topic on production and cost functions and their estimation
TRANSCRIPT
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Topic onProduction and Cost Functions and Their
Estimation
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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
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Production functionThomas Machine Company
Amount of Labor Output of Parts AP Labor MP Labor(annual # units) (hundreds/year)
1 12 12.0 12 27 13.5 153 42 14.0 154 56 14.0 145 68 13.6 126 76 12.7 87 76 10.9 08 74 9.3 -2
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Production functionThomas Machine Company
0
20
40
60
80
0 2 4 6 8 10
Labor
Par
ts
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Production functionThomas Machine Company
-5
0
5
10
15
20
0 5 10
Labor
Par
ts AP Labor
MP Labor
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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.
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Marginal revenue product
The amount that an additional unit of the variable input adds to the firm’s total revenue
MRPY = TR/Y
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Marginal expenditure
The amount that an additional unit of the variable input adds to the firm’s total costs.
MEY = TC/Y
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Optimal level of input use
MRPY = MEY
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Production functions with two variable inputs
Number of Machine ToolsAmount of Labor 3 4 5 6
1 5 11 18 242 14 30 50 723 22 60 80 994 30 81 115 1255 35 84 140 144
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1 2 3 4 5
Number ofMachine Tools
0
50
100
150
Labor
Q = f (labor, machine Tools)
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Isoquant
A curve showing all possible (efficient) combinations of inputs that are capable of producing a certain quantity of output
Iso quant
same quantity
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Labor
Capital
0
K2
100
200
300K1
L2 L1
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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 = -X2 / X1
= -MP1 / MP2
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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.
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Labor
Capital
0
M/PK
M/PL
Slope = -PK /PL
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Maximization of output for given cost
Labor
Capital
0100
200300
R
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MPL/PL = MPK/PK
Labor
Capital
0100
200300
R
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Optimal Lot Size
• To consider the size of inventory
• Find the relationship between size of lot and total annual cost.
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What Toyota Taught the World?
• Lower the cost per setup
• Reduce the optimal lot size
• Just-in-time production system
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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
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Output elasticity
The percentage change in output resulting from 1 percent increase in all inputs.
> 1 ==> increasing returns < 1 ==> decreasing returns = 1 ==> constant returns
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Example: Xerox
Sending out teams of engineers and technicians to visit other firms to obtain information concerning best-practice methods and procedures.
• Competitive Benchmarking
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Measurement of Production Functions
Three types of statistical analysis
• Time series data
• Cross section data
• Technical information
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The Analysis of Costs
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Opportunity costs
The value of the other products that the resources used in production could have produced at their next best alternative
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Historical costs
The amount the firm actually paid for a particular input
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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
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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
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Three concepts of total costs
• Total fixed costs = FC
• Total variable costs = VC
• Total costs = FC + VC
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OUTPUT FC VC TC0 2000 0 20001 2000 100 21002 2000 180 21803 2000 280 22804 2000 392 23925 2000 510 25106 2000 650 26507 2000 800 28008 2000 960 29609 2000 1140 3140
10 2000 1340 334011 2000 1560 356012 2000 2160 4160
Fixed, variable, and total costs Media Corp.
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Fixed, Variable, and Total Costs -- Media Corp.
010002000300040005000
0 10 20
Units of Output
dolla
rs
FC
VC
TC
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Average and marginal costsMedia Corp.
OUTPUT AFC AVC ATC MC01 2000.0 100.0 2100.0 1002 1000.0 90.0 1090.0 803 666.7 93.3 760.0 1004 500.0 98.0 598.0 1125 400.0 102.0 502.0 1186 333.3 108.3 441.7 1407 285.7 114.3 400.0 1508 250.0 120.0 370.0 1609 222.2 126.7 348.9 180
10 200.0 134.0 334.0 20011 181.8 141.8 323.6 22012 166.7 180.0 346.7 600
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Average and marginal costsMedia Corp.
0500
100015002000
0 2 4 6 8 10 12
Units of output
$$$ AFC
AVCATCMC
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Long-run cost functions• Often considered to be the firm’s planning horizon• Describes alternative scales of operation when all
inputs are variable
Quantity of output
Average cost
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Long-run average cost function
Shows the minimum cost per unit of producing each output level when any scale of operation is available
Quantity of output
Average cost
SR average cost functions
LR average cost
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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
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Minimum efficient scale
The smallest output at which long-run average cost is a minimum.
Quantity of output
Average cost
Qmes
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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
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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)
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Break-even analysis
Quantity of output
DollarsTotal Revenue
Total Cost
Loss
Profit