Units 2&3 prod. & cost functions

1

Production Analysis

• Factors of Production– Land:

materials and forces that nature gives to man—land, water, air, light, heat, etc.

• Renewable and non renewable; inelastic supply.

– Labour• Time or service that individuals put into production• Quantity of labour vs. quality of labour• Division of labour.

– Capital:

‘produced means of production’.– Entrepreneurship

2

You run General Motors.

• List 3 different costs you have.

• List 3 different business decisions that are affected by your costs.

A C T I V E L E A R N I N G Brainstorming the concept of costs

2

3

Total Revenue, Total Cost, Profit

• We assume that the firm’s goal is to maximize profit.

Profit = Total revenue – Total cost

the amount a firm receives from the sale of its output

the market value of the inputs a firm uses in production

4

Costs: Explicit vs. Implicit

• Explicit costs require an outlay of money,e.g., paying wages to workers.

• Implicit costs do not require a cash outlay,e.g., the opportunity cost of the owner’s time.

• Remember one of the Ten Principles:The cost of something is what you give up to get it.

• This is true whether the costs are implicit or explicit. Both matter for firms’ decisions.

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Explicit vs. Implicit Costs: An ExampleYou need $100,000 to start your business.

The interest rate is 5%. • Case 1: borrow $100,000

– explicit cost = $5000 interest on loan

• Case 2: borrow $60,000, and use $40,000 of your savings– explicit cost = $3000 (5%) interest on the loan

– implicit cost = $2000 (5%) foregone interest you could have earned on your $40,000.

In both cases, total (expl + impl) costs are $5000.

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Economic Profit vs. Accounting Profit

• Economic profit

= total revenue minus total costs (including explicit and implicit costs)

• Accounting profit

= total revenue minus total explicit costs

Accounting profit ignores implicit costs, so it’s higher than economic profit.

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Economists versus Accountants

Revenue

Totalopportunitycosts

How an EconomistViews a Firm

How an AccountantViews a Firm

Revenue

Economicprofit

Implicitcosts

Explicitcosts

Explicitcosts

Accountingprofit

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The equilibrium rent on office space has just increased by $500/month.

Compare the effects on accounting profit and economic profit if

a. you take your office space on rent

b. you own your office space

A C T I V E L E A R N I N G Economic profit vs. accounting profit

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9

The rent on office space increases $500/month.

a.You take your office space on rent.Explicit costs increase $500/month. Accounting profit & economic profit each fall $500/month.

b.You own your office space.Explicit costs do not change, so accounting profit does not change. Implicit costs increase $500/month (opp. cost of using your space instead of renting it out), so economic profit falls by $500/month.

A C T I V E L E A R N I N G 2 Answers

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10

Theory of Production

Concepts of product:

• Total product:

of a factor of production is the amount of total output produced by that factor, other factors being kept constant.

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Total Product Curve

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Total Product Curve

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Concepts of product

Average Product:

of a factor of production is the total output produced per unit of the factor.

AP = TP/(number of units of the factor)

If the factor is L, APL = Q/L [OR]

APL = TP/L

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Concepts of product

• Marginal product (MP) of variable input:– Change in output, (ΔQ), resulting from a unit change

of the variable input

– Holding all other inputs constant

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Marginal Product

If capital is the variable input:

then marginal product of capital is

If labor is the variable input:

then marginal product of labour is

• MP is analogous to the concept of marginal utility, except that MP is a cardinal number.– Distances between any levels of MP are of a known size

measured in physical quantities like bushels, bottles, kilograms, litres, etc.

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The Production Function

• A production function shows the relationship between the quantity of inputs used to produce a good, and the quantity of output of that good.

• Can be represented by a table, equation, or graph.

Q = f (L, K, D)

• Example 1: Farmer cultivating wheat– Farmer Jack cultivates wheat. – He has 5 acres of land. – He can hire as many workers as he wants.

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0

500

1,000

1,500

2,000

2,500

3,000

0 1 2 3 4 5

No. of workers

Qu

anti

ty o

f o

utp

ut

Example 1: Farmer Jack’s Production Function

30005

28004

24003

18002

10001

00

Q (bushels of wheat)

L(no. of

workers)

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Marginal Product• If Jack hires one more worker, his output rises by

the marginal product of labor. • The marginal product of any input is the increase

in output arising from an additional unit of that input, holding all other inputs constant.

• Notation: ∆ (delta) = “change in…”

Examples:

∆Q = change in output, ∆L = change in labor

• Marginal product of labor (MPL) = ∆Q∆L

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30005

28004

24003

18002

10001

00


L(no. of

workers)

EXAMPLE 1: Total & Marginal Product

200

400

600

800

1000

MPL

∆Q = 1000∆L = 1

∆Q = 800∆L = 1

∆Q = 600∆L = 1

∆Q = 400∆L = 1

∆Q = 200∆L = 1

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MPL equals the slope of the production function.

Notice that MPL diminishes as L increases.

This explains why the production function gets flatter as L increases.

0

500

1,000

1,500

2,000

2,500

3,000

0 1 2 3 4 5

No. of workers

Qu

anti

ty o

f o

utp

ut

EXAMPLE 1: MPL = Slope of Prod Function

30005200

28004400

24003600

18002800

100011000

00

MPL

Q(bushels of wheat)

L(no. of

workers)

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Why MPL Is Important• Recall one of the Ten Principles:

‘Rational people think at the margin.’

• When Farmer Jack hires an extra worker, – his costs rise by the wage he pays the extra worker

– his output rises by MPL

• Comparing them helps Jack decide whether he would benefit from hiring the worker.

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Why MPL Diminishes• Farmer Jack’s output rises by a smaller and smaller

amount for each additional worker. Why?

• As Jack adds workers, the each worker has less land to work with, and so, will be less productive.

• In general, MPL diminishes as L rises, regardless of whether the fixed input is land or capital (equipment, machines, etc.).

• Diminishing Marginal Product: the marginal product of an input declines as the quantity of the input increases (other things being constant).

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Production Function with One Variable Input

• Law of Variable Proportions (a.k.a. Law of Diminishing Returns)

• The law deals with the short run production function

• Explains the short-run changes in P• Quantity of one factor of production is changed;

other factors held constant– Varying proportion of the factors--‘variable proportions’

“As the proportion of one factor in a combination of factors is increased, first the marginal, and then the average product of that factor will diminish.”

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Law of Variable Proportions

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TP, MP, and AP in the 3 stages

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The Optimum Stage of Production: Stage II is the choice of a rational producer.

• Stage I: Fixed factors too much in proportion to variable factor.

• Stage II: Fixed factors and variable factor in ideal proportion.

• Stage III: Fixed factor too little in proportion to variable factor.

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Production Function with Two Variable Inputs

Isoquant:“An isoquant is the locus of different combinations of two

factors of production, such that every combination yields the same quantity of output.”

• Each combination on an isoquant produces the same quantity of output.

• Iso-product curve, equal-product curve, production-indifference curve.

• Similar to indifference curve, but cardinal value used.

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• Factor Combinations

Factor Combination

Labour Capital

A 1 12

B 2 8

C 3 5

D 4 3

E 5 2

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• Construct isoquant from the preceding table.

• Isoquant Map:– Family of Isoquants

– Each isoquant represents a different quantity of output• Therefore, an Isoquant map represents the

production function of a product with two factors.

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• Marginal Rate of Technical Substitution:

“MRTS of labour for capital (MRTSLK) is the number of units of capital that can be replaced by one unit of labour, the quantity of output remaining the same.”

MRTSLK = ∆K/∆L

∆K/∆L = MPL/MPK

Therefore, MRTSLK = MPL/MPK

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∆K/∆L = MPL/MPK

Proof:

On an isoquant, Loss of output due to reduction of K

=

Gain in output due to addition of L

(∆K * MPK) = (∆L * MPL)

∆K/∆L = MPL/MPK

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Diminishing Marginal Rate of Technical Substitution:

As we go on replacing K with L, the quantity of K that can be replaced by one additional unit of L goes on decreasing.

This is due to:

the principle of diminishing returns.

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General Properties of Isoquants:• Slope downward to the right• Can’t touch or intersect one another• Convex to the origin

35


Iso-Cost Line:

Iso-cost line is the locus of different combinations of factors that a firm can buy with a constant outlay.

Also known as outlay line.

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• Slope of the iso-cost line:slope of the isocost line = ratio of prices of the two factors

Proof: C Total Outlay (i.e., amount of money spent)

r Price of Capital; w Price of Labour

Maximum quantity of Capital = OB

Maximum quantity of Labour = OL

Therefore, slope of the Isocost line = OB/OL

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If C is used to buy only Labour,

C = OL * w OL = C/w

If C is used to buy only Capital,

C = OB * r OB = C/r

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Therefore,

OB/OL = (C/r) ÷ (C/w)(C/r) * (w/C)

w/r

Thus, OB/OL = w/r

Slope of isocost line = Ratio of prices of the two factors

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Shifts in Iso-Cost Line

Three causes of shifts-- – Shifts due to changes in cost of one factor at a time

– Shifts due to changes in cost of both factors

– Shifts due to changes in outlay

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• Two approaches to deciding output and cost of production:– Maximising output for a given outlay.

– Minimising the outlay for a given quantity of output. (least-cost combination of factors)

Both involve isoquants and iso-cost lines.

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• Maximising Output for a given outlay:

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• Minimising outlay for a given output:

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Expansion Path:“The expansion path is the locus of the various least-

cost combinations of the two factors as the firm ‘expands’ its output.”

• Diagram of Expansion Path.

• Note that an expansion path only shows us the cheapest (i.e., most efficient) way of producing each level of output. It does not tell us where exactly on the path a producer is situated.

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Returns to Scale• ‘Scale’ refers to the proportion of the factors used.

• Proportional change in all the factors is called a change in the scale.

Returns to scale refers to how output responds to an equiproportionate change in all inputs.

45


Returns to Scale Increasing Returns to Scale:

If the change in output is in greater proportion than the change in input, returns to scale are said to be increasing.

In other words, if an increase in scale leads to an increase in the output by a greater proportion, the returns to scale are said to be increasing.

• Diagram: (Q2/Q1) > (OA2/OA1)

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Returns to Scale Constant Returns to Scale:If the change in output is equal in proportion to the

change in input, returns to scale are said to be constant.

If an increase in scale leads to an increase in the output by the same proportion, the returns to scale are said to be constant.

• Diagram: (Q2/Q1) = (OA2/OA1)

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Returns to Scale

Decreasing Returns to Scale:

If the change in output is in a smaller proportion than the change in input, returns to scale are said to be decreasing.

In other words, if an increase in scale leads to an increase in the output by a smaller proportion, the returns to scale are said to be decreasing.

• Diagram: (Q2/Q1) < (OA2/OA1)

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Returns to Scale

In reality, all three types of returns to scale are found in within a firm.

• Diagram

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Cost-Benefit Analysis in an Advertisement

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Cost Concepts

• Fixed Costs; Variable Costs; Total Cost

• Average Fixed Cost; Average Variable Cost; Average Total Cost [a.k.a. Average Cost]

• Marginal Cost

51

EXAMPLE 1: Farmer Jack’s Costs

• Farmer Jack must pay $1,000 per month for the land, regardless of how much wheat he grows.

• The market wage for a farm worker is $2,000 per month.

• So Farmer Jack’s costs are related to how much wheat he produces….

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Fixed and Variable Costs• Fixed cost (FC) – • does not vary with the quantity of output produced.

– For Farmer Jack, FC = $1000 for his land– Other examples:

cost of equipment, loan payments

• Variable cost (VC) – • varies with the quantity produced.

– For Farmer Jack, VC = wages he pays workers– Other example: cost of materials

• Total cost (TC) FC + VC

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EXAMPLE 1: Farmer Jack’s Costs

$11,000

$9,000

$7,000

$5,000

$3,000

$1,000

Total Cost

30005

28004

24003

18002

10001

$10,000

$8,000

$6,000

$4,000

$2,000

$0

$1,000

$1,000

$1,000

$1,000

$1,000

$1,00000

Cost of labor

Cost of land

Q(bushels of wheat)

L(no. of

workers)

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EXAMPLE 1: Farmer Jack’s Total Cost Curve


Total Cost

0 $1,000

1000 $3,000

1800 $5,000

2400 $7,000

2800 $9,000

3000 $11,000

$0

$2,000

$4,000

$6,000

$8,000

$10,000

$12,000

0 1000 2000 3000

Quantity of wheat

To

tal c

ost

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Marginal Cost

• Marginal Cost (MC):

is the increase in Total Cost due theproduction of one more unit of the output.

∆TC∆Q

MC =

56

EXAMPLE 1: Total and Marginal Cost

$10.00

$5.00

$3.33

$2.50

$2.00

Marginal Cost (MC)

$11,000

$9,000

$7,000

$5,000

$3,000

$1,000

Total Cost

3000

2800

2400

1800

1000

0

Q(bushels of wheat)

∆Q = 1000 ∆TC = $2000

∆Q = 800 ∆TC = $2000

∆Q = 600 ∆TC = $2000

∆Q = 400 ∆TC = $2000

∆Q = 200 ∆TC = $2000

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MC usually rises as Q rises, as in this example.

EXAMPLE 1: The Marginal Cost Curve

$11,000

$9,000

$7,000

$5,000

$3,000

$1,000

TC

$10.00

$5.00

$3.33

$2.50

$2.00

MC

3000

2800

2400

1800

1000

0

Q(bushels of wheat)

$0

$2

$4

$6

$8

$10

$12

0 1,000 2,000 3,000Q

Mar

gin

al C

ost

($)

58

Why MC Is Important

• Farmer Jack is rational and wants to maximize his profit. To increase profit, should he produce more or less wheat?

• To find the answer, Farmer Jack needs to “think at the margin.”

• If the cost of producing additional wheat (MC) is less than the revenue he would get from selling it, then Jack’s profits rise if he produces more.

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EXAMPLE 2

The next example is more general, applies to any type of firm, producing any good with any types of inputs.

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Example 2: Costs

7

6

5

4

3

2

1

620

480

380

310

260

220

170

$100

520

380

280

210

160

120

70

$0

100

100

100

100

100

100

100

$1000

TCVCFCQ

$0

$100

$200

$300

$400

$500

$600

$700

$800

0 1 2 3 4 5 6 7

Q

Co

sts

FC

VC

TC

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Recall, Marginal Cost (MC) is the change in total cost from producing one more unit:

Usually, MC rises as Q rises, due to diminishing marginal product.

Sometimes (as here), MC falls before rising.

(In other examples, MC may be constant.)

EXAMPLE 2: Marginal Cost

6207

4806

3805

3104

2603

2202

1701

$1000

MCTCQ

140

100

70

50

40

50

$70

∆TC∆Q

MC =

$0

$25

$50

$75

$100

$125

$150

$175

$200

0 1 2 3 4 5 6 7

Q

Co

sts

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EXAMPLE 2: Average Fixed Cost

1007

1006

1005

1004

1003

1002

1001

14.29

16.67

20

25

33.33

50

$100

n.a.$1000

AFCFCQ Average fixed cost (AFC) is the fixed cost per unit of the quantity of output:

AFC = FC/Q

Notice that AFC falls as Q rises: The firm is spreading its fixed costs over a larger and larger number of units.

$0

$25

$50

$75

$100

$125

$150

$175

$200

0 1 2 3 4 5 6 7

Q

Co

sts

63

EXAMPLE 2: Average Variable Cost

5207

3806

2805

2104

1603

1202

701

74.29

63.33

56.00

52.50

53.33

60

$70

n.a.$00

AVCVCQ Average variable cost (AVC) is the variable cost per unit of the output:

AVC = VC/Q

As Q rises, AVC may fall initially. In most cases, AVC will eventually rise as output rises.

$0

$25

$50

$75

$100

$125

$150

$175

$200

0 1 2 3 4 5 6 7Q

Co

sts

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EXAMPLE 2: Average Total Cost [a.k.a. Average Cost]

88.57

80

76

77.50

86.67

110

$170

n.a.

ATC

6207

4806

3805

3104

2603

2202

1701

$1000

74.2914.29

63.3316.67

56.0020

52.5025

53.3333.33

6050

$70$100

n.a.n.a.

AVCAFCTCQ Average total cost (ATC) is the total cost per unit of the output:

ATC = TC/Q

Also,

ATC = AFC + AVC

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Usually, as in this example, the ATC curve is U-shaped.

$0

$25

$50

$75

$100

$125

$150

$175

$200

0 1 2 3 4 5 6 7

Q

Co

sts

EXAMPLE 2: Average Total Cost

88.57

80

76

77.50

86.67

110

$170

n.a.

ATC

6207

4806

3805

3104

2603

2202

1701

$1000

TCQ

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EXAMPLE 2: The Various Cost Curves Together

AFCAVCATC

MC

$0

$25

$50

$75

$100

$125

$150

$175

$200

0 1 2 3 4 5 6 7

Q

Co

sts

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AA CC TT II VV E LE L EE AA RR NN II NN G G 33: : CostsCosts

Fill in the blank spaces of this table.

67

210

150

100

30

10

VC

43.33358.332606

305

37.5012.501504

36.672016.673

802

$60.00$101

n.a.n.a.n.a.$500

MCATCAVCAFCTCQ

60

30

$10

68

Use AFC = FC/QUse AVC = VC/QUse relationship between MC and TCUse ATC = TC/QFirst, deduce FC = $50 and use FC + VC = TC.

AA CC TT II VV E LE L EE AA RR NN II NN G G 33: : AnswersAnswers

68

210

150

100

60

30

10

$0

VC

43.33358.332606

40.003010.002005

37.502512.501504

36.672016.671103

40.001525.00802

$60.00$10$50.00601

n.a.n.a.n.a.$500

MCATCAVCAFCTCQ

60

50

40

30

20

$10

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$0

$25

$50

$75

$100

$125

$150

$175

$200

0 1 2 3 4 5 6 7

Q

Co

sts

EXAMPLE 2: Why ATC Is Usually U-Shaped

As Q rises:

Initially, falling AFC pulls ATC down.

Eventually, rising AVC pulls ATC up.

70

EXAMPLE 2: ATC and MC

ATCMC

$0

$25

$50

$75

$100

$125

$150

$175

$200

0 1 2 3 4 5 6 7

Q

Co

sts

When MC < ATC,

ATC is falling.

When MC > ATC,

ATC is rising.

The MC curve crosses the ATC curve at the ATC curve’s minimum. That is, when MC=AC, ATC is at its minimum.

71

Costs in the Short Run & Long Run

• Short run: Some inputs are fixed (e.g., factories, land). The costs of these inputs are FC.

• Long run: All inputs are variable (e.g., firms can build more factories, or sell existing ones)

• In the long run, ATC at any Q is cost per unit using the most efficient mix of inputs for that Q (e.g., the factory size with the lowest ATC).

72

EXAMPLE 3: LRATC with 3 factory Sizes

ATCSATCM ATCL

Q

AvgTotalCost

Firm can choose from 3 factory sizes: S, M, L.

Each size has its own SRATC curve.

The firm can change to a different factory size in the long run, but not in the short run.

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EXAMPLE 3: LRATC with 3 factory Sizes

ATCSATCM ATCL

Q

AvgTotalCost

QA QB

LRATC

To produce less than QA, firm will

choose size S in the long run.

To produce between QA

and QB, firm will

choose size M in the long run.

To produce more than QB, firm will

choose size L in the long run.

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A Typical LRATC Curve

Q

ATCIn the real world, factories come in many sizes, each with its own SRATC curve.

So a typical LRATC curve looks like this:

LRATC

75

How ATC Changes As the Scale of Production Changes

Economies of scale: ATC falls as Q increases.

Constant returns to scale: ATC stays the same as Q increases.

Diseconomies of scale: ATC rises as Q increases.

LRATC

Q

ATC

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How ATC Changes As the Scale of Production Changes

• Economies of scale occur when increasing production allows greater specialization: workers more efficient when focusing on a narrow task.

– More common when Q is low.

• Diseconomies of scale are due to coordination problems in large organizations. E.g., management becomes stretched, can’t control costs.

– More common when Q is high.

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Summary

• Implicit costs do not involve a cash outlay, yet are just as important as explicit costs to firms’ decisions.

• Accounting profit is revenue minus explicit costs. Economic profit is revenue minus total (explicit + implicit) costs.

• The production function shows the relationship

between output and inputs.

78

Summary

• The marginal product of labor is the increase in output from a one-unit increase in labor, holding other inputs constant. The marginal products of other inputs are defined similarly.

• Marginal product usually diminishes as the input increases. Thus, as output rises, the production function becomes flatter, and the total cost curve becomes steeper.

• Variable costs vary with output; fixed costs do not.

79

Summary

• Marginal cost is the increase in total cost from an extra unit of production. The MC curve is usually upward-sloping.

• Average variable cost is variable cost divided by output.

• Average fixed cost is fixed cost divided by output. AFC always falls as output increases.

• Average total cost (sometimes called “cost per unit”) is total cost divided by the quantity of output. The ATC curve is usually U-shaped.

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Summary

• The MC curve intersects the ATC curve at minimum average total cost. When MC < ATC, ATC falls as Q rises. When MC > ATC, ATC rises as Q rises.

• In the long run, all costs are variable.

• Economies of scale: ATC falls as Q rises. Diseconomies of scale: ATC rises as Q rises. Constant returns to scale: ATC remains constant as Q rises.

81

CONCLUSION

• Costs are critically important to many business decisions, including production, pricing, and hiring.

• These slides have introduced the various cost concepts.

• The following unit will show how firms use these concepts to maximize profits in various market

structures.

82

Law of Diminishing Marginal Returns

• A firm’s costs will depend on– Prices it pays for inputs – Technology of combining inputs into output

• In short run firm can change its output by adding variable inputs to fixed inputs– Output may at first increase at an increasing rate– However, given a constant amount of fixed inputs, output will at

some point increase at a decreasing rate• Occurs because at first variable input is limited compared with fixed input

– As additional workers are added, productivity remains very high – Output, or TP, increases at an increasing rate– However, as more of variable input is added, it is no longer as limited

» Eventually, TP will still be increasing, but at a decreasing rate

» MPL will still be positive, but declining

83

Law of DMR• Diminishing marginal

returns starts at point A – MPL is at a maximum

• To the left of point A there are increasing returns and at point A constant returns exist

• Between points A and B, where MPL is declining, diminishing marginal returns exist

• To the right of point B, marginal productivity is both diminishing and negative (MPL < 0), which violates Monotonicity Axiom

84

Law of DMR

• TP curve will at some point increase only at a decreasing rate (concave) due to Law of Diminishing Marginal Returns

Units 2&3 prod. & cost functions

News & Politics

total costs

total marginal product

total revenue total

total product curve

concept of costs

impl costs

different costs

factor of production