Topic1 Cost of Production 12 13 xModo de Compatibilidadx

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Microeconomics. Antoni Cunyat

Topic1.TheCostofProduction

Bibliography: Pindyck and Rubinfeld.

Chapters 6 (pages 201-215 and 223-224)and 7 (pages 229-242 and 253-260)


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2 of 49Microeconomics. Antoni Cunyat

Preliminaries: Production


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THE TECHNOLOGY OF PRODUCTION

The Production Function

factors of production Inputs into the productionprocess (e.g., labor, capital, and materials).

Remember the following:

( , )q F K L

Equation (6.1) applies to a given technology.

Production functions describe what is technically feasible

when the firm operates efficiently.

production function Function showing the highest

output that a firm can produce for every specifiedcombination of inputs.

(6.1)


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THE TECHNOLOGY OF PRODUCTION

The Short Run versus the Long Run

short run Period of time in which quantities of one ormore production factors cannot be changed.

fixed input Production factor that cannot be varied.

long run Amount of time needed to make allproduction inputs variable.


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TABLE 6.1 Production with One Variable Input

0 10 0

1 10 10 10 10

2 10 30 15 20

3 10 60 20 30

4 10 80 20 20

5 10 95 19 15

6 10 108 18 13

7 10 112 16 4

8 10 112 14 0

9 10 108 12 4

10 10 100 10 8

PRODUCTION WITH ONE VARIABLE INPUT

(SHORT RUN)

TotalOutput (q)

Amountof Labor (L)

Amountof Capital (K)

Marginal

Product (q/L)

AverageProduct (q/L)


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(SHORT RUN)

Average and Marginal Products

average product Output per unit of a particular input.

marginal product Additional output produced as an input isincreased by one unit.

Average product of labor = Output/labor input = q/L

Marginal product of labor = Change in output/change in labor input

= q/L


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(SHORT RUN)

The Slopes of the Product Curve

The total product curve in (a) showsthe output produced for different

amounts of labor input.

The average and marginal products

in (b) can be obtained (using thedata in Table 6.1) from the total

product curve.

At pointA in (a), the marginalproduct is 20 because the tangent

to the total product curve has a

slope of 20.

At point B in (a) the average productof labor is 20, which is the slope ofthe line from the origin to B.

The average product of labor at

point Cin (a) is given by the slopeof the line 0C.

Production with One Variable Input

Figure 6.1


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(SHORT RUN)

The Slopes of the Product Curve

To the left of point Ein (b), themarginal product is above the

average product and the average is

increasing; to the right ofE, the

marginal product is below the

average product and the average is

decreasing.

As a result, Erepresents the point

at which the average and marginal

products are equal, when the

average product reaches its

maximum.

At D, when total output is

maximized, the slope of the tangent

to the total product curve is 0, as is

the marginal product.

Production with One Variable Input

(continued)

Figure 6.1


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(SHORT RUN)

The Law of Diminishing Marginal Returns

Labor productivity (output

per unit of labor) can

increase if there are

improvements in technology,

even though any given

production process exhibits

diminishing returns to labor.

As we move from pointA on

curve O1 to B on curve O2 to

Con curve O3 over time,

labor productivity increases.

The Effect of TechnologicalImprovement

Figure 6.2

law of diminishing marginal returns Principle that as the

use of an input increases with other inputs fixed, the resulting

additions to output will eventually decrease.


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PRODUCTION WITH TWO VARIABLE INPUTS

(LONG RUN).

RETURNS TO SCALE

returns to scale Rate at which output increases as

inputs are increased proportionately.

increasing returns to scale Situation in which outputmore than doubles when all inputs are doubled.

constant returns to scale Situation in which outputdoubles when all inputs are doubled.

decreasing returns to scale Situation in which output

less than doubles when all inputs are doubled.


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THE MEASUREMENT OF COSTS1.1


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Economic Cost versus Accounting Cost

accounting cost Actual expensesplus depreciation charges for capital

equipment.

economic cost Cost to a firm ofutilizing economic resources in

production, including opportunity cost.

Opportunity Cost

opportunity cost Cost associated withopportunities that are forgone when a

firms resources are not put to their bestalternative use.


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Sunk Costs

sunk cost Expenditure that hasbeen made and cannot be

recovered.

Because a sunk cost cannot be recovered, it should not

influence the firms decisions.

For example, consider the purchase of specializedequipment for a plant. Suppose the equipment can be used

to do only what it was originally designed for and cannot be

converted for alternative use. The expenditure on this

equipment is a sunk cost. Because it has no alternative use,

its opportunity cost is zero. Thus it should not be included aspart of the firms economic costs.


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1.1

The Northwestern University Law School has been located in Chicago. However, the

main campus is located in the suburb of Evanston.

In the mid-1970s, the law school began planning the construction of a new building

and needed to decide on an appropriate location.

Should it be built on the current site, near downtown Chicago law firms?

Should it be moved to Evanston, physically integrated with the rest of the university?

Some argued it was cost-effective to locate the new building in the city because the

university already owned the land. Land would have to be purchased in Evanston if

the building were to be built there.

Does this argument make economic sense?

No. It makes the common mistake of failing to appreciate opportunity costs. From aneconomic point of view, it is very expensive to locate downtown because the property

could have been sold for enough money to buy the Evanston land with substantial

funds left over.

Northwestern decided to keep the law school in Chicago.

THE MEASUREMENT OF COSTS


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Fixed Costs and Variable Costs

total cost (TC orC) Total economic

cost of production, consisting of fixedand variable costs.

fixed cost (FC) Cost that does notvary with the level of output and that

can be eliminated only by shuttingdown.

variable cost (VC) Cost that variesas output varies.

The only way that a firm can eliminate its fixed costs is by

shutting down.


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Fixed Costs and Variable Costs

Shutting Down

Shutting down doesnt necessarily mean going out of business.

By reducing the output of a factory to zero, the company could eliminate thecosts of raw materials and much of the labor. The only way to eliminate fixed

costs would be to close the doors, turn off the electricity, and perhaps even sell

off or scrap the machinery.

Fixed or Variable?How do we know which costs are fixed and which are variable?

Over a very short time horizonsay, a few monthsmost costs are fixed.

Over such a short period, a firm is usually obligated to pay for contracted

shipments of materials.

Over a very long time horizonsay, ten yearsnearly all costs are variable.

Workers and managers can be laid off (or employment can be reduced by

attrition), and much of the machinery can be sold off or not replaced as it

becomes obsolete and is scrapped.


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Fixed versus Sunk Costs

Sunk costs are costs that have been incurred and cannot be

recovered.

An example is the cost of R&D to a pharmaceutical company todevelop and test a new drug and then, if the drug has been

proven to be safe and effective, the cost of marketing it.

Whether the drug is a success or a failure, these costs cannot be

recovered and thus are sunk.


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It is important to understand the characteristics of production costs and to be able to

identify which costs are fixed, which are variable, and which are sunk.Good examples include the personal computer industry (where most costs are

variable), the computer software industry (where most costs are sunk), and the

pizzeria business (where most costs are fixed).

Because computers are very similar, competition is intense, and profitability

depends on the ability to keep costs down. Most important are the variable cost ofcomponents and labor.

A software firm will spend a large amount of money to develop a new application.

The company can try to recoup its investment by selling as many copies of the

program as possible.

For the pizzeria, sunk costs are fairly low because equipment can be resold if the

pizzeria goes out of business. Variable costs are lowmainly the ingredients for

pizza and perhaps wages for a couple of workers to help produce, serve, and

deliver pizzas.


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Marginal and Average Cost

Marginal Cost (MC)

marginal cost (MC) Increasein cost resulting from the

production of one extra unit of

output.

Because fixed cost does not change as the firms level of output changes,

marginal cost is equal to the increase in variable cost or the increase in

total cost that results from an extra unit of output.

We can therefore write marginal cost as


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TABLE 7.1 A Firms Costs

Rate of Fixed Variable Total Marginal Average Average AverageOutput Cost Cost Cost Cost Fixed Cost Variable Cost Total Cost(Units (Dollars (Dollars (Dollars (Dollars (Dollars (Dollars (Dollars

per Year) per Year) per Year) per Year) per Unit) per Unit) per Unit) per Unit)

(FC) (VC) (TC) (MC) (AFC) (AVC) (ATC)(1) (2) (3) (4) (5) (6) (7)

0 50 0 50 -- -- -- --1 50 50 100 50 50 50 100

2 50 78 128 28 25 39 64

3 50 98 148 20 16.7 32.7 49.3

4 50 112 162 14 12.5 28 40.5

5 50 130 180 18 10 26 36

6 50 150 200 20 8.3 25 33.3

7 50 175 225 25 7.1 25 32.1

8 50 204 254 29 6.3 25.5 31.8

9 50 242 292 38 5.6 26.9 32.4

10 50 300 350 58 5 30 35

11 50 385 435 85 4.5 35 39.5

Marginal Cost (MC)


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Average Total Cost (ATC)

average total cost (ATC)Firms total cost divided by its

level of output.

average fixed cost (AFC)Fixed cost divided by the level of

output.

average variable cost (AVC)Variable cost divided by the level ofoutput.


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COST IN THE SHORT RUN1.2


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The Determinants of Short-Run Cost

The change in variable cost is the per-unit cost of the extra laborwtimes

the amount of extra labor needed to produce the extra output L. Because

VC = wL, it follows that

The extra labor needed to obtain an extra unit of output is L/q = 1/MPL. As

a result,(7.1)

Diminishing Marginal Returns and Marginal Cost

Diminishing marginal returns means that the marginal product of labor

declines as the quantity of labor employed increases.

As a result, when there are diminishing marginal returns, marginal cost

will increase as output increases.


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The Shapes of the Cost Curves

Cost Curves for a Firm

In (a) total cost TC is thevertical sum of fixed cost

FC and variable cost VC.

In (b) average total costATC is the sum of

average variable cost

AVC and average fixedcost AFC.

Marginal cost MC crosses

the average variable cost

and average total cost

curves at their minimum

points.

Figure 7.1VC and TC grow

slowly (concave

shape). MPL is

increasing

VC and TC grow

quickly (convex

shape). MPL is

decreasing

MC is decreasing

MC is increasing


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The Shapes of the Cost Curves

The Average-MarginalRelationship

-When MCAVC, AVC curve

is increasing.

-When MC=AVC, minimum ofthe AVC curve.

-When MCATC, ATC curve

is increasing.

-When MC=ATC, minimum of

the ATC curve.


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ECONOMIES AND DISECONOMIES OF SCALE1.3


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Long-Run Total Cost

long-run total cost curve (LTC) Curverelating total cost of production to output when

all inputs, including capital, are variable.


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Long-Run Average Cost

long-run average cost curve (LAC) Curverelating average cost of production to output

when all inputs, including capital, are variable.

In contrast to:

short-run average cost curve (SAC) Curverelating average cost of production to output when

level of capital is fixed.


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Long-Run Marginal Cost

long-run marginal cost curve (LMC) Curve

showing the change in long-run total cost asoutput is increased incrementally by 1 unit.


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Shape of the Long-Run Average Cost

Long-Run Average and

Marginal Cost

LAC is U-shaped

-When LMCLAC, LAC curve

is increasing.

-When LMC>LAC, minimum

of the LAC curve.


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Long run total costs and returns to scale

constant returns to scale: long run total costs are linear inoutput, i.e., total costs increase in the same proportion as output.

increasing returns to scale: long run total costs are less thanlinearly in output (concave), i.e., total costs increase in a lower

proportion than output.

decreasing returns to scale: long run total costs are morethan linearly in output (convex), i.e., total costs increase in a

greater proportion than output.


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Long run average costs and returns to scale

constant returns to scale: average costs are constant sincetotal costs increase in the same proportion than output.

increasing returns to scale: average costs are decreasingsince total costs increase in a lower proportion than output.

decreasing returns to scale: average costs are increasing sincetotal costs increase in a greater proportion than output.


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Economies and Diseconomies of Scale

economies of scale Situationin which output can be doubled

for less than a doubling of cost.

diseconomies of scaleSituation in which a doubling of

output requires more than a

doubling of cost.

Increasing Returns to Scale: Output more than doubles when

the quantities of all inputs are

doubled.

Economies of Scale: A doubling of output requires less

than a doubling of cost.


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For lower levels of output, as output increases, the firms average

cost of producing that output is likely to decline (economies of scale),

at least to a point.

This can happen for the following reasons:

1. If the firm operates on a larger scale, workers can specialize

in the activities at which they are most productive.2. Scale can provide flexibility. By varying the combination of

inputs utilized to produce the firms output, managers can

organize the production process more effectively.

3. The firm may be able to acquire some production inputs atlower cost because it is buying them in large quantities and

can therefore negotiate better prices. The mix of inputs

might change with the scale of the firms operation if

managers take advantage of lower-cost inputs.


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Long-Run Average Cost and economies of scale

Economies of scale


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At some point, however, it is likely that the average cost of

production will begin to increase with output.

There are three reasons for this shift:

1. At least in the short run, factory space and machinery maymake it more difficult for workers to do their jobs effectively.

2. Managing a larger firm may become more complex andinefficient as the number of tasks increases.

3. The advantages of buying in bulk may have disappearedonce certain quantities are reached. At some point,

available supplies of key inputs may be limited, pushingtheir costs up.


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Long-Run Average Cost and diseconomies of scale

Diseconomies of scale


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LCT

Q

Q

LTC

LACLMC

CMLLMC

LAC

38

Economies of scale Diseconomies of scale


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The Relationship Between Short-Run and Long-Run Cost.Economies and diseconomies of scale

Output

Cost

SMC1

SAC1(K1)

SAC2(K2)

SMC2LMC

LAC with threeplant sizes is the

blue line.LAC with many

plant sizes is thered line

10$

q1

8$B

A

LALSAC3(K3)

SMC3

q2 q3


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The Relationship Between Short-Run and Long-Run Cost.Constant returns to scale

Output

Cost

q3

SAC3(K3)

SMC3

q2

SAC2(K2)

SMC2

LAC=LMC

LAC is the envelope of the short-run average curves SAC1, SAC2, SAC3:It is a straight line

q1

SAC1(K1)

SMC1

Topic1 Cost of Production 12 13 xModo de Compatibilidadx

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