Production and Cost Function
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Transcript of Production and Cost Function
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7/31/2019 Production and Cost Function
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The Firm:
Production FunctionCost Function
BASIC PRODUCTION
CONCEPTS
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The Firm
Firm
An organization that brings together factors of
productionlabor, land, physical capital, human
capital, and entrepreneurial skillto produce aproduct or service that it hopes can be sold at a
profit
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The Firm
Profit and costs
Accounting profits = total revenues - explicit costs
Explicit Costs
Costs that business managers must take account of
because they must be paid
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The Firm
The goal of the firm: profit maximization
Firms are expected to try to make the positive
difference between total revenues and totalcosts as large as they can.
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The Relationship
Between Output and Inputs
Production Function
The relationship between inputs and output
A technological, not an economic, relationship
The relationship between inputs and maximum
physical output
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The Relationship
Between Output and Inputs
Production
Any activity that results in the conversion of
resources into products that can be used in
consumption
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PRODUCTIONINPUTS
PRODUCTION
PROCESS
PRODUCTIONOUTPUT
Land
Labor
CapitalRaw Materials
Entrepreneur
Manufacturing
Assembly
ProcessingService
Finished Products
Semi-processed products
Services
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The Relationship
Between Output and Inputs
*Q= output/time periodK= capital
L = labor
Q = (K,L)*
or
Output/time period = some function of capital and labor inputs
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Two types of Production Inputs
Fixed Input
Variable Input
Point of comparison Fixed Input Variable Input
Necessity in Production Supplementary; even in
their absence some
amount of production canbe carried out
Without these factors no
production can be carried
out
Examples Plant, machinery, manager,
land, factory premises
Labor, raw materials,
transport, frieght
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THE LAW OF DIMINISHING RETURNS
When one of the factors of production is held
fixed in supply, successive additions of otherfactors will lead to an increase in returns up to
a point, but beyond this point returns will
diminish
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The Law of Diminishing Returns
NUMBER OFWORKERS
TOTAL PHYSICALPRODUCT (TPP)
MARGINALPHYSICAL
PRODUCT (MPP)
AVERAGE PHYSICALPRODUCT (APP)
1 10 10 10
2 30 30-10=20 15
3 90 90-30=60 30
4 120 120-90=30 30
5 130 130-120=10 26
6 120 120-130=-10 20
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The Relationship
Between Output and Inputs
Marginal Physical Product
The physical output that is due to the addition ofone more unit of a variable factor of production
The change in total product occurring when avariable input is increased and all other inputs areheld constant
Also called marginal productor marginal return
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Diminishing Returns, the Production Function,
and Marginal Product
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Diminishing Returns, the Production Function,
and Marginal Product: A Hypothetical Case
Figure 22-2, Panel (b)
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Figure 22-2, Panel (c)
Diminishing Returns, the Production Function,
and Marginal Product
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COST & PROFIT CONCEPT
Types of Cost
Variable Cost : are expenses
incurred in production that
tend to change directly asproduction increases
Fixed Cost : are expenses
that do not change or vary
with production
TC = TFC + TVC
TVC = (VC/u) (u)
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Revenue : sales generated by anenterprise
TR = (Sp/u) (u)
Profits : difference between the totalrevenue and total cost
TP = TR- TC
TR= TC (Break Even)
TR> TC (Profit)
TC>TR (Losses)
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Cost of Production: An Example
Figure 22-2, Panel (a)
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Costs(dollarperday)
2
4
6
8
12
2 4 6 8 100 1 3 5 7 9 11
16
Output (calculators per day)
10
14
ATC
AVC
AFC
Cost of Production: An Example
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AFC
AVC
Costs(dollar
perday)
Output (calculators per day)
ATC
Cost of Production: An Example
TP
ATC = AVC + AFC
AFC = ATC - AVC
AVC
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Short-Run Costs to the Firm
Marginal Cost
The change in total costs due to a one-unit
change in production rate
Marginal costs (MC) =change in total cost
change in output
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TotalTotal Variable Total Marginal
Output Costs Costs Cost(Q/day) (TVC) (TC) (MC)
0 0
1 5
2 8
3 10
4 11
5 13
6 16
7 20
8 25
9 31
10 38
11 46
10
15
18
20
21
23
26
30
35
41
48
56
5
32
1
2
3
45
6
7
8
C
osts(dollarper
day)
2
4
6
8
12
2 4 6 8 100 1 3 5 7 9 11
16
Output (calculators per day)
10
14
MC
Cost of Production: An Example
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Cost of Production: An Example
1110
AFC
AVC
MC
ATC
9876543210
2
4
6
8
Panel (c)
16
14
12
10
Output (recordable DVDs per day)
Costs(d
ollarsperrecordableDVD)
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Short-Run Costs to the Firm
Answer
As long as marginal physical product rises,
marginal cost will fall, and when marginalphysical product starts to fall (after reaching
the point of diminishing marginal returns),
marginal cost will begin to rise.
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The Relationship Between Diminishing Marginal
Returns and Cost Curves
Labor cost assumed constant
MC =DTC
D
Output
Recall: labor is the variable input
MC =
W
MPP
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The Relationship Between Diminishing Marginal
Returns and Cost Curves
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Figure 22-3, Panels (b) and (c)
The Relationship Between
Physical Output and Costs
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The Relationship Between
Physical Output and Costs
Figure 22-3, Panels (c) and (d)
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The Relationship Between Diminishing Marginal
Returns and Cost Curves
Firms short-run cost curves are a reflection of
the law of diminishing marginal returns.
Given any constant price of the variable input,
marginal costs decline as long as the marginal
product of the variable resource is rising.
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The Relationship Between Diminishing Marginal
Returns and Cost Curves
At the point at which diminishing marginal
returns begin, marginal costs begin to rise as
the marginal product of the variable input
begins to decline.
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The Relationship Between Diminishing Marginal
Returns and Cost Curves
AVC =TVC
output
AVC =W
AP
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TR = TC
TR =100; TC= 100; TR=TC
TR=100; TC =50, P/L= TR-TC= 100-50= 50Profit
TR=100; TC=200, P/L =TR-TC = 100-200= (100) Breakeven?
P200price shirt; P200,000(machine)); (80/hr labor)
TR= TC
(sp/u) (u)= TFC+TVC 200(x) = 200,000 + 80(x)
200x-80x = 200,000
120x = 200,000
X= 200,000/120 1,667 pairs will have to be sold to break even
< = profit; >=loss
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200x= 200,000 + 80 x; 2,000 (P/L) Profit= how
much profit
200(2,000) = 200,000 + 80 (2,000)
400,000 = 200,000 + 160,000
TR= 400,000
TC =360,000
P/L = 400,000-360,000 P= 40,000
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Preferable Plant Size
and the Long-Run Average Cost Curve
Figure 22-4, Panels (a) and (b)
Panel (b)
Output per Time PeriodQ2Q1
C3
C1
C4C2
Panel (a)
Output per Time Period
SAC2
1SAC
SAC3
LAC
1SAC
2SAC
3SAC
4SAC
5SAC
6SAC
SAC7
SAC8
AverageCost(dollarsperunit
ofoutput)
AverageC
ost(dollarsperunitofoutput)
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Long-Run Cost Curves
Long-Run Average Cost Curve
The locus of points representing the minimum
unit cost of producing any given rate of output,
given current technology and resource prices
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Why the Long-Run Average Cost Curve is U-
Shaped
Economies of Scale
Decreases in long-run average costs resulting from
increases in output
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Why the Long-Run Average Cost Curve is U-
Shaped
Reasons for economies of scale
Specialization
Dimensional factor
Improved productive equipment
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Why the Long-Run Average Cost Curve is U-
Shaped
Explaining diseconomies of scale
Limits to the efficient functioning of management
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Minimum Efficient Scale
Minimum Efficient Scale (MES)
The lowest rate of output per unit time at which
long-run average costs for a particular firm are at
a minimum
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Minimum Efficient Scale
Small MES relative to industry demand:
High degree of competition
Large MES relative to industry demand:
Small degree of competition
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Minimum Efficient Scale
Figure 22-6
0
Output per Time Period
LAC
B
1,000
A
10
Lon
g-RunAverage
Costs
(dollarsperunit)
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The Firm: Cost and Output
Determination
End