7 Production and Cost in the FirmProduction and Cost in the Firm

How do economists calculate profit?

What is a production function? What is marginal product? How are they related?

What are the various costs, and how are they related to each other and to output?

How are costs different in the short run vs. the long run?

What are “economies of scale”?

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

Costs: Explicit vs. Implicit

Explicit costs – actual cash payments for resources, such as paying wages to workers

Implicit costs – opportunity cost of using owner-supplied resources, such as the opportunity cost of the owner’s time

Remember: The cost of something is the value of the next best alternative.

This is true whether the costs are implicit or explicit. Both matter for a firm’s decisions.

Explicit vs. Implicit Costs: An Example

Suppose you need $100,000 to start your business. The interest rate is 5%.

Case 1: borrow $100,000

• explicit cost =

Case 2: use $40,000 of your savings, borrow the other $60,000

• explicit cost =

• implicit cost =

Economic Profit vs. Accounting Profit

Accounting profit

= total revenue minus total explicit costs

Economic profit

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

Accounting profit ignores implicit costs, so it will be greater than economic profit.

AA CC TT II VV E LE L EE AA RR NN II NN G G 22: : Economic profit vs. accounting profitEconomic profit vs. accounting profit

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

Compare the effects on your firm’s accounting profit and economic profit if

a. you rent your office space

b. you own your office space

6

Production in the Short Run

Some resources are considered to be variable and some are considered to be fixed.

• It depends on how quickly the level can be altered to change the rate of output.

In the short run, at least one resource is fixed.

In the long run, all resources are variable.

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.

It can be represented by a table, equation, or graph.

Example 1:

• Farmer Jack grows wheat.

• He has 5 acres of land.

• He can hire as many workers as he wants.

0

500

1,000

1,500

2,000

2,500

3,000

0 1 2 3 4 5

# of workers

Qu

anti

ty o

f o

utp

ut

EXAMPLE 1: Farmer Jack’s Production Function

3,0005

2,8004

2,4003

1,8002

1,0001

00

Q (bushels of wheat)

L(# of

workers)

Marginal Product

The marginal product of any input is the increase in output arising from an additional unit of that input, holding all other inputs constant.

If Farmer Jack hires one more worker, his output rises by the marginal product of labor.

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

3,0005

2,8004

2,4003

1,8002

1,0001

00

Q (bushels of wheat)

L(# of

workers)

EXAMPLE 1: Total & Marginal Product

MPL

∆Q = 1,000∆L = 1

∆Q = 800∆L = 1

∆Q = 600∆L = 1

∆Q = 400∆L = 1

∆Q = 200∆L = 1

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

3,0005200

2,8004400

2,4003600

1,8002800

1,00011,000

00

MPLQ

(bushels of wheat)

L(# of

workers)

Why MPL Is Important

Recall from Chapter 1: Rational people choose actions for which the expected marginal benefit exceeds the expected marginal cost.

When Farmer Jack hires an extra worker,

• his costs rise by the wage he pays the worker

• his output rises by MPL

Comparing the wage and the change in his output helps Jack decide whether he would benefit from hiring the worker.

EXAMPLE 2: A “Fold-It” Factory

We are going to create a factory that produces a product known as a “fold-it”

Resources:• factory• paper• stapler• staples• labor

Why MPL Diminishes

The Law of Diminishing Marginal Returns: the marginal product of a variable resource eventually falls as the quantity of the resource used increases (other things equal)

If we increases the # of workers but not the # of staplers or the desk area, each add’l worker has less to work with and will be less productive.

In general, MPL diminishes as L rises whether the fixed resource is land (as would be the case with Jack the wheat farmer) or capital (our desk and stapler).

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….

EXAMPLE 1: Farmer Jack’s Costs

Total Cost

3,0005

2,8004

2,4003

1,8002

1,0001

00

Cost of labor

Cost of land

Q(bushels of wheat)

L(# of

workers)

EXAMPLE 1: Farmer Jack’s Total Cost Curve

Q (bushels of wheat)

Total Cost

0 $1,000

1,000 $3,000

1,800 $5,000

2,400 $7,000

2,800 $9,000

3,000 $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

Marginal Cost

Marginal Cost (MC) is the increase in Total Cost from producing one more unit:

∆TC∆Q

MC =

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

3,000

2,800

2,400

1,800

1,000

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

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

3,000

2,800

2,400

1,800

1,000

0

Q(bushels of wheat)

$0

$2

$4

$6

$8

$10

$12

0 1,000 2,000 3,000Q

Mar

gin

al C

ost

($)

Why MC Is Important

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

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

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

(In the next chapter, we will learn more about how firms choose Q to maximize their profits.)

EXAMPLE 3

Our third example is more general, and applies to any type of firm producing any good with any types of resources.

EXAMPLE 3: Costs

7

6

5

4

3

2

1

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

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 3: 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

EXAMPLE 3: Average Fixed Cost

1007

1006

1005

1004

1003

1002

1001

$1000

AFCFCQ Average fixed cost (AFC) is fixed cost divided by 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

----

EXAMPLE 3: Average Variable Cost

5207

3806

2805

2104

1603

1202

701

$00

AVCVCQ Average variable cost (AVC) is variable cost divided by the quantity of 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

----

EXAMPLE 3: Average Total Cost

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

--------

AVCAFCTCQ Average total cost (ATC) equals total cost divided by the quantity of output:

ATC = TC/Q

Also,

ATC = AFC + AVC

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 3: Average Total Cost

88.57

80

76

77.50

86.67

110

$170

----

ATC

6207

4806

3805

3104

2603

2202

1701

$1000

TCQ

EXAMPLE 3: The 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

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.

31

210

150

100

30

10

VC

43.33358.332606

305

37.5012.501504

36.672016.673

802

$60.00$101

------------$500

MCATCAVCAFCTCQ

60

30

$10

$0

$25

$50

$75

$100

$125

$150

$175

$200

0 1 2 3 4 5 6 7

Q

Co

sts

EXAMPLE 3: Why ATC Is Usually U-shaped

As Q rises:

Initially, falling AFC pulls ATC down.

Eventually, rising AVC pulls ATC up.

EXAMPLE 3: 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.

Costs in the Long Run Short run:

Some inputs are fixed

Long run: All inputs are variable (firms can build new factories, or remodel 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 (the factory size with the lowest ATC).

EXAMPLE 4: LRAC with 3 Factory Sizes

ATCSATCM ATCL

Q

Cost ($)

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.

EXAMPLE 4: LRAC with 3 Factory Sizes

ATCSATCM ATCL

Q

Cost ($)

QA QB

LRATC

A Typical LRAC Curve

Q

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

So a typical LRAC curve looks like this:

LRAC

How LRAC Changes as the Scale of Production ChangesEconomies of scale: LRAC falls as Q increases.

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

Diseconomies of scale: LRAC rises

as Q increases.

LRAC

Q

Cost