Lecture 9 costs

Chapter 7

The Cost of Production

©2005 Pearson Education, Inc. Chapter 7 2

Expansion Path

Expansion Path

The expansion path illustratesthe least-cost combinations oflabor and capital that can be used to produce each level of

output in the long-run.

Capitalper

year

25

50

75

100

150

50Labor per year

100 150 300200

A

$2000

200 Units

B

$3000

300 Units

C


Optimal Inputs

The minimum cost combination can then be written as:

Increase in output for every dollar spent on an input is same for all inputs.

rwKL MPMP

©2005 Pearson Education, Inc.

Expansion Path

It shows optimal input combinations to minimize cost to produce different levels of output

It shows the minimum cost to produce different levels of output

It shows the maximum amount of output that can be produced for different levels of expenditure.


A Firm’s Long Run Total Cost Curve

Long Run Total Cost

Output, Units/yr100 300200

Cost/ Year

1000

2000

3000

D

E

F


LONG RUN AND SHORT RUN COSTS

Chapter 7 7


Long Run Versus Short Run Cost Curves

In the short run, some costs are fixedIn the long run, firm can change anything

including plant sizeCan produce at a lower average cost in long

run than in short runCapital and labor are both flexible

We can show this by holding capital fixed in the short run and flexible in long run


Capital is fixed at K1.To produce q1, min cost at K1,L1.If increase output to Q2, min cost

is K1 and L3 in short run.

The Inflexibility of Short Run Production

Long-RunExpansion Path

Labor per year

Capitalper

year

L2

Q2

K2

D

C

F

E

Q1

A

BL1

K1

L3

PShort-RunExpansion Path

In LR, can change capital and min costs falls to K2 and L2.


Production technology measures the relationship between input and output

Production technology, together with prices of factor inputs, determine the firm’s cost of production


Introduction

The optimal, cost minimizing, level of inputs can be determined

A firm’s costs depend on the rate of output

The characteristics of the firm’s production technology affect costs in the long run and short run


Measuring Cost:Which Costs Matter?

For a firm to minimize costs, we must clarify what is meant by costs and how to measure them

It is clear that if a firm has to rent equipment or buildings, the rent they pay is a cost

What if a firm owns its own equipment or building?

How are costs calculated here?



Accounting CostActual expenses plus depreciation charges

for capital equipment

Economic CostCost to a firm of utilizing economic resources

in production, including opportunity cost


Opportunity Cost

An ExampleA firm owns its own building and pays no rent

for office spaceDoes this mean the cost of office space is

zero?The building could have been rented insteadForegone rent is the opportunity cost of

using the building for production and should be included in the economic costs of doing business


Opportunity Cost

A person starting their own business must take into account the opportunity cost of their timeCould have worked elsewhere making a

competitive salary



Some costs vary with output, while some remain the same no matter the amount of output

Total cost can be divided into:

1. Fixed Cost Does not vary with the level of output

2. Variable Cost Cost that varies as output varies


Fixed and Variable Costs

Total output is a function of variable inputs and fixed inputs

Therefore, the total cost of production equals the fixed cost (the cost of the fixed inputs) plus the variable cost (the cost of the variable inputs), or…

VC FC TC


Fixed and Variable Costs

Which costs are variable and which are fixed depends on the time horizon

Short time horizon – most costs are fixedLong time horizon – many costs become

variable



Personal ComputersMost costs are variable Largest component: labor

SoftwareMost costs are sunkInitial cost of developing the software


Narayan Hridalaya

Providing health care

involves high costs and low accessibilityWhat does a hospital produce?What does a hospital use to produce this?Narayan Hridalaya founded on the principle

of providing low cost and accessible health care to all

20


Daily Bread

Multiple outlets in and

around Bangalore

What are the outputs they produce?

What are the inputs?

21


AVERAGE AND MARGINAL COST

Chapter 7 22


Marginal and Average Cost

In completing a discussion of costs, must also distinguish between

Average CostMarginal Cost


Measuring Costs

Marginal Cost (MC):The cost of expanding output by one unitFixed costs have no impact on marginal cost,

so it can be written as:

Δq

ΔTC

Δq

ΔVC MC


Measuring Costs

Average Total Cost (ATC)Cost per unit of outputAlso equals average fixed cost (AFC) plus

average variable cost (AVC)

q

TVC

q

TFC

q

TC ATC

AVCAFC q

TC ATC


A Firm’s Short Run Costs


MC AND AC CURVES

Chapter 7 27


Determinants of Short Run Costs – An Example

Assume the wage rate (w) is fixed relative to the number of workers hired

Variable costs is the per unit cost of extra labor times the amount of extra labor: wL

q

Lw

q

VC MC



Remembering that

L MPL

Q

LMP

1

Q

L Qunit 1 afor L

And rearranging



We can conclude:

LMP MC

w

…and a low marginal product (MPL) leads to a high marginal cost (MC) and vice versa


Determinants of Short Run Costs

The rate at which these costs increase depends on the amount of input changes with change in output

i.e. Costs depend upon the nature of production process..



If marginal product of labor decreases significantly as more labor is hired

Costs of production increase rapidly

Greater and greater expenditures must be made to produce more output



Consequently (from the table):

MC decreases initially with increasing returns 0 through 4 units of output

MC increases with decreasing returns5 through 11 units of output


Cost Curves for a Firm

Output

Cost($ peryear)

100

200

300

400

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

VC

Variable costincreases with production and

the rate varies withincreasing and

decreasing returns.

TC

Total costis the vertical

sum of FC and VC.

FC50

Fixed cost does notvary with output


Cost Curves

0

20

40

60

80

100

120

0 2 4 6 8 10 12

Output (units/yr)

Co

st (

$/u

nit

)

MC

ATC

AVC

AFC


Cost Curves

When MC is below AVC, AVC is fallingWhen MC is above AVC, AVC is risingWhen MC is below ATC, ATC is fallingWhen MC is above ATC, ATC is risingTherefore, MC crosses AVC and ATC at

the minimumsThe Average – Marginal relationship


Cost Curves for a FirmThe line drawn from

the origin to the variable cost curve: Its slope equals AVCThe slope of a point

on VC or TC equals MC

Therefore, MC = AVC at 7 units of output (point A)

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

Output

P

100

200

300

400

FC

VC

TC

A


LONG RUN COSTS

Chapter 7 39


Long Run Cost with Economiesand Diseconomies of Scale


Long Run Cost withConstant Returns to Scale

The optimal plant size will depend on the anticipated outputIf expect to produce q0, then should build

smallest plant: AC = $8If produce more, like q1, AC rises

If expect to produce q2, middle plant is least cost

If expect to produce q3, largest plant is best


Long Run Cost with Economiesand Diseconomies of Scale



What is the firm’s long run cost curve?Firms can change scale to change output in

the long runThe long run cost curve is the dark blue

portion of the SAC curve which represents the minimum cost for any level of output

Firm will always choose plant that minimizes the average cost of production



The long-run average cost curve envelops the short-run average cost curves

The LAC curve exhibits economies of scale initially but exhibits diseconomies at higher output levels


RETURNS TO SCALE

Chapter 7 47


BIG CITIES

Metropolis twice the size of one, number of gas stations, length of pipelines, infrastructure decreases by 15%

Why?

48


Narayan Hridalaya

Provide health care at full price

To patients from well to do background

These patients subsidize `poor’ patientsRun at a profit of 7.7%Why is Narayan Hridalaya able to do this?

49


Narayan Hridalaya

Number of Beds, 2001: 225

Current No. of Beds across India: 30,000

How does number of beds play a role in profits?

50

©2005 Pearson Education, Inc. 51

Returns to Scale

Rate at which output increases as inputs are increased proportionately

Increasing returns to scaleConstant returns to scaleDecreasing returns to scale


Returns to Scale

Increasing returns to scale: output more than doubles when all inputs are doubled

What happens to the isoquants?


Increasing Returns to Scale

10

20

30

The isoquants move closer together

Labor (hours)5 10

Capital(machine

hours)

2

4

A



Increasing Returns to Scale

If input is doubled, output will more than double

To double output input is less than doubled AC decreases at all levels of output


Long Run Costs

As output increases, firm’s AC of producing is likely to decline to a point

1. On a larger scale, workers can better specialize

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

3. Firm may be able to get inputs at lower cost if can get quantity discounts. Lower prices might lead to different input mix.


Returns to Scale

Constant returns to scale: output doubles when all inputs are doubled

Isoquants are equidistant apart


Returns to Scale

Constant Returns:

Isoquants are

equally spaced

20

30

Labor (hours)155 10

A

10

Capital(machine

hours)

2

4

6


Long Run VersusShort Run Cost Curves

Constant Returns to Scale

If input is doubled, output will double To double output, input has to less than

double AC cost is constant at all levels of output


Returns to Scale

Decreasing returns to scale: output less than doubles when all inputs are doubled

Isoquants become farther apart



Decreasing Returns to Scale

If input is doubled, output will less than double

To double output has to more than double

AC increases at all levels of output


Long Run Costs

At some point, AC will begin to increase1. Factory space and machinery may make it

more difficult for workers to do their jobs efficiently

2. Managing a larger firm may become more complex and inefficient as the number of tasks increase

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



In the long run:Firms experience increasing and decreasing

returns to scale and therefore long-run average cost is “U” shaped.

Long-run marginal cost curve measures the change in long-run total costs as output is increased by 1 unit



Long-run marginal cost leads long-run average cost:If LMC < LAC, LAC will fallIf LMC > LAC, LAC will riseTherefore, LMC = LAC at the minimum of

LAC

In special case where LAC is constant, LAC and LMC are equal


Long Run Average and Marginal Cost

Output

Cost($ per unitof output

LAC

LMC

A


Economies and Diseconomies of Scale

Economies of ScaleIncrease in output is greater than the

increase in inputsDiseconomies of Scale

Increase in output is less than the increase in inputs

U-shaped LAC shows economies of scale for relatively low output levels and diseconomies of scale for higher levels


Long Run Costs

Increasing Returns to ScaleOutput more than doubles when the

quantities of all inputs are doubled

Economies of ScaleDoubling of output requires less than a

doubling of cost


COST OUTPUT ELASTICITY

Chapter 7 68


Long Run Costs

Economies of scale are measured in terms of cost-output elasticity, EC

EC is the percentage change in the cost of production resulting from a 1-percent increase in output

ACMC

QQCCEC


Long Run Costs

EC is equal to 1, MC = ACCosts increase proportionately with outputNeither economies nor diseconomies of scale

EC < 1 when MC < ACEconomies of scaleBoth MC and AC are declining

EC > 1 when MC > ACDiseconomies of scaleBoth MC and AC are rising


ECONOMIES OF SCOPE

Chapter 7 71


Economies of Scope

P&G produces different types of anti aging creams

Would it benefit P&G to

Produce them separately?

Chapter 7 72


Production with Two Outputs – Economies of Scope

Many firms produce more than one product and those products are closely linked

Examples:Chicken farm--poultry and eggsAutomobile company--cars and trucksUniversity--teaching and research



Advantages

1. Both use capital and labor

2. The firms share management resources

3. Both use the same labor skills and types of machinery



The degree of economies of scope (SC) can be measured by percentage of cost saved producing 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

)qC(q)C(q)C(q SC

,

,

21

2121



With economies of scope, the joint cost is less than the sum of the individual costs

Interpretation:If SC > 0 Economies of scopeIf SC < 0 Diseconomies of scopeThe greater the value of SC, the greater the

economies of scope



There is no direct relationship between economies of scope and economies of scaleMay experience economies of scope and

diseconomies of scaleMay have economies of scale and not have

economies of scope

Lecture 9 costs

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