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The Production & Costs
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The Production Function The production function specifies the
maximum amount of output that can
be produced with a given quantity ofinputs. It is defined for a given stateof technical knowledge.
The concept of a production function
is a useful way of describing theproductive capabilities of a firm.
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The Production Function Contd. Mathematically, Y = F (x);
where x = level of input
Y = The maximum level of output Or more generally, Y = F (K, L)
This equation states that output is a function ofthe amount of capital and the amount of labor
The production function reflects the availabletechnology for turning capital and labor intooutput
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Production Function
1. The slope of
production functionequals marginal product
2. As moreinput added, MPdeclines
x
YWith the
available
technology
This curve
shows howoutput
depends on
input,
Y = F(x)
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Total, Average and MarginalP
roductTotal Product is the total amount of output produced in physicalunits such as bushels of wheat or number of sneakers.
Marginal Product of an input is the extra product or output
produced by 1 additional unit of that input while other inputsare held constant.For example, assume that we are holding land, machinery andall other inputs constant. Then labors marginal product is theextra output obtained by adding 1 unit of labor.
Average Product is the total output divided by total units ofinput.Average product of labor or APL = Q/LThis is the accounting measure of productivity.
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A numerical exampleUnits oflabor (a)
Total product(b)
Marginalproduct (c)
Averageproduct(d=b/a)
0 0
1 2000 2000 2000
2 3000 1000 1500
3 3500 500 11674 3800 300 950
5 3900 100 780
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Production Function
1
1
1
MPL
MPL
MPL
1. The slope of
production functionequals marginal product
2. As morelabor is added,MPL declines
Labor, L
Output,
Y
This curve
shows
how
output
dependson labor
input,
holding
the
amount of
capitalconstant
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Marginal Product of Labor Marginal product curve is downward slopping.
MPL = DQ/DLMeasures the output produced by the
last worker.Slope of the production function
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Production Function
Diminishing Marginal Product
Diminishing marginal productis the
property whereby the marginal productof an input declines as the quantity ofthe input increases.
Example: As more and more workers arehired at a firm, each additional worker
contributes less and less to productionbecause the firm has a limited amount ofequipment.
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From the Production Function to
the Total-Cost Curve The relationship between the quantity
a firm can produce and its costs
determines pricing decisions. The total-cost curve shows this
relationship graphically.
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Table 1 A Production Function and Total Cost:Hungry Helens Cookie Factory
Copyright2004 South-Western
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Figure : Hungry Helens Total-Cost Curve
Copyright 2004 South-Western
Total
Cost
$80
70
60
50
40
30
20
10
Quantity
of Output(cookies per hour)
0 10 20 30 15013011090705040 1401201008060
Total-costcurve
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THE VARIOUS MEASURES OF COST
Everywhere that production goes, costs follow
close behind like a shadow.
Costs of production may be divided intofixedcosts and variable costs.
Fixed costsFixed costs are those costs that do notvary with the quantity
of output produced.
Variable costsVariable costs are those costs that do vary with the quantity of
output produced
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$ Cost
Q
FC
C(Q) = FC+ VC
Total Cost=Fixed Cost + Variable Cost
VC(Q)
Fixed Cost & Variable Cost
TC
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Figure 4 Thirsty Thelmas Total-Cost Curves
Copyright 2004 South-Western
Total Cost
$15.00
14.00
13.00
12.00
11.00
10.00
9.00
8.00
7.00
6.00
5.00
4.003.00
2.00
1.00
Quantity
of Output
(glasses of lemonade per hour)
0 1 432 765 98 10
Total-cost curve
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Average costs can be determined by dividing the
firms costs by the quantity of output it produces.
The average cost is the cost of each typical unitof product.
Average Fixed Costs (AFC)
AverageVariable Costs (AVC)
Average Total Costs (ATC)ATC= AFC+ AVC
Average Costs
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Average CostsAFC
FC
Q! !
Fixed cost
Quantity
AVCVC
Q! !
Variable cost
uantity
ATCTC
Q! !
Total cost
uantity
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Marginal Cost Marginal cost(MC) measures the increase
in total cost that arises from an extra unitof production.
Marginal cost helps answer the followingquestion:
How much does it cost to produce anadditional unit of output?
MCTC
Q! !
(change in total cost)
(change in quantity)
(
(
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Marginal Cost
Quantity TotalCost
MarginalCost
Quantity TotalCost
MarginalCost
0 $3.00
1 3.30 $0.30 6 $7.80 $1.30
2 3.80 0.50 7 9.30 1.503 4.50 0.70 8 11.00 1.70
4 5.40 0.90 9 12.90 1.90
5 6.50 1.10 10 15.00 2.10
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Figure 5 Thirsty Thelmas Average-Cost and Marginal-CostCurves
Copyright 2004 South-Western
Costs
$3.50
3.25
3.00
2.75
2.50
2.25
2.00
1.75
1.50
1.25
1.00
0.75
0.50
0.25
Quantity
of Output
(glasses of lemonade per hour)
0 1 432 765 98 10
MC
ATC
AVC
AFC
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Cost Curves and Their Shapes Marginal cost rises with the amount
of output produced.
This reflects the property ofdiminishingmarginal product.
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Figure 5 : Marginal-Cost Curves
Copyright 2004 South-Western
Costs
$3.50
3.25
3.00
2.75
2.50
2.25
2.00
1.75
1.50
1.25
1.00
0.75
0.50
0.25
Quantity
of Output
(glasses of lemonade per hour)
0 1 432 765 98 10
MC
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Cost Curves and Their Shapes The average totalaverage total--costcost curve is U-
shaped.
At very low levels of output averagetotal cost is high because fixed cost isspread over only a few units.
Average total cost declines as outputincreases.
Average total cost starts risingbecause average variable cost rises
substantially.
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Cost Curves and Their Shapes The bottom of the U-shaped ATC
curve occurs at the quantity that
minimizes average total cost. Thisquantity is sometimes called theefficient scale of the firm.
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Cost Curves and Their Shapes Relationship between Marginal Cost
and Average Total Cost
Whenever marginal cost is less than averagetotal cost, average total cost is falling.
Whenever marginal cost is greater thanaverage total cost, average total cost isrising.
The marginal-cost curve crosses the average-total-cost curve at the efficient scaleefficient scale.
Efficient scale is the quantity that minimizesaverage total cost.
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Figure :Average-Cost and Marginal-Cost Curves
Copyright 2004 South-Western
Costs
$3.50
3.25
3.00
2.75
2.50
2.25
2.00
1.75
1.50
1.25
1.00
0.75
0.50
0.25
Quantity
of Output
(glasses of lemonade per hour)
0 1 432 765 98 10
ATC
MC
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Typical Cost Curves Three Important Properties of Cost Curves
Marginal cost eventually rises with thequantity of output.
The average-total-cost curve is U-shaped.
The marginal-cost curve crosses theaverage-total-cost curve at the minimum ofaverage total cost.
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COSTS IN THE SHORT RUN AND IN
THE
LONG RUN For many firms, the division of total costs
between fixed and variable costs depends onthe time horizon being considered.
In the short run, some costs are fixed. In the long run, fixed costs become variable
costs.
Because many costs are fixed in the short runbut variable in the long run, a firms long-runcost curves differ from its short-run costcurves.
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Figure 7 Average Total Cost in the Short and Long Run
Copyright 2004 South-Western
Quantity of
Cars per Day
0
AverageTotal
Cost
1,200
$12,000
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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The Firms Objective
The Firms Objective
The economic goal of the firm is tomaximize profits.
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Total Revenue, Total Cost, and Profit Total Revenue
The amount a firm receives for the saleof its output.
TotalCost
The market value of the inputs a firmuses in production.
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Total Revenue, Total Cost, and Profit Profitis the firms total revenue
minus its total cost.
Profit = Total revenueProfit = Total revenue -- TotalTotalcostcost
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Costs as Opportunity Costs
A firms cost of production includes allthe opportunity costs of making its
output of goods and services. Explicit and Implicit Costs
A firms cost of production includeexplicit costs and implicit costs.
Explicitcosts are input costs that require adirect outlay of money by the firm.
Implicitcosts are input costs that do notrequire an outlay of money by the firm.
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Economic Profit versus AccountingProfit
Economists measure a firms economicprofitas total revenue minus total cost,including both explicit and implicit costs.
Accountants measure the accountingprofitas the firms total revenue minus
only the firms explicit costs.
When total revenue exceeds both explicit andimplicit costs, the firm earns economic profit.
Economic profit is smaller than accountingprofit.
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Figure 1 Economic versus Accountants
Copyright 2004 South-Western
Revenue
Total
opportunitycosts
How an Economist
Views a Firm
How an Accountant
Views a Firm
Revenue
Economicprofit
Implicitcosts
Explicitcosts
Explicitcosts
Accountingprofit