Transcript Chapter 7 Production Theory

Topic on
Production and Cost
Functions and Their
Estimation
Production function
A table, graph, or equation showing the maximum
output rate of the product that can be achieved
from any specified set of usage rates of inputs
Production function
Thomas Machine Company
Amount of Labor
(annual # units)
1
2
3
4
5
6
7
8
Output of Parts
(hundreds/year)
12
27
42
56
68
76
76
74
AP Labor
12.0
13.5
14.0
14.0
13.6
12.7
10.9
9.3
MP Labor
1
15
15
14
12
8
0
-2
Production function
Thomas Machine Company
Parts
80
60
40
20
0
0
2
4
6
Labor
8
10
Production function
Thomas Machine Company
20
Parts
15
10
AP Labor
5
MP Labor
0
-5 0
5
Labor
10
Law of diminishing marginal
returns
If equal increments of an input are added to a
production process, and the quantities of other
inputs are held constant, eventually the marginal
product of the input will diminish
Note: 1) This is an empirical generalization.
2) Technology remains fixed.
3) The quantity of at least one input is
held fixed.
Marginal revenue product
The amount that an additional unit of the
variable input adds to the firm’s total revenue
MRPY = DTR/DY
Marginal expenditure
The amount that an additional unit of the
variable input adds to the firm’s total costs.
MEY = DTC/DY
Optimal level of input use
MRPY = MEY
Production functions with two
variable inputs
Amount of Labor
1
2
3
4
5
Number of Machine Tools
3
4
5
6
5
11
18
24
14
30
50
72
22
60
80
99
30
81
115
125
35
84
140
144
Q = f (labor, machine Tools)
150
100
50
0
1
2
Labor
3
4
5
Number of
Machine Tools
Isoquant
A curve showing all possible (efficient)
combinations of inputs that are capable of
producing a certain quantity of output
Iso
same
quant
quantity
Capital
K2
300
K1
200
100
0
L2
L1
Labor
Marginal rate of technical
substitution
Shows the rate at which one input can be
substituted for another input, if output remains
constant. (Slope of the isoquant.)
Given Q = f(X1, X2)
MRTS = -dX2 / dX1
= -MP1 / MP2
Isocost curves
Various combinations of inputs that a firm can
buy with the same level of expenditure
PLL + PKK = M
where M is a given money outlay.
Capital
M/PK
Slope = -PK /PL
0
M/PL
Labor
Maximization of output for given
cost
Capital
R
300
200
100
0
Labor
MPL/PL = MPK/PK
Capital
R
300
200
100
0
Labor
Optimal Lot Size
• To consider the size of inventory
• Find the relationship between size of lot
and total annual cost.
What Toyota Taught the World?
• Lower the cost per setup
• Reduce the optimal lot size
• Just-in-time production system
Returns to scale
If the firm increases the amount of all inputs by
the same proportion:
• Increasing returns means that output
increases by a larger proportion
• Decreasing returns means that output
increases by a smaller proportion
• Constant returns means that output increases
by the same proportion
Output elasticity
The percentage change in output resulting from 1
percent increase in all inputs.
 e > 1 ==> increasing returns
 e < 1 ==> decreasing returns
 e = 1 ==> constant returns
Example: Xerox
Sending out teams of engineers and
technicians to visit other firms to obtain
information concerning best-practice
methods and procedures.
• Competitive Benchmarking
Measurement of Production
Functions
Three types of statistical analysis
• Time series data
• Cross section data
• Technical information
The Analysis of Costs
Opportunity costs
The value of the other products that the resources
used in production could have produced at their
next best alternative
Historical costs
The amount the firm actually paid for a particular
input
Explicit vs. implicit costs
• Explicit costs include the ordinary items that an
accountant would include as the firms expenses
• Implicit costs include opportunity costs of
resources owned and used by the firm’s owner
Short run
A period of time so short that the firm cannot alter
the quantity of some of its inputs
• Typically plant and equipment are fixed inputs
in the short run
• Fixed inputs determine the scale of the firm’s
operation
Three concepts of total costs
• Total fixed costs = FC
• Total variable costs = VC
• Total costs = FC + VC
Fixed, variable, and total costs
Media Corp.
OUTPUT
0
1
2
3
4
5
6
7
8
9
10
11
12
FC
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
VC
0
100
180
280
392
510
650
800
960
1140
1340
1560
2160
TC
2000
2100
2180
2280
2392
2510
2650
2800
2960
3140
3340
3560
4160
dollars
Fixed, Variable, and Total Costs
-- Media Corp.
5000
4000
3000
2000
1000
0
FC
VC
TC
0
10
Units of Output
20
Average and marginal costs
Media Corp.
OUTPUT
0
1
2
3
4
5
6
7
8
9
10
11
12
AFC
AVC
ATC
MC
2000.0
1000.0
666.7
500.0
400.0
333.3
285.7
250.0
222.2
200.0
181.8
166.7
100.0
90.0
93.3
98.0
102.0
108.3
114.3
120.0
126.7
134.0
141.8
180.0
2100.0
1090.0
760.0
598.0
502.0
441.7
400.0
370.0
348.9
334.0
323.6
346.7
100
80
100
112
118
140
150
160
180
200
220
600
$$$
Average and marginal costs
Media Corp.
2000
1500
1000
500
0
0
2 4
6 8 10 12
Units of output
AFC
AVC
ATC
MC
Long-run cost functions
• Often considered to be the firm’s planning horizon
• Describes alternative scales of operation when all
inputs are variable
Average
cost
Quantity of output
Long-run average cost function
Shows the minimum cost per unit of producing each output
level when any scale of operation is available
Average
cost
SR average cost
functions
LR average cost
Quantity of output
Key steps:
Cost estimation process
Definition of costs
 Correction for price level changes
 Relating cost to output
 Matching time periods
 Controlling product, technology, and plant
 Length of period and sample size
Minimum efficient scale
The smallest output at which long-run average
cost is a minimum.
Average
cost
Qmes
Quantity of output
The survivor technique
• Classify the firms in an industry by size and
compute the percentage of industry output
coming from each size class at various times
• If the share of one class diminishes over time,
it is assumed to be inefficient
• These firms are then operating below
minimum efficient scale
Economies of scope
Exist when the cost of producing two (or more)
products jointly is less than the cost of
producing each one alone.
S = C(Q1) + C(Q2) - C(Q1+ Q2)
C(Q1+ Q2)
Break-even analysis
Dollars
Total Revenue
Total Cost
Profit
Loss
Quantity of output