Outputs and Costs

8/13/2019 Outputs and Costs

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2010 Pearson Addison-Wesley

CHAPTER 1


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Decision Time Frames

The firm makes many decisions to achieve its mainobjective:profit maximization.

Some decisions are critical to the survival of the firm.

Some decisions are irreversible (or very costly to reverse).

Other decisions are easily reversed and are less critical tothe survival of the firm, but still influence profit.

All decisions can be placed in two time frames:

The short run

The long run


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The Short Run

The short runis a time frame in which the quantity of oneor more resources used in production is fixed.

For most firms, the capital, called the firmsplant, is fixedin the short run.

Other resources used by the firm (such as labor, rawmaterials, and energy) can be changed in the short run.

Short-run decisions are easily reversed.



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The Long Run

The long runis a time frame in which the quantities of allresourcesincluding the plant sizecan be varied.

Long-run decisions are not easily reversed.

A sunk costis a cost incurred by the firm and cannot bechanged.

If a firms plant has no resale value, the amount paid for itis a sunk cost.

Sunk costs are irrelevant to a firms current decisions.



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Short-Run Technology Constraint

To increase output in the short run, a firm must increasethe amount of labor employed.

Three concepts describe the relationship between output

and the quantity of labor employed:

1. Total product

2. Marginal product

3. Average product


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Product Schedules

Total productis the total output produced in a givenperiod.

Themarginal productof labor is the change in totalproduct that results from a one-unit increase in thequantity of labor employed, with all other inputs remainingthe same.

Theaverage productof labor isequal to total productdivided by the quantity of labor employed.




Table 11.1shows a firms productschedules.

As the quantity of labor employed

increases:Total product increases.

Marginal product increasesinitially but eventually decreases.

Average product increasesinitially but eventually decreases.




Product Curves

Product curves are graphs of the three product conceptsthat show how total product, marginal product, and

average product change as the quantity of labor employedchanges.




Total Product Curve

Figure 11.1 shows a totalproduct curve.

The total product curveshows how total productchanges with the quantity

of labor employed.




The total product curve issimilar to the PPF.

It separates attainableoutput levels fromunattainable output levelsin the short run.




Marginal Product Curve

Figure 11.2 shows themarginal product of laborcurve and how themarginal product curverelates to the total productcurve.

The first worker hiredproduces 4 units of output.




The second worker hiredproduces 6 units of outputand total product becomes10 units.

The third worker hiredproduces 3 units of outputand total product becomes13 units.

And so on.




The height of each barmeasures the marginalproduct of labor.

For example, when laborincreases from 2 to 3, totalproduct increases from 10to 13,

so the marginal product ofthe third worker is 3 unitsof output.




To make a graph of themarginal product of labor,we can stack the bars inthe previous graph side byside.

The marginal product oflabor curve passes

through the mid-points ofthese bars.




Almost all productionprocesses are like the oneshown here and have:

Increasing marginalreturns initially

Diminishing marginal

returns eventually




Increasing Marginal

Returns Initially

When the marginal product

of a worker exceedsthemarginal product of theprevious worker, themarginal product of labor

increasesand the firmexperiences increasingmarginal returns.




Diminishing Marginal

Returns Eventually

When the marginal product

of a worker is lessthan themarginal product of theprevious worker, themarginal product of labor

decreases.The firm experiencesdiminishing marginal

returns.




Increasing marginal returns arise from increasedspecialization and division of labor.

Diminishing marginal returns arises from the fact thatemploying additional units of labor means each worker has

less access to capital and less space in which to work.

Diminishing marginal returns are so pervasive that they areelevated to the status of a law.

The law of diminishing returnsstates that:

As a firm uses more of a variable input with a givenquantity of fixed inputs, the marginal product of the variableinput eventuallydiminishes.




Average Product Curve

Figure 11.3 shows theaverage product curveand its relationship withthe marginal productcurve.

When marginal product

exceedsaverage product,average productincreases.




When marginal product isbelowaverage product,average product

decreases.When marginal productequals average product,average product is at its

maximum.




Short-Run Cost

To produce more output in the short run, the firm mustemploy more labor, which means that it must increase itscosts.

We describe the way a firms costs change as totalproduct changes by using three cost concepts and threetypes of cost curve:

Total cost

Marginal cost

Average cost



Total Cost

A firms total cost(TC)is the cost of allresources used.

Total fixed cost(TFC)is the cost of the firms fixed

inputs. Fixed costs do not change with output.

Total variable cost(TVC)is the cost of the firms variableinputs. Variable costs do change with output.

Total cost equals total fixed cost plus total variable cost.That is:

TC= TFC+ TVC

Short-Run Cost


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Figure 11.4 shows a firms

total cost curves.

Total fixed cost is the same

at each output level.

Total variable costincreases as outputincreases.

Total cost, which is the sumof TFCand TVCalsoincreases as outputincreases.

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The total variable costcurve gets its shape fromthe total product curve.

Notice that the TPcurvebecomes steeper at lowoutput levels and then lesssteep at high output levels.

In contrast, the TVCcurvebecomes less steep at lowoutput levels and steeperat high output levels.

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To see the relationshipbetween the TVCcurveand the TPcurve, lets lookagain at the TPcurve.

But let us add a secondx-axis to measure totalvariable cost.

1 worker costs $25; 2workers cost $50: and soon, so the twox-axes lineup.

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We can replace thequantity of labor on thex-axis with total variablecost.

When we do that, we mustchange the name of thecurve. It is now the TVCcurve.

But it is graphed with coston thex-axis and outputon the y-axis.

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Redraw the graph withcost on the y-axis andoutput on thex-axis, andyouve got the TVCcurve

drawn the usual way.

Put the TFCcurve back inthe figure,

and add TFCto TVC, andyouve got the TCcurve.

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Marginal Cost

Marginal cost(MC)is the increase in total cost thatresults from a one-unit increase in total product.

Over the output range withincreasing marginal returns,marginal cost falls as output increases.

Over the output range withdiminishing marginal returns,marginal cost rises as output increases.

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Average Cost

Average cost measures can be derived from each of thetotal cost measures:

Average fixed cost(AFC)is total fixed cost per unit ofoutput.

Average variable cost(AVC)is total variable cost per unitof output.

Average total cost(ATC)is total cost per unit of output.

ATC = AFC + AVC.

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Figure 11.5 shows the MC,AFC,AVC, andATCcurves.

TheAFCcurve shows that

average fixed cost falls asoutput increases.

TheAVCcurve is U-shaped.As output increases,

average variable cost falls toa minimum and thenincreases.

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TheATCcurve is alsoU-shaped.

The MCcurve is veryspecial.

The outputs over whichAVCis falling, MCis belowAVC.

The outputs over whichAVC

is rising, MCis aboveAVC.The output at whichAVC is atthe minimum, MCequalsAVC.

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Similarly, the outputs overwhichATCis falling, MCis

belowATC.The outputs over whichATCis rising, MCis aboveATC.

At the minimumATC, MCequalsATC.

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Why the Average Total Cost Curve Is U-Shaped

TheAVCcurve is U-shaped because:

Initially, marginal product exceeds average product, which

brings rising average product and fallingAVC.

Eventually, marginal product falls below average product,which brings falling average product and risingAVC.

TheATC curve is U-shaped for the same reasons. Inaddition,ATCfalls at low output levels becauseAFCisfalling steeply.

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Cost Curves and Product Curves

The shapes of a firms cost curves are determined by the

technology it uses:

MCis at its minimum at the same output level at whichmarginal product is at its maximum.

When marginal product is rising, marginal cost is falling.

AVCis at its minimum at the same output level at whichaverage product is at its maximum.

When average product is rising, average variable cost isfalling.

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Figure 11.6 shows theserelationships.

Short-Run Cost


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Shifts in Cost Curves

The position of a firms cost curves depend on two factors:

Technology

Prices of factors of production

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Technology

Technological change influences both the productivitycurves and the cost curves.

An increase in productivity shifts the average and marginalproduct curves upward and the average and marginal costcurves downward.

If a technological advance brings more capital and less

labor into use, fixed costs increase and variable costsdecrease.

In this case, average total cost increases at low outputlevels and decreases at high output levels.

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Prices of Factors of Production

An increase in the price of a factor of production increasescosts and shifts the cost curves.

An increase in a fixedcost shifts the total cost (TC ) andaverage total cost (ATC ) curves upward but does notshiftthe marginal cost (MC ) curve.

An increase in a variablecost shifts the total cost (TC ),average total cost (ATC ), and marginal cost (MC ) curvesupward.

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Long-Run Cost

In the long run, all inputs are variable and all costs arevariable.

The Production Function

The behavior of long-run cost depends upon the firmsproduction function.

The firmsproduction functionis the relationship betweenthe maximum output attainable and the quantities of both

capital and labor.


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Long-Run Cost

Table 11.3 shows a firms

production function.

As the size of the plant

increases, the output that agiven quantity of labor canproduce increases.

But as the quantity of labor

increases, diminishingreturns occur for each plant.


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Diminishing Marginal Product of Capital

The marginal product of capitalis the increase in outputresulting from a one-unit increase in the amount of capital

employed, holding constant the amount of labor employed.A firms production function exhibits diminishing marginal

returns to labor (for a given plant) as well as diminishingmarginal returns to capital (for a quantity of labor).

For eachplant, diminishing marginal product of laborcreates a set of short run, U-shaped costs curves for MC,AVC,andATC.

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Short-Run Cost and Long-Run Cost

The average cost of producing a given output varies anddepends on the firms plant.

The larger the plant, the greater is the output at whichATCis at a minimum.

The firm has 4 different plants: 1, 2, 3, or 4 knittingmachines.

Each plant has a short-runATCcurve.

The firm can compare theATCfor each output at differentplants.

Long-Run Cost


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ATC1is theATCcurve for a plant with 1 knitting machine.Long-Run Cost


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ATC2is theATCcurve for a plant with 2 knitting machines.Long-Run Cost


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ATC3is theATCcurve for a plant with 3 knitting machines.

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ATC4is theATCcurve for a plant with 4 knitting machines.

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The long-run average cost curve is made up from thelowestATCfor each output level.

So, we want to decide which plant has the lowest cost for

producing each output level.

Lets find the least-cost way of producing a given outputlevel.

Suppose that the firm wants to produce 13 sweaters aday.

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13 sweaters a day cost $7.69 each onATC1.Long-Run Cost


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13 sweaters a day cost $6.80 each onATC2.

Long-Run Cost


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Long-Run Cost


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Long-Run Cost


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13 sweaters a day cost $6.80 each onATC2.The least-cost way of producing 13 sweaters a day.

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Long-Run Average Cost Curve

The long-run average cost curveis the relationshipbetween the lowest attainable average total cost and

output when both the plant and labor are varied.

The long-run average cost curve is a planning curve thattells the firm the plant that minimizes the cost of producinga given output range.

Once the firm has chosen its plant, the firm incurs thecosts that correspond to theATCcurve for that plant.

Long-Run Cost


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Figure 11.8 illustrates the long-run average cost (LRAC) curve.

Long-Run Cost


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Economies and Diseconomies of Scale

Economies of scaleare features of a firms technologythat lead to falling long-run average cost as output

increases.

Diseconomies of scaleare features of a firmstechnology that lead to rising long-run average cost asoutput increases.

Constant returns to scaleare features of a firmstechnology that lead to constant long-run average cost asoutput increases.

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Figure 11.8 illustrates economies and diseconomies of scale.

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Minimum Efficient Scale

A firm experiences economies of scale up to some outputlevel.

Beyond that output level, it moves into constant returns toscale or diseconomies of scale.

Minimum efficient scaleis the smallest quantity of outputat which the long-run average cost reaches its lowest

level.If the long-run average cost curve is U-shaped, theminimum point identifies the minimum efficient scaleoutput level.

Long-Run Cost

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Outputs and Costs