production costs [compatibility mode]

8/3/2019 Production Costs [Compatibility Mode]

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Production Decisions of a Firm

Production Technology

Describes how inputs can be transformedinto outputs

• In uts: land, labor, ca ital and raw materials

• Outputs: cars, desks, books, etc.

Firms can produce different amounts of outputs using different combinations of inputs

The Technology of Production

• The production function for two inputs:

q = F(K,L)

– Output (q ) is a function of capital (K) and

– The production function is true for a giventechnology

• If technology increases, more output can beproduced for a given level of inputs

The Technology of Production

• Short Run – Period of time in which quantities of one or

more production factors cannot be changed

– These inputs are called fixed inputs

• Long Run – Amount of time needed to make all

production inputs variable

• Short run and long run are not timespecific

Production and Costs

• What do the terms “fixed” and “variable” mean?• Some inputs are more readily changed than

others. It can take five years or more to orderand obtain new passenger aircraft, four years tobuild an electricity generation facility or a pulpand paper mill.

• Very skilled labor – experienced engineers,animators, patent attorneys – is often hard tofind and challenging to hire. It usually takesthree to five years to hire even a small number

of academic economists.




• On the other hand, it is possible to buyshovels, telephones, and computers and tohire a variety of temporary workers quiterapidly, in a matter of a day or so.

• Moreover, additional hours of work can beobtained by an existing labor force simplyby hiring them “overtime,” at least on atemporary basis.

• The amount of water or electricity aproduction facility uses can be variedsecond by second.

Production: One Variable Input

• We will begin looking at the short runwhen only one input can be varied

• We assume capital is fixed and labor is

– Output can only be increased by increasinglabor

– Must know how output changes as theamount of labor is changed


• We can relate the total amount of outputproduced to the amount of labor use

• We will then get a total product curve

• We can grap t e in ormation in t e ta eto show

– How output varies with changes in labor

• Output is maximized at 112 units




Outputper

Month112

D


At point D, output is

maximized.

Labor per Month0 2 3 4 5 6 7 8 9 101

Total Product

60

A

B

C


• Average product of Labor - Output perunit of a particular product

• Measures the productivity of a firm’s labor, ,

worker can produce

L

q

Input Labor

Output AP L


• Marginal Product of Labor – additionaloutput produced when labor increases byone unit

•labor

L

q

Input Labor

Output MP

L


• We can graph the information in the tableto show

– Average and Marginal Products

is increasing

• Marginal Product crosses Average Product at itsmaximum




Outputper

Worker

30

Marginal Product

•Left of E: MP > AP & AP is increasing•Right of E: MP < AP & AP is decreasing•At E: MP = AP & AP is at its maximum

•At 8 units, MP is zero and output is at max

Average Product

10

20

80 2 3 4 5 6 7 9 101 Labor per Month

E

Marginal and Average Product

• When marginal product is greater than theaverage product, the average product isincreasing

• When marginal product is less than the averageproduct, the average product is decreasing

• When marginal product is zero, total product(output) is at its maximum

• Marginal product crosses average product at itsmaximum

Law of Dim inishing Marginal Returns

• If at least one input is a fixed input, thenthe marginal product of any other inputwill, eventually, decrease as more of that

• If the production function is graphed, itappears as a concave curve

Law of Diminishing Marginal Returns

• Assumes a constant technology

– Changes in technology will cause shifts in thetotal product curve

–inputs

– Labor productivity can increase if there areimprovements in technology, even though anygiven production process exhibits diminishingreturns to labor



The Effect of TechnologicalImprovement

Output

100

C

O 3

B

Moving from A to B toC, labor productivity isincreasing over time

50

Labor pertime period

0 2 3 4 5 6 7 8 9 101

A

O 1

O 2

Costs

Short run versus long run

In the long run, the firm can vary all itsinputs

,be varied

In the short run, we usually assume thatcapital inputs cannot be varied – fixedinputs

But over a longer period of time, a firm can

buy new plants and machinery


• Consider a short run situation

• A firm can increase or decrease its outputonly by varying the number of workers

• T e wage cost wi vary wit t e amount oproduction

• The rental cost of capital will be fixed

• TC = wL + rK, where K is fixed

Measuring Cost

• Some costs vary with output, while someremain the same no matter the amountof output in the short run

1. Fixed Cost

– Does not vary with the level of output

2. Variable Cost

– Cost that varies as output varies



Fixed and Variable Costs

• Therefore, the total cost of productionequals the fixed cost (the cost of the fixedinputs) plus the variable cost (the cost of

, …

TC = TFC + TVC

where

TFC = rK, TVC = wL

The Total Cost

Assume:

Cost associated with fixed input (plant andmachinery) is 30 – does not vary with

Wage paid to each employee is 10

– total wage payment is a variable cost

- depends on amount of output produced

Total product

Workers Output Wage Cost

0 0 0

1 50 10

2 90 20

3 120 30

4 140 40

5 150 50

The Total Cost

Workers Total fixed Total variable Total cost

cost cost

0 30 0 30

1 30 10 40

2 30 20 50

3 30 30 60

4 30 40 70

5 30 50 80



The Total Cost Curve

Quantity of output Total cost Marginal cost

0 30

50 40 1/5

90 50 1/4

120 60 1/3

140 70 1/2

150 80 1

Marginal cost = TC/Q

Total-Cost Curve

Cost Curves for a Firm

Cost($ peryear)

300

400

VC

Variable costincreases with

TC

Total costis the vertical

sum of FCand VC.

Output

100

200

0 1 2 3 4 5 6 7 8 9 10 11 12 13

production andthe rate varies with

increasing anddecreasing returns.

FC50

Fixed cost does notvary with output

Average costs

• Total, fixed and variable costs

• Corresponding to each, we have anaverage concept:

- Average tota cost ATC = TC Q

- Average fixed cost (AFC) = FC/Q

- Average variable cost (AVC) = VC/Q

Note: ATC = AFC + AVC



The Total Cost

Q TFC TVC TC AFC AVC AC

0 30 0 30 -

90 30 20 50 1/3 2/9 5/9

120 30 30 60 ¼ ¼ 1/2

140 30 40 70 3/14 2/7 1/2

150 30 50 80 1/5 1/3 8/15

Total Cost and Marg inal Cost Curves

Why is the marginal cost curve upward sloping?

Because there are diminishing returns to inputs in this example. As output increases, the marginal product of the variable inputdeclines. This implies that more and more of the variable inputmust be used to produce each additional unit of output as theamount of output already produced rises. And since each unit of the variable input must be paid for, the cost per additional unit of output also rises.

The MC curve

• The diagram shows that the MC curve isupward sloping

• That is, for high levels of output, marginalcost kee s on increasin

• This follows from the assumption of diminishing marginal returns

• Even with input prices fixed, it requires

more and more variable inputs at themargin to increase output

The MC curve

TC = wL + rK

TC = wL = (wL2 – wL1) = w(L2 – L1)

= wL

TC/Q = w(L/Q) = w/(Q/L)

MC = w/MPL

Then by law of diminishing marginal returns,eventually MC must rise



Marginal Cost and Average Cost Curves

The bottom of the U curve is at the level of output at which themarginal cost curve crosses the average total cost curve frombelow. Is this an accident? No!

The Relationship Betw een the AverageTotal Cost and the Marginal Cost Curves

When marginal cost equals average total cost, we must be at thebottom of the U, because only at that point is average total costneither falling nor rising.

Cost Curves

• When MC is below ATC, ATC is falling

• When MC is above ATC, ATC is rising

• When MC is below AVC, AVC is falling

• When MC is above AVC, AVC is rising

• Therefore, MC crosses AVC and ATC at theminimums

– The Average – Marginal relationship

Average Total Cost Curve

Increasing output, therefore, has two opposingeffects on average total cost—the “spreading effect ” and the “diminishing returns effect ”:

The spreading effect : the larger the output, “ ”

cost, and therefore the lower the averagefixed cost.The diminishing returns effect : the more

output produced, the more variable input it

requires to produce additional units, andtherefore the higher the average variable cost.



Average Total Cost Curve

The average total cost curve is U-shaped. At low levels of output,average total cost falls because the “spreading effect” of fallingaverage fixed cost dominates the “diminishing returns effect” of rising average variable cost. At higher levels of output, the

opposite is true and average total cost rises.

Long Run

• In the long run, all inputs are variable.

• The firm’s problem is to select that inputcombination that minimizes the cost of

.

• In the long run, the firm is free to vary allinputs. Therefore it has more flexibilityand in general achieves a lower cost of production than in the short run.

Long Run VersusShort Run Cost Curves

• Long-Run Average Cost (LAC)

– Most important determinant of the shape of the LR AC and MC curves is relationshipbetween scale of the firm’s o eration andinputs required to minimize cost

1. Constant Returns to Scale

– If input is doubled, output will double

– AC cost is constant at all levels of output

Long Run Versus Short Run CostCurves

2. Increasing Returns to Scale

– If input is doubled, output will more thandouble

–

3. Decreasing Returns to Scale

– If input is doubled, output will less thandouble

– AC increases at all levels of output




• In the long run:

– Firms experience increasing and decreasingreturns to scale and therefore long-runavera e cost is “U” sha ed.

– Source of U-shape is due to returns to scaleinstead of decreasing marginal returns like theshort-run curve

Long Run Costs

• As output increases, firm’s AC of producing is likely to decline to a point1. On a larger scale, workers can better

specialize

2. Scale can provide flexibility – managers canorganize production more effectively

3. Firm may be able to get inputs at lower costif can get quantity discounts. Lower pricesmight lead to different input mix.

We say that there are economies of scale.

Long Run Costs

• At some point, AC will begin to increase

1. Factory space and machinery may make it moredifficult for workers to do their jobs efficiently

2. Managing a larger firm may become morecomplex and inefficient as the number of tasksincrease

3. Bulk discounts can no longer be utilized. Limitedavailability of inputs may cause price to rise.

We say that there are diseconomies of scale.

Diseconomies of Scale

• U-shaped LAC shows economies of scalefor relatively low output levels anddiseconomies of scale for higher levels




• We will use short and long run costs todetermine the optimal plant size

• We can show the short run average costsfor 3 different lant sizes

• Which plant is optimal for which level of output?

• This is important because once built, thefirm may not be able to change plant sizefor a while

Long Run Cost

• The optimal plant size will depend on theanticipated output

– If expect to produce q0, then should build=

– If produce more, like q1, AC rises

– If expect to produce q2, middle plant is leastcost

– If expect to produce q3, largest plant is best

Long Run Cost with Economiesand Diseconomies of Scale

Example

Inkjet printer versus a laser printer: Short-term versus long-term

• Suppose that a firm can choose between ann e pr n er w c cos s s. or a aserprinter which costs Rs.8000.

• The per page printing cost for an inkjet isRs.1.80 and that for a laser printer isRs.1.50.

• Which one should the firm buy?



Example contd.

• If q denotes the number of pagesprinted, the total costs will be

• CIJ = 5000 + 1.8q and

• CL = 8,000 + 1.5q

• The average cost curves are given by

• ACIJ = 5000/q + 1.8 and

• ACL = 8,000/q + 1.5

Example contd.

• It can be seen that

ACL - ACIJ = 3000/q – 0.3

and therefore, for q > 10,000, AC < ACIJ.

Whether the firm should then buy theinkjet printer or the laser printer willthen depend on its expected rate of printing of pages.

Example contd.

If, for example, only 10 pages are to beprinted every day, then it will take1000 days (almost three years) before

- effective.

On the other hand, if the expected rateof usage is (say) 100 pages per day,

then the laser printer will become cost-effective after 100 days.

Long Run Marginal Cost Curves

Long-run marginal cost curve measures thechange in long-run total costs as output isincreased by 1 unit

• Long-run marginal cost leads long-run average

– If LMC < LAC, LAC will fall

– If LMC > LAC, LAC will rise

– Therefore, LMC = LAC at the minimum of LAC

• In special case where LAC is constant, LAC andLMC are equal



Long Run Average and Marginal Cost

Cost($ per unitof output

LAC

LMC

Output

A

Production with Two Outputs –Economies of Scope

• Many firms produce more than oneproduct and those products are closelylinked

•

– Chicken farm--poultry and eggs

– Automobile company--cars and trucks

– University--teaching and research

Production with Two Outputs

• Advantages

1. Both use capital and labor

2. The firms share management resources

3. Both use the same labor skills and typesof machinery

Multi-product firms

Economies of scope refer to thepossibility of achieving lower costs byproducing goods jointly rather thanseparately (sometimes referred to as ‘synergy effects’).



Multi-product firms

• Such economies exist when

C(q1, q2) < C(q1, 0) + C(0, q2).

Example

Let C(q1, q2) = q12 + q2 - q1 q2.

Then C(q1,0) = q12

C(0, q2) = q2

herefore

• C(q1,0) + C(0, q2) = q12 + q2 > q1

2 + q2 - q1 q2.

Economies of Scope

• The degree of economies of scope (SC) canbe measured by percentage of cost savedproducing two or more products jointly:

– C(q1) is the cost of producing q1

– C(q2) is the cost of producing q2

– C(q1,q2) is the joint cost of producing both products

)qC(q SC

,

,

21

2121

Economies of Scope

• Interpretation:

– If SC > 0 Economies of scope

– If SC < 0 Diseconomies of scope

– The greater the value of SC, the greater theeconomies of scope

Example: C(q1, q2) = q12 + q2 - q1 q2.

• SC = [C(q1, 0) + C(0, q2) - C(q1, q2)]/C(q1, q2)= q1 q2 /(q1

2 + q2 - q1 q2)

production costs [compatibility mode]

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