc-on the same How does a firm decide, in the long run, the best way to increase output? •  Rate at which output increases as inputs are increased propor-onately Same output can
only be produced
with one set of
inputs. Q3
C
Q2
B
K1
5. Returns to Scale A
(a) Increasing returns to scale (b) Constant returns to scale (c) Decreasing returns to scale Q1
Labor
per month
L1
35
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6 19/09/16 Increasing Returns to Scale Returns to Scale (a) Increasing returns to scale: output more than doubles when all inputs are doubled Capital
(machine
hours)
–  Larger output associated with lower cost (cars) –Economies of scales –  One firm is more efficient than many small ones (electricity) –  On graph: isoquants get closer together A
4
30
20
2
10
5
37
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The isoquants
move closer
together
Labor (hours)
10
38
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Returns to Scale (b) Constant returns to scale: output doubles when all inputs are doubled – 
Size does not affect produc-vity – 
Isoquants are equidistant from one another Constant Returns to Scale Capital
(machine
hours)
A
6
30
Constant Returns:
Isoquants are
equally spaced
4
20
2
10
5
39
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Returns to Scale (c) Decreasing returns to scale: output less than doubles when all inputs are doubled – 
Large firms are less efficient – 
Isoquants get further away from one another Decreasing Returns to Scale Capital
(machine
hours)
A
4
20
2
Decreasing Returns:
Isoquants get further
apart
10
5
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Labor (hours)
15
40
10
Labor (hours)
42
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