THEORY OF PRODUCTION AND COST

THEORY OF PRODUCTION AND COST

Production is the use of factors of production to produce and market goods and services.

Inputs include the broad categories of land, labor, capital, other intermediate inputs and entrepreneurship.

In a mixed economy, both firms and governments organize the production of various goods and services.

Production in the Short-run

An input that cannot vary in quantity during the relevant time period is called a fixed input or fixed factor.

An input having a quantity that can change during the relevant time period is called a variable input or variable factor.

The short-run is a period of time such that there is at least one fixed factor.

The long-run is a period of time such that all inputs are variable in quantity.

A production function summarizes the relationship between all combinations of inputs and the corresponding maximum attainable levels of output, for a given technology.

The total product, TP, of a variable input is the amount of output produced over the period when that input is used with fixed quantities of all other inputs.

The marginal product of an input F, MPF, is the

additional output per unit increase in the input, holding all other inputs (and technology) constant; F

TPMPF

Total Product

0

50

100

150

200

250

0 2 4 6 8 10

pounds of fertilizer

bush

els

of p

otat

oes

TP

Marginal Product

0

10

20

30

0 2 4 6 8 10

pounds of fertilizer

bush

els

of p

otat

oes

per

unit

of fe

rtili

zer

. MP

fertilizer TP,

Output

MP,

Marginal output

per unit of input

0 0 ---1 15 152 38 233 68 304 103 355 137 346 168 317 192 248 211 199 226 15

10 235 9

Diminishing marginal product results from the process of adding additional units of a variable input to given quantities of other inputs.

Diminishing marginal product: As more of a variable input is employed, with the quantities of all other inputs held constant, the marginal product of the variable input will decline after some point.

Measuring costs and profitsTotal (Economic) Cost is the monetary value of all inputs used in a particular activity over a given period.

Explicit Costs correspond to the monetary payments for inputs.

Implicit Costs are the opportunity costs of inputs that have no explicit monetary payments as a result of the inputs not being purchased in markets.

All opportunity costs, both explicit and implicit, are part of economic costs.

Economic depreciation is the reduction in the value of a capital good over the relevant period that results from wear and tear as well as obsolescence.

Accounting depreciation measures the annual accounting cost of capital, expressed as some portion of the capital’s monetary cost.

Accounting costs measure the explicit costs of production during a given period plus accounting depreciation.

Measuring costs

Measuring costs and profits

Total revenue is the explicit monetary return associated with an economic activity over a given period.

Economic activities can also yield implicit returns.

The total return includes both total revenues and implicit returns.

Economic and accounting profits are defined below:Total return Total revenueless: less: explicit costs explicit costs economic depreciation accounting depreciation other implicit costs

Economic Profits Accounting Profits

Economic profits measure the net (private) economic gain resulting from an economic activity.

When economic profits are zero the returns to owner supplied inputs exactly equal the opportunity costs of those inputs. These returns are called normal profits.

Related Cost Measures

Variable cost, VC, is the cost of the variable input(s) used to produce any given level of output.

Fixed costs, FC, is the cost of all fixed inputs.

Total cost, TC, is the sum of the costs of all inputs used to produce output during the period; TC = VC + FC.

Example of Potato Production (The price of fertilizer is $50 per unit and the costs associated with fixed input $40.)

F Q FC VC TC

fert.bushels of potatoes $ $ $

0 0 40 0 401 15 40 50 902 38 40 100 1403 68 40 150 1904 103 40 200 2405 137 40 250 2906 168 40 300 3407 192 40 350 3908 211 40 400 4409 226 40 450 49010 235 40 500 540

Related Cost Measures

Marginal cost, MC, is the increase in total or variable cost per unit increase in output, Q;

QTC

QVCMC

Average variable cost, AVC, is the variable cost of production per unit of output;

Average fixed cost, AFC, is the fixed cost per unit of output;

Average cost, AC, is the total cost of all inputs per unit of output;

.Q

VCAVC

.Q

FCAFC

.Q

TCAC

AFCAVCACQ

FCQ

VCQ

FCVCQ

TCAC

Marginal, Average, Average Variable and Average Fixed Costs

0.00.51.01.52.02.53.03.54.04.55.05.56.0

0 50 100 150 200 250Q, quantity of output

dolla

rs p

er u

nit o

f Q

AC

AVC

MC

AFC

103

1.43

Marginal, Average, Average Variable and Average Fixed Costs

0.00.51.01.52.02.53.03.54.04.55.05.56.0

0 50 100 150 200 250Q, quantity of output

dolla

rs p

er u

nit o

f Q

AC

AVC

MC

AFC

103

0.39

1.942.33

Family of Average Costs

AFC= Fixed costQuantity

= FCQ

AVC= Variable costQuantity

= VCQ

ATC= Total costQuantity

= TCQ

AFC= Fixed costQuantity

= FCQ

AVC= Variable costQuantity

= VCQ

ATC= Total costQuantity

= TCQ

Marginal Cost

QTC=

quantity) in (Changecost) total in (Change=MC

Note the relationship between MP and MC.

fertilizer TP MP Q TC MC0 0 --- 0 40 ---1 15 15 15 90 3.332 38 23 38 140 2.173 68 30 68 190 1.674 103 35 103 240 1.435 137 34 137 290 1.476 168 31 168 340 1.617 192 24 192 390 2.088 211 19 211 440 2.639 226 15 226 490 3.3310 235 9 235 540 5.56

The marginal cost of output directly depends upon the marginal product and price of each variable input;

.LMPpriceinputMC

For example, if MPL= 0.5 widgets per hour and the wage rate is a constant $10.00 per hour, MC = ($10 per hour) / (0.5 widgets per hour) = $20 per widget .Intuition: If MPL= 0.5, it takes two hours of work to create one widget. With a wage of $10 per hour, this translates into a marginal cost of $20.00 for an additional widget.

Implications:

• An increase in the price of a variable input, ceteris paribus,

will result in an increase in the marginal cost of output.

• Holding the input price constant, an increase in the marginal

product of a variable input will cause MC to decrease.

• Often we talk about MC increasing as output increases (after

some point). The underlying reason is diminishing marginal

product of the variable input(s).

.LMPpriceinputMC

Total-Cost Curve...(Another Example)

$0.00

$2.00

$4.00

$6.00

$8.00

$10.00

$12.00

$14.00

$16.00

0 2 4 6 8 10 12Quantity of Output

Tota

l Cos

t

Total-cost curve

ΔQ = 1

ΔTC = 0.70

MC = 0.70

MC = 1.30

MC = 1.90

AVC

MC

Average-Cost and Marginal-Cost Curves...

$0.00

$0.50

$1.00

$1.50

$2.00

$2.50

$3.00

$3.50

0 2 4 6 8 10 12

Quantity of Output

Cos

ts

Relationship Between Marginal Cost and Average Variable Cost

Whenever MC is greater than AVC, AVC will be rising.

Whenever MC is less than AVC, AVC will be falling.

MCATC

Relationship Between Marginal Cost and Average Total Cost

$0.00

$0.50

$1.00

$1.50

$2.00

$2.50

$3.00

$3.50

0 2 4 6 8 10 12

Quantity of Output

Cos

ts

Relationship Between Marginal Cost and Average Total Cost

Whenever MC is less than ATC, ATC will be falling.

Whenever MC is greater than ATC, ATC will be rising.

ATCAVC

MC

Average-Cost and Marginal-Cost Curves...

$0.00

$0.50

$1.00

$1.50

$2.00

$2.50

$3.00

$3.50

0 2 4 6 8 10 12

Quantity of Output

Cos

ts

AFC

Cost Curves and Their Shapes

The average total-cost curve is U-shaped. At very low levels of output ATC is high because

fixed cost is spread over only a few units. ATC initially declines as output increases because of

the decline in AFC. ATC eventually starts to rise because AVC rises

substantially.

Total-Cost Curve...

$0.00

$2.00

$4.00

$6.00

$8.00

$10.00

$12.00

$14.00

$16.00

0 2 4 6 8 10 12Quantity of Output

Tota

l Cos

t

Total-cost curve

Big Bob’s Cost Curves...

$0.00

$2.00

$4.00

$6.00

$8.00

$10.00

$12.00

$14.00

$16.00

$18.00

$20.00

0 2 4 6 8 10 12 14 16Quantity of Output(bagels per hour)

Tota

l Cos

t

Total Cost Curve

AVC

MC

Big Bob’s Cost Curves...

0

0.5

1

1.5

2

2.5

3

3.5

0 2 4 6 8 10 12 14 16Quantity of Output

Cos

ts

AFC

AVC

MC

Big Bob’s Cost Curves...

0

0.5

1

1.5

2

2.5

3

3.5

0 2 4 6 8 10 12 14 16Quantity of Output

Cos

ts

AFC

AVC

MC

Big Bob’s Cost Curves...

0

0.5

1

1.5

2

2.5

3

3.5

0 2 4 6 8 10 12 14 16Quantity of Output

Cos

ts

ATC

Three Important Properties of Cost Curves:

Marginal cost eventually rises with the quantity of output.

The average-total-cost curve is U-shaped.

The marginal-cost curve crosses the average-total-cost and average-variable-cost curves at their minimums.

Cost Curves and Their Shapes

•The bottom of the U-shape AC curve corresponds to the quantity that minimizes the average cost of production. •This quantity is sometimes called the efficient scale of the firm.•The marginal-cost curve crosses the average-total-cost curve at the efficient scale.

Costs in the Long Run

For many firms, the division of total costs between fixed and variable costs depends on the time horizon being considered. In the short run some costs are fixed. In the long run fixed costs become

variable costs.

Average Total Cost in the Short and Long Runs...

Quantity ofCars per Day

0

AverageTotalCost

ATC in shortrun with

small factory

ATC in shortrun with

medium factory

ATC in shortrun with

large factory

ATC in long run

Economies and Diseconomies of Scale

Economies of scale occur when long-run average total cost declines as output increases.

Diseconomies of scale occur when long-run average total cost rises as output increases.

Constant returns to scale occur when long-run average total cost does not vary as output increases.

Economies and Diseconomies of Scale

Diseconomies

of scaleQuantity of

Cars per Day0

AverageTotalCost

ATC in long run

Economies

of scale

Constant Returnsto scale