production and cost theory

The Theory of the Firm:Production and Cost

Ephesians 5: 1-7

1 Follow God’s example, therefore, as dearly loved children 2 and walk in the way of love, just as Christ loved us and gave himself up for us as a fragrant offering and sacrifice to God. 3 But among you there must not be even a hint of sexual immorality, or of any kind of impurity, or of greed, because these are improper for God’s holy people. 4 Nor should there be obscenity, foolish talk or coarse joking, which are out of place, but rather thanksgiving. 5 For of this you can be sure: No immoral, impure or greedy person—such a person is an idolater—has any inheritance in the kingdom of Christ and of God. 6 Let no one deceive you with empty words, for because of such things God’s wrath comes on those who are disobedient. 7 Therefore do not be partners with them.

What Is A Firm?

A firm is an organization that comes into being when a person or a group of people decides to produce a good or service to meet a perceived demand. Most firms exist to make a profit.

Production is not limited to firms.

Production

Production is the process by which inputs are combined, transformed, and turned into outputs.

Competitive Firms are Price Takers

In a perfectly competitive market, individual firms are price-takers. This means that firms have no control over price. Price is determined by the interaction of market supply and demand.

Demand Facing a Single Firm in a Perfectly Competitive Market

If a representative firm in a perfectly competitive market rises the price of its output above $2.45, the quantity demanded of that firm’s output will drop to zero. Each firm faces a perfectly elastic demand curve, d.

The Behavior ofProfit-Maximizing Firms

The three decisions that all firms must make include:

How much of How much of each input to each input to

demanddemand

3.3.

Which Which production production

technology to technology to useuse

2.2.

How much How much output to output to

supplysupply

1.1.

The Theory of the Firm

The Production Process

Production technology refers to the quantitative relationship between inputs and outputs.

A labor-intensive technology relies heavily on human labor instead of capital.

A capital-intensive technology relies heavily on capital instead of human labor.

Production Function

The Production Function

The production function or total product function is a numerical or mathematical expression of a relationship between inputs and outputs. It shows units of total product as a function of units of inputs.

Production Function

Mathematical representation of the relationship:

Q = f (K, L, La) Output (Q) is dependent upon the amount of

capital (K), Land (L) and Labour (La) used

Production Function

States the relationship between inputs and outputs Inputs – the factors of production classified as:

• Land – all natural resources of the earth – not just ‘terra firma’!

• Price paid to acquire land = Rent

• Labour – all physical and mental human effort involved in production

• Price paid to labour = Wages

• Capital – buildings, machinery and equipment not used for its own sake but for the contribution it makes to production

• Price paid for capital = Interest

Production Function

Inputs Process Output

Land

Labour

Capital

Product or service

generated– value added

Analysis of Production Function:Short Run

In the short run at least one factor fixed in supply but all other factors capable of being changed

Reflects ways in which firms respond to changes in output (demand)

Can increase or decrease output using more or less of some factors but some likely to be easier to change than others

Increase in total capacity only possible in the long run

Short-Run Versus Long-Run Decisions

The short run is a period of time for which two conditions hold:1. The firm is operating under a fixed

scale (fixed factor) of production, and

2. Firms can neither enter nor exit an industry.


In times of rising sales (demand) firms can increase labour and capital but only up to a certain level – they will be limited by the amount of space. In this example, land is the fixed factor which cannot be altered in the short run.


If demand slows down, the firm can reduce its variable factors – in this example it reduces its labour and capital but again, land is the factor which stays fixed.


If demand slows down, the firm can reduce its variable factors – in this example, it reduces its labour and capital but again, land is the factor which stays fixed.

Short-Run Versus Long-Run Decisions

The long run is a period of time for which there are no fixed factors of production. Firms can increase or decrease scale of operation, and new firms can enter and existing firms can exit the industry.

Analysing the Production Function: Long Run The long run is defined as the period of time taken to vary all factors of

production• By doing this, the firm is able to increase its total capacity – not

just short term capacity• Associated with a change in the scale of production• The period of time varies according to the firm

and the industry• In electricity supply, the time taken to build new capacity could be

many years; for a market stall holder, the ‘long run’ could be as little as a few weeks or months!

Analysis of Production Function:Long Run

In the long run, the firm can change all its factors of production thus increasing its total capacity. In this example it has doubled its capacity.

Marginal Product and Average Product

Marginal product is the additional output that can be produced by adding one more unit of a specific input, ceteris paribus.

• Average productAverage product is the average amount is the average amount produced by each unit of a variable factor of produced by each unit of a variable factor of production.production.

av erag e p ro d u c t o f lab o r = to ta l p ro d u c t

to ta l u n its o f lab o r

m arg in a l p ro d u c t o f lab o r = ch an g e in to ta l p ro d u c t

ch an g e in u n its o f lab o r u sed

The Law of DiminishingMarginal Returns

The law of diminishing marginal returns states that:When additional units of a variable input are added to fixed inputs, the marginal product of the variable input declines.

Production Function for Sandwiches

Production FunctionProduction Function

(1)(1)LABOR UNITS LABOR UNITS (EMPLOYEES)(EMPLOYEES)

(2)(2)TOTAL PRODUCT TOTAL PRODUCT

(SANDWICHES (SANDWICHES PER HOUR)PER HOUR)

(3)(3)MARGINAL MARGINAL

PRODUCT OF PRODUCT OF LABORLABOR

(4)(4)AVERAGE AVERAGE PRODUCT PRODUCT OF LABOROF LABOR

00 00

11 1010 1010 10.010.0

22 2525 1515 12.512.5

33 3535 1010 11.711.7

44 4040 55 10.010.0

55 4242 22 8.48.4

66 4242 00 7.07.0

0

5

10

15

20

25

30

35

40

45

0 1 2 3 4 5 6 7

Number of employees

Tot

al p

rodu

ct

0

5

10

15

0 1 2 3 4 5 6 7

Number of employees

Mar

gina

l Pro

duct

Total, Average, and Marginal Product

Marginal product is the slope of the total product function.

• At point C, total product is At point C, total product is maximum, the slope of the maximum, the slope of the total product function is zero, total product function is zero, and marginal product and marginal product intersects the horizontal axis.intersects the horizontal axis.

• At point A, the slope of the At point A, the slope of the total product function is total product function is highest; thus, marginal product highest; thus, marginal product is highest.is highest.


When a ray drawn from the origin falls tangent to the total product function, average product is maximum and equal to marginal product.

• Then, average product falls to Then, average product falls to the left and right of point B.the left and right of point B.


As long as marginal product rises, average product rises.

When average product is maximum, marginal product equals average product.

When average product falls, marginal product is less than average product.

Production Functions with Two Variable Factors of Production

In many production processes, inputs work together and are viewed as complementary.

• For example, increases in capital usage lead to increases in the productivity of labor.

Inputs Required to Produce 100 Diapers Inputs Required to Produce 100 Diapers Using Alternative TechnologiesUsing Alternative Technologies

TECHNOLOGYTECHNOLOGYUNITS OF UNITS OF

CAPITAL (K)CAPITAL (K)UNITS OF UNITS OF LABOR (L)LABOR (L)

AA 22 1010

BB 33 66

CC 44 44

DD 66 33

EE 1010 22

• Given the technologies available, the cost-minimizing choice depends on input prices.

Production Functions with Two Variable Factors of Production

Cost-Minimizing Choice Among Alternative Cost-Minimizing Choice Among Alternative Technologies (100 Diapers)Technologies (100 Diapers)

(1)(1)TECHNOLOGYTECHNOLOGY

(2)(2)UNITS OF UNITS OF

CAPITAL (K)CAPITAL (K)

(3)(3)UNITS OF UNITS OF

LABORLABOR

(4) (4) COST WHEN COST WHEN

PPLL = $1 P = $1 PKK = $1 = $1

(5) (5) COST WHEN COST WHEN

PPLL = $1 P = $1 PKK = $1 = $1

AA 22 1010 $12$12 $52$52

BB 33 66 99 3333

CC 44 44 88 2424

DD 66 33 99 2121

EE 1010 22 1212 2020

Profits and Economic Costs

Profit (economic profit) is the difference between total revenue and total cost.

Total revenue is the amount received from the sale of the product:

(q X P)

Total cost (total economic cost) is the total of

1. Out of pocket costs,

2. Normal rate of return on capital, and

3. Opportunity cost of each factor of production.

Normal Rate of Return

The normal rate of return is a rate of return on capital that is just sufficient to keep owners and investors satisfied.

For relatively risk-free firms, it should be nearly the same as the interest rate on risk-free government bonds.

Calculating Total Revenue, Total Cost, and Profit

Initial Investment:Initial Investment:Market Interest Rate Available:Market Interest Rate Available:

$20,000$20,000.10 or 10%.10 or 10%

Total Revenue (3,000 belts x $10 each)Total Revenue (3,000 belts x $10 each) $30,000$30,000

CostsCosts

Belts from supplierBelts from supplier $15,000$15,000

Labor CostLabor Cost 14,00014,000

Normal return/opportunity cost of capital ($20,000 x .10)Normal return/opportunity cost of capital ($20,000 x .10) 2,0002,000

Total CostTotal Cost $31,000$31,000

Profit = total revenue Profit = total revenue total cost total cost $ 1,000$ 1,000aa

aaThere is a loss of $1,000.There is a loss of $1,000.

Determining the Optimal Methodof Production

Price of outputPrice of output Production techniquesProduction techniques Input pricesInput prices

Determines Determines total revenuetotal revenue

Determine total cost and Determine total cost and optimal method of optimal method of

productionproduction

Total revenueTotal revenueTotal cost with optimal methodTotal cost with optimal method

=Total profit=Total profit

• The The optimal method of productionoptimal method of production is the is the method that minimizes cost.method that minimizes cost.

Costs

In buying factor inputs, the firm will incur costs

Costs are classified as:• Fixed costs – costs that are not related directly to

production – rent, rates, insurance costs, admin costs. They can change but not in relation to output

• Variable Costs – costs directly related to variations in output. Raw materials primarily

Costs

Total Cost - the sum of all costs incurred in production

TC = FC + VC Average Cost – the cost per unit

of output AC = TC/Q

Marginal Cost – the cost of one more or one fewer units of production

MC = ∆TC / ∆Q

38

Q (units/yr)

TC ($/yr)

TFC

Example: Short Run Total Cost, Total Variable Cost and Total Fixed Cost

39

Q (units/yr)

TC ($/yr)

TVC(Q, K0)

TFC


40

Q (units/yr)

TC ($/yr)

TVC(Q, K0)

TFC

STC(Q, K0)


Fixed Costs

Firms have no control over fixed costs in the short run. For this reason, fixed costs are sometimes called sunk costs.

Average fixed cost (AFC) is the total fixed cost (TFC) divided by the number of units of output (q):

AFCTFC

q

Short-Run Fixed Cost (Total and Average) of a Hypothetical Firm

AFC falls as output rises; a phenomenon sometimes called spreading overhead.

(1)(1)qq

(2)(2)TFCTFC

(3)(3)AFC (TFC/q)AFC (TFC/q)

00 $1,000$1,000 $ $

11 1,0001,000 1,0001,000

22 1,0001,000 500500

33 1,0001,000 333333

44 1,0001,000 250250

55 1,0001,000 200200

Derivation of Total Variable Cost Schedule from Technology and Factor Prices

The total variable cost curve shows the cost of production using the best available technique at each output level, given current factor prices.

PRODUCTPRODUCTUSINGUSING

TECHNIQUETECHNIQUE

UNITS OFUNITS OFINPUT REQUIREDINPUT REQUIRED

(PRODUCTION FUNCTION)(PRODUCTION FUNCTION)

TOTAL VARIABLETOTAL VARIABLECOST ASSUMINGCOST ASSUMING

PPKK = $2, = $2, PPLL = $1 = $1

TVCTVC = ( = (KK x x PPKK) + () + (LL x x PPLL))KK LL

11 Units ofUnits of AA 44 44 (4 x $2) +(4 x $2) + (4 x $1) =(4 x $1) = $12$12outputoutput BB 22 66 (2 x $2) +(2 x $2) + (6 x $1) =(6 x $1) =

22 Units ofUnits of AA 77 66 (7 x $2) +(7 x $2) + (6 x $1) =(6 x $1) = $20$20outputoutput BB 44 1010 (4 x $2) +(4 x $2) + (10 x $1) =(10 x $1) =

33 Units ofUnits of AA 99 66 (9 x $2) +(9 x $2) + (6 x $1) =(6 x $1) = outputoutput BB 66 1414 (6 x $2) +(6 x $2) + (14 x $1) =(14 x $1) = $26$26

$10

$18

$24

Average Variable Cost

Average variable cost (AVC) is the total variable cost divided by the number of units of output.

Marginal cost is the cost of one additional unit. Average variable cost is the average variable cost per unit of all the units being produced.

Average variable cost follows marginal cost, but lags behind.

Marginal Cost

Marginal cost (MC) is the increase in total cost that results from producing one more unit of output.

Marginal cost reflects changes in variable costs.

MCTC

Q

TFC

Q

TVC

Q

Derivation of Marginal Cost fromTotal Variable Cost

UNITS OF OUTPUTUNITS OF OUTPUTTOTAL VARIABLE COSTS TOTAL VARIABLE COSTS

($)($)MARGINAL COSTS MARGINAL COSTS

($)($)

00 00 00

11 1010 1010

22 1818 88

33 2424 66

Marginal cost measures the additional cost of inputs required to produce each successive unit of output.

The Shape of the Marginal Cost Curve in the Short Run

The fact that in the short run every firm is constrained by some fixed input means that:1. The firm faces diminishing returns to

variable inputs, and

2. The firm has limited capacity to produce output.

As a firm approaches that capacity, it becomes increasingly costly to produce successively higher levels of output.

The Shape of the Marginal Cost Curve in the Short Run

Marginal costs ultimately increase with output in the short run.

Graphing Total Variable Costs and Marginal Costs

Total variable costs always increase with output. The marginal cost curve shows how total variable cost changes with single unit increases in total output.

• Below 100 units of output, Below 100 units of output, TVCTVC increases at a increases at a decreasing ratedecreasing rate. Beyond . Beyond 100 units of output, 100 units of output, TVCTVC increases at an increases at an increasing increasing rate.rate.

Relationship Between Average Variable Cost and Marginal Cost

When marginal cost is below average cost, average cost is declining.

• When marginal cost is When marginal cost is above average cost, above average cost, average cost is increasing.average cost is increasing.

• Rising marginal cost Rising marginal cost intersects average variable intersects average variable cost at the minimum point cost at the minimum point of of AVCAVC..

• At 200 units of output, AVC is At 200 units of output, AVC is minimum, and minimum, and MCMC = = AVCAVC..

Short-Run Costs of a Hypothetical Firm

(1)(1)qq

(2)(2)TVCTVC

(3)(3)MCMC

(( TVCTVC))

(4)(4)AVCAVC

((TVC/qTVC/q))(5)(5)

TFCTFC

(6)(6)TCTC

((TVCTVC + + TFCTFC))

(7)(7)AFCAFC

((TFCTFC//qq))

(8)(8)ATCATC

(TC/q (TC/q oror AFC + AVC) AFC + AVC)

00 $$ 00 $$ $$ $$1,0001,000 $$ 1,0001,000 $$ $$

11 1010 1010 1010 1,0001,000 1,0101,010 1,0001,000 1,0101,010

22 1818 88 99 1,0001,000 1,0181,018 500500 509509

33 2424 66 88 1,0001,000 1,0241,024 333333 341341

44 3232 88 88 1,0001,000 1,0321,032 250250 258258

55 4242 1010 8.48.4 1,0001,000 1,0421,042 200200 208.4208.4

500500 8,0008,000 2020 1616 1,0001,000 9,0009,000 22 1818

Total Costs

Adding TFC to TVC means adding the same amount of total fixed cost to every level of total variable cost.

• Thus, the total cost curve Thus, the total cost curve has the same shape as the has the same shape as the total variable cost curve; it total variable cost curve; it is simply higher by an is simply higher by an amount equal to amount equal to TFCTFC..

TC TFC TVC

Average Total Cost

Average total cost (ATC) is total cost divided by the number of units of output (q).

ATC AFC AVC

ATCTC

q

TFC

q

TVC

q

• Because Because AFCAFC falls with falls with output, an ever-declining output, an ever-declining amount is added to amount is added to AVCAVC..

Relationship Between Average Total Cost and Marginal Cost

If marginal cost is below average total cost, average total cost will decline toward marginal cost.

If marginal cost is above average total cost, average total cost will increase.

Marginal cost intersects average total cost and average variable cost curves at their minimum points.

9-55

Output FC VC TC MC AFC AVC ATC

3 50 38 88 — 16.67 12.66 29.334 50 50 100 12 12.50 12.50 25.009 50 100 150 — 5.56 11.11 16.67

10 50 108 158 8 5.00 10.80 15.8016 50 150 200 — 3.13 9.38 12.5017 50 157 207 7 2.94 9.24 12.1822 50 200 250 — 2.27 9.09 11.3623 50 210 260 10 2.17 9.13 11.3027 50 255 305 — 1.85 9.44 11.3028 50 270 320 15 1.79 9.64 11.42

Costs of Production

9-56Total Cost Curves

Tot

al c

ost

$400

350

300

250

200

150

100

50

0

FC

2 4

M

6 8 10 20 30

Quantity of earrings

VCTC

L

O

TC = VC + FC

Per Unit Output Cost CurvesC

ost

$30 28 26 24 22 20 18 16 14 12 10

8 6 4 2 0

Quantity of earrings2 4 6 8 10 12 14 1618 2022 2426 28 30 32

AFC

AVCATCMC

Total AverageTotal Fixed Fixed

Output Costs Costs(Q/day) (TFC) (AFC)

0 101 102 103 104 105 106 107 108 109 10

10 1011 10

———10.005.003.332.502.001.671.431.251.111.00.91

Cos

ts (

dolla

r pe

r da

y)

2

4

6

8

12

2 4 6 8 100 1 3 5 7 9 11

16

Output (calculators per day)

10

14

Cost of Production: An Example

AFC

Total AverageTotal Variable Variable

Output Costs Costs(Q/day) (TVC) (AVC)

0 01 52 83 104 115 136 167 208 259 31

10 3811 46

———5.004.003.332.752.602.672.863.133.443.804.18

Cos

ts (

dolla

r pe

r da

y)

2

4

6

8

12

2 4 6 8 100 1 3 5 7 9 11

16


10

14


AVC

AverageTotal Total Total

Output Costs Costs(Q/day) (TVC) (AVC)

0 101 152 183 204 215 236 267 308 359 41

10 4811 56

———15.009.006.675.254.604.334.284.384.564.805.09

Cos

ts (

dolla

r pe

r da

y)

2

4

6

8

12

2 4 6 8 100 1 3 5 7 9 11

16


10

14


ATC

Cos

ts (

dolla

r pe

r da

y)

2

4

6

8

12

2 4 6 8 100 1 3 5 7 9 11

16


10

14

ATCAVC

AFC


AVC

Cos

ts (

dolla

r pe

r da

y)



AFC

ATC

TP

AVCATC

Difference between AVC and ATC = AFC

AFC

AFC

AVC

Cos

ts (

dolla

r pe

r da

y)


ATC


TP

ATC = AVC + AFCAFC = ATC - AVC

AVC

Marginal Cost• The change in total costs due to a one-unit

change in production rate

Short-Run Costs to the Firm

Marginal costs (MC) = change in total cost

change in output

TotalTotal Variable Total Marginal

Output Costs Costs Cost(Q/day) (TVC) (TC) (MC)

0 01 52 83 104 115 136 167 208 259 31

10 3811 46

101518202123263035414856

$5

32

1

23

45

67

8

Cos

ts (

dolla

r pe

r da

y)

2

4

6

8

12

2 4 6 8 100 1 3 5 7 9 11

16


10

14

MC


The Relationship Between Diminishing Marginal Returns and Cost Curves

Labor cost assumed constant

MC = TC

Output

Recall: labor is the variable input

MC = W

MPP

The Relationship Between Diminishing Marginal Returns and Cost Curves

Figure 22-3, Panel (a)

Costs

Short run – Diminishing marginal returns results from adding successive quantities of variable factors to a fixed factor

Long run – Increases in capacity can lead to increasing, decreasing or constant returns to scale

Revenue

Revenue

Total revenue – the total amount received from selling a given output

TR = P x Q Average Revenue – the average amount

received from selling each unit AR = TR / Q

Marginal revenue – the amount received from selling one extra unit of output

MR = dTR/dQ

Total Revenue (TR) andMarginal Revenue (MR)

Total revenue (TR) is the total amount that a firm takes in from the sale of its output.

TR P q

MRTR

q

P q

q

( )

• Marginal revenue (MR)Marginal revenue (MR) is the additional revenue is the additional revenue that a firm takes in when it increases output by that a firm takes in when it increases output by one additional unit.one additional unit.

• In perfect competition, In perfect competition, P = MRP = MR..

P

Profit

Profit

Profit = TR – TC The reward for enterprise Profits help in the process of directing resources

to alternative uses in free markets Relating price to costs helps a firm to assess

profitability in production

Profit

Normal Profit – the minimum amount required to keep a firm in its current line of production

Abnormal or Supernormal profit – profit made over and above normal profit• Abnormal profit may exist in situations where firms

have market power• Abnormal profits may indicate the existence of

welfare losses • Could be taxed away without altering resource

allocation

Profit

Sub-normal Profit – profit below normal profit• Firms may not exit the market even if sub-normal

profits made if they are able to cover variable costs

• Cost of exit may be high• Sub-normal profit may be temporary (or

perceived as such!)

Comparing Costs and Revenues to Maximize Profit

The profit-maximizing level of output for all firms is the output level where MR = MC.

In perfect competition, MR = P, therefore, the profit-maximizing perfectly competitive firm will produce up to the point where the price of its output is just equal to short-run marginal cost.

The key idea here is that firms will produce as long as marginal revenue exceeds marginal cost.

Profit Analysis for a Simple Firm

(1)(1)qq

(2)(2)TFCTFC

(3)(3)TVCTVC

(4)(4)MCMC

(5)(5)P P == MR MR

(6)(6)TRTR

((PP x x qq))

(7)(7)TCTC

((TFC TFC ++ TVC TVC))

(8)(8)PROFITPROFIT((TR TR TC TC))

00 $$ 1010 $$ 00 $$ $$ 1515 $$ 00 $$ 1010 $$ -10-10

11 1010 1010 1010 1515 1515 2020 -5-5

22 1010 1515 55 1515 3030 2525 55

33 1010 2020 55 1515 4545 3030 1515

44 1010 3030 1010 1515 6060 4040 2020

55 1010 5050 2020 1515 7575 6060 1515

66 1010 8080 3030 1515 9090 9090 00

The Short-Run Supply Curve

At any market price, the marginal cost curve shows the output level that maximizes profit. Thus, the marginal cost curve of a perfectly competitive profit-maximizing firm is the firm’s short-run supply curve.

Thank You!

production and cost theory

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