theory of production and cost production is the use of factors of production to produce and market...
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THEORY OF PRODUCTION AND COST
Production is the use of factors of production to produce and market goods and services.
Inputs include the broad categories of land, labor, capital, other intermediate inputs and entrepreneurship.
In a mixed economy, both firms and governments organize the production of various goods and services.
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Production in the Short-run
An input that cannot vary in quantity during the relevant
time period is called a fixed input or fixed factor.
An input having a quantity that can change during the
relevant time period is called a variable input or
variable factor.
The short-run is a period of time such that there is at least
one fixed factor.
The long-run is a period of time such that all inputs are
variable in quantity.
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A production function summarizes the relationship
between all combinations of inputs and the corresponding
maximum attainable levels of output, for a given
technology.
The total product, TP, of a variable input is the amount
of output produced over the period when that input is used
with fixed quantities of all other inputs.
The marginal product of an input F, MPF, is the
additional output per unit increase in the input, holding all
other inputs (and technology) constant; F
TPMPF
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Total Product
0
50
100
150
200
250
0 2 4 6 8 10
pounds of fertilizer
bu
sh
els
of
po
tato
es
TP
Marginal Product
0
10
20
30
0 2 4 6 8 10
pounds of fertilizer
bush
els
of p
otat
oes
per
unit
of fe
rtili
zer
. MP
fertilizer TP,
Output
MP,
Marginal output
per unit of input
0 0 ---
1 15 15
2 38 23
3 68 30
4 103 35
5 137 34
6 168 31
7 192 24
8 211 19
9 226 15
10 235 9
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Diminishing marginal product results from the process of adding additional units of a variable input to given quantities of other inputs.
Diminishing marginal product: As more of a variable input is employed, with the quantities of all other inputs held constant, the marginal product of the variable input will decline after some point.
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Measuring costs and profitsTotal (Economic) Cost is the monetary value of all inputs used in a particular activity over a given period.
Explicit Costs correspond to the monetary payments for inputs.
Implicit Costs are the opportunity costs of inputs that have no explicit monetary payments as a result of the inputs not being purchased in markets.
All opportunity costs, both explicit and implicit, are part of economic costs.
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Economic depreciation is the reduction in the value of a capital good over the relevant period that results from wear and tear as well as obsolescence.
Accounting depreciation measures the annual accounting cost of capital, expressed as some portion of the capital’s monetary cost.
Accounting costs measure the explicit costs of production during a given period plus accounting depreciation.
Measuring costs
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Measuring costs and profits
Total revenue is the explicit monetary return associated with an economic activity over a given period.
Economic activities can also yield implicit returns.
The total return includes both total revenues and implicit returns.
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Economic and accounting profits are defined below:
Total return Total revenue
less: less:
explicit costs explicit costs
economic depreciation accounting depreciation
other implicit costs
Economic Profits Accounting Profits
Economic profits measure the net (private) economic gain resulting from an economic activity.
When economic profits are zero the returns to owner supplied inputs exactly equal the opportunity costs of those inputs. These returns are called normal profits.
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Related Cost Measures
Variable cost, VC, is the cost of the variable input(s) used to produce any given level of output.
Fixed costs, FC, is the cost of all fixed inputs.
Total cost, TC, is the sum of the costs of all inputs used to produce output during the period;
TC = VC + FC.
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Example of Potato Production (The price of fertilizer is $50 per unit and the costs associated with fixed input $40.)
F Q FC VC TC
fert.bushels of potatoes $ $ $
0 0 40 0 40
1 15 40 50 90
2 38 40 100 140
3 68 40 150 190
4 103 40 200 240
5 137 40 250 290
6 168 40 300 340
7 192 40 350 390
8 211 40 400 440
9 226 40 450 490
10 235 40 500 540
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Related Cost Measures
Marginal cost, MC, is the increase in total or variable cost per unit increase in output, Q;
Q
TC
Q
VCMC
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Average variable cost, AVC, is the variable cost
of production per unit of output;
Average fixed cost, AFC, is the fixed cost per
unit of output;
Average cost, AC, is the total cost of all inputs
per unit of output;
.Q
VCAVC
.Q
FCAFC
.Q
TCAC
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AFCAVCAC
Q
FC
Q
VC
Q
FCVC
Q
TCAC
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Marginal, Average, Average Variable and Average Fixed Costs
0.00.51.01.52.02.53.03.54.04.55.05.56.0
0 50 100 150 200 250Q, quantity of output
dolla
rs p
er u
nit o
f Q
AC
AVC
MC
AFC
103
1.43
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Marginal, Average, Average Variable and Average Fixed Costs
0.00.51.01.52.02.53.03.54.04.55.05.56.0
0 50 100 150 200 250Q, quantity of output
dolla
rs p
er u
nit o
f Q
AC
AVC
MC
AFC
103
0.39
1.942.33
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Family of Average Costs
AFC=Fixed costQuantity
=FCQ
AVC=Variable cost
Quantity=
VCQ
ATC=Total costQuantity
=TCQ
AFC=Fixed costQuantity
=FCQ
AVC=Variable cost
Quantity=
VCQ
ATC=Total costQuantity
=TCQ
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Marginal Cost
QTC=
quantity) in (Changecost) total in (Change
=MC
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Note the relationship between MP and MC.
fertilizer TP MP Q TC MC0 0 --- 0 40 ---1 15 15 15 90 3.332 38 23 38 140 2.173 68 30 68 190 1.674 103 35 103 240 1.435 137 34 137 290 1.476 168 31 168 340 1.617 192 24 192 390 2.088 211 19 211 440 2.639 226 15 226 490 3.33
10 235 9 235 540 5.56
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The marginal cost of output directly depends upon the marginal product and price of each variable input;
.LMP
priceinputMC
For example, if MPL= 0.5 widgets per hour and the wage rate is a constant $10.00 per hour,
MC = ($10 per hour) / (0.5 widgets per hour)
= $20 per widget .
Intuition: If MPL= 0.5, it takes two hours of work to create one widget. With a wage of $10 per hour, this translates into a marginal cost of $20.00 for an additional widget.
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Implications:
• An increase in the price of a variable input, ceteris paribus,
will result in an increase in the marginal cost of output.
• Holding the input price constant, an increase in the marginal
product of a variable input will cause MC to decrease.
• Often we talk about MC increasing as output increases (after
some point). The underlying reason is diminishing marginal
product of the variable input(s).
.LMP
priceinputMC
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Total-Cost Curve...(Another Example)
$0.00
$2.00
$4.00
$6.00
$8.00
$10.00
$12.00
$14.00
$16.00
0 2 4 6 8 10 12
Quantity of Output
Tota
l C
ost
Total-cost curve
ΔQ = 1
ΔTC = 0.70
MC = 0.70
MC = 1.30
MC = 1.90
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AVC
MC
Average-Cost and Marginal-Cost Curves...
$0.00
$0.50
$1.00
$1.50
$2.00
$2.50
$3.00
$3.50
0 2 4 6 8 10 12
Quantity of Output
Costs
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Relationship Between Marginal Cost and Average Variable Cost
Whenever MC is greater than AVC, AVC will be rising.
Whenever MC is less than AVC, AVC will be falling.
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MC
ATC
Relationship Between Marginal Cost and Average Total Cost
$0.00
$0.50
$1.00
$1.50
$2.00
$2.50
$3.00
$3.50
0 2 4 6 8 10 12
Quantity of Output
Costs
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Relationship Between Marginal Cost and Average Total Cost
Whenever MC is less than ATC, ATC will be falling.
Whenever MC is greater than ATC, ATC will be rising.
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ATCAVC
MC
Average-Cost and Marginal-Cost Curves...
$0.00
$0.50
$1.00
$1.50
$2.00
$2.50
$3.00
$3.50
0 2 4 6 8 10 12
Quantity of Output
Costs
AFC
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Cost Curves and Their Shapes
The average total-cost curve is U-shaped. At very low levels of output ATC is high because
fixed cost is spread over only a few units. ATC initially declines as output increases because of
the decline in AFC. ATC eventually starts to rise because AVC rises
substantially.
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Total-Cost Curve...
$0.00
$2.00
$4.00
$6.00
$8.00
$10.00
$12.00
$14.00
$16.00
0 2 4 6 8 10 12
Quantity of Output
Tota
l C
ost
Total-cost curve
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Big Bob’s Cost Curves...
$0.00
$2.00
$4.00
$6.00
$8.00
$10.00
$12.00
$14.00
$16.00
$18.00
$20.00
0 2 4 6 8 10 12 14 16
Quantity of Output(bagels per hour)
To
tal
Co
st
Total Cost Curve
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AVC
MC
Big Bob’s Cost Curves...
0
0.5
1
1.5
2
2.5
3
3.5
0 2 4 6 8 10 12 14 16Quantity of Output
Co
sts
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AFC
AVC
MC
Big Bob’s Cost Curves...
0
0.5
1
1.5
2
2.5
3
3.5
0 2 4 6 8 10 12 14 16Quantity of Output
Co
sts
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AFC
AVC
MC
Big Bob’s Cost Curves...
0
0.5
1
1.5
2
2.5
3
3.5
0 2 4 6 8 10 12 14 16Quantity of Output
Co
sts
ATC
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Three Important Properties of Cost Curves:
Marginal cost eventually rises with the quantity of output.
The average-total-cost curve is U-shaped.
The marginal-cost curve crosses the average-total-cost and average-variable-cost curves at their minimums.
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Cost Curves and Their Shapes
•The bottom of the U-shape AC curve corresponds to the quantity that minimizes the average cost of production.
•This quantity is sometimes called the efficient scale of the firm.
•The marginal-cost curve crosses the average-total-cost curve at the efficient scale.
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Costs in the Long Run
For many firms, the division of total costs between fixed and variable costs depends on the time horizon being considered. In the short run some costs are fixed. In the long run fixed costs become
variable costs.
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Average Total Cost in the Short and Long Runs...
Quantity ofCars per Day
0
AverageTotalCost
ATC in shortrun with
small factory
ATC in shortrun with
medium factory
ATC in shortrun with
large factory
ATC in long run
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Economies and Diseconomies of Scale
Economies of scale occur when long-run average total cost declines as output increases.
Diseconomies of scale occur when long-run average total cost rises as output increases.
Constant returns to scale occur when long-run average total cost does not vary as output increases.
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Economies and Diseconomies of Scale
Diseconomies
of scale
Quantity ofCars per Day
0
AverageTotalCost
ATC in long run
Economies
of scale
Constant Returnsto scale