Lecture Notes: Econ 203 Introductory Microeconomics
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Lecture Notes: Econ 203 Introductory Microeconomics Lecture/Chapter 13: Costs of Production M. Cary Leahey Manhattan College Fall 2012. Goals. Introduction to the theory of the firm New “buzz words” developed here: Production function Price and marginal revenue (MR) and cost (MC)

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Goals

Lecture Notes: Econ 203 Introductory MicroeconomicsLecture/Chapter 13: Costs of Production M. Cary LeaheyManhattan CollegeFall 2012


Goals

Goals

  • Introduction to the theory of the firm

  • New “buzz words” developed here:

  • Production function

  • Price and marginal revenue (MR) and cost (MC)

  • Marginal costs and average total costs (ATC)

  • Classification of costs:

  • Fixed versus variable

  • Implicit versus explicit

  • Distinction between short- and long-runs

  • Economies of scale


Introduction what do firms want to do

Introduction: what do firms want to do?

Review of what are firm’s costs in your opinion (e.g. Ford)

Company goal – profit maximization

Profit = Total revenue – total costs

Total revenue – total amount received from sale of output

Total costs – market value of the inputs used to produce output

Alternatives – revenue maximization (ML)

market share maximization (Japan)

social profit/sustainability

3


Costs explicit or implicit profit economic or accounting

Costs: explicit or implicit; profit: economic or accounting

Explicit costs are money costs (determined by the market)

Usually largest costs are wages/benefits followed by IT

Implicit costs do not require a cash outlay

Opportunity cost of the owner’s time

Example: Interest costs

Explicit: borrow $100K at 5% interest with a cash cost of $5K

Explicit: borrow $60K at 5% interest with a cash cost of $3K

Implicit: borrow $40K from yourself at an implicit 5% cost for $2K

Costs are the case in two examples = $5K

Profits: Accounting profit = revenues less explicit costs

Economic profit = revenues less explicit and implicit costs

Economic profit usually lower than accounting profit

4


The production function

The production function

The production function shows the relationship between inputs and outputs-specifically the quantity of inputs needed to produce a quantity of output

Can be displayed as an equation, table or graph

Best-known (macro) production function is Cobb-Douglas

Y = AF(K,L), where Y – output. L – labor, K – capital, and A is unexplained residual

The residual is the amount of output that cannot be attributed to labor or capital, such as the layout of the factory floor

5


Production function an example

Production function: an example

L(no. of workers)

Q(bushels of wheat)

3,000

2,500

0

0

2,000

1

1000

1,500

Quantity of output

2

1800

1,000

3

2400

500

4

2800

0

0

1

2

3

4

5

5

3000

No. of workers

0


Marginal product

Marginal product

In the previous example, hiring the next incremental worker increases output by the marginal product of labor

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

∆ (delta) = “change in…”

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

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

7


Example total and marginal product

Example: Total and marginal product

L(no. of workers)

Q(bushels of wheat)

0

0

∆Q = 1000

∆L = 1

1

1000

∆Q = 800

∆L = 1

2

1800

∆L = 1

∆Q = 600

3

2400

∆Q = 400

∆L = 1

4

2800

∆L = 1

∆Q = 200

5

3000

0

MPL

1000

800

600

400

200


Example mpl slope of production function

Example: MPL = slope of production function

3,000

2,500

2,000

Quantity of output

1,500

1,000

500

0

0

1

2

3

4

5

No. of workers

0

L(no. of workers)

Q(bushels of wheat)

MPL

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

0

1000

1

1000

800

2

1800

600

3

2400

400

4

2800

200

5

3000


Importance of the concept of diminishing marginal product

Importance of the concept of (diminishing) marginal product

Allows the producer to think along the margin and help make the decision to hire another worker or add another input

Why does the marginal product of labor decline

Additional worker in the agricultural example has less land to cultivate and is hence less productive

In general, the more intense use of labor with any fixed input such as capital, land etc mans diminishing MPL

So diminishing MP is that the MP of an input declines as the quantity of the input increases (other things equal)

10


Example 1 costs

Example 1: Costs

$1,000

$0

$1,000

$1,000

$2,000

$3,000

$1,000

$4,000

$5,000

$1,000

$6,000

$7,000

$1,000

$8,000

$9,000

$1,000

$10,000

$11,000

0

L(no. of workers)

Q(bushels of wheat)

Cost of land

Cost of labor

Total Cost

0

0

1

1000

2

1800

3

2400

4

2800

5

3000


Example 1 total cost curve

Example 1: Total cost curve


Marginal costs

Marginal costs

Marginal cost (MC) is the increase in total costs from producing one more unit

MC = ∆TC/ ∆Q

If marginal cost in less than the incremental revenue obtained, the additional use of the input is not profitable or makes sense.

13


Example 1 total and marginal cost

Example 1: Total and marginal cost

Q(bushels of wheat)

Total Cost

0

$1,000

∆TC = $2000

∆Q = 1000

1000

$3,000

∆TC = $2000

∆Q = 800

1800

$5,000

∆TC = $2000

∆Q = 600

2400

$7,000

∆TC = $2000

∆Q = 400

2800

$9,000

∆TC = $2000

∆Q = 200

3000

$11,000

Marginal Cost (MC)

$2.00

$2.50

$3.33

$5.00

$10.00


Example 1 the marginal cost curve

Example 1: The marginal cost curve

$2.00

$2.50

$3.33

$5.00

$10.00

Q(bushels of wheat)

TC

MC

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

0

$1,000

1000

$3,000

1800

$5,000

2400

$7,000

2800

$9,000

3000

$11,000


Fixed and variable costs

Fixed and variable costs

Fixed costs (FC) do not vary with the quantity of output produced

Examples: land, capital, loan payment, rent

Variable costs (VC) vary with the quantity produced

Examples: cost of labor and materials

Total cost (TC). TC = FC + VC

Marginal cost (MC) is the increase in total costs from producing one more unit

MC = ∆TC/ ∆Q

If marginal cost in less than the incremental revenue obtained, the additional use of the input is not profitable or makes sense.

16


Example 2 costs

Example 2: Costs

$100

$0

$100

100

70

170

100

120

220

100

160

260

100

210

310

100

280

380

100

380

480

100

520

620

0

$800

FC

Q

FC

VC

TC

VC

$700

TC

0

$600

1

$500

2

Costs

$400

3

$300

4

$200

5

$100

6

$0

7

0

1

2

3

4

5

6

7

Q


Example 2 marginal costs

Example 2: Marginal costs

MC =

∆TC

∆Q

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

Q

TC

MC

0

$100

$70

1

170

50

2

220

40

3

260

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.)

50

4

310

70

5

380

100

6

480

140

7

620


Example 2 average fixed cost

Example 2: Average fixed cost

n/a

$100

50

33.33

25

20

16.67

14.29

0

Average fixed cost (AFC)is fixed cost divided by the quantity of output:

AFC = FC/Q

Q

FC

AFC

0

$100

1

100

2

100

3

100

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

4

100

5

100

6

100

7

100


Example 2 average variable cost

Example 2: Average variable cost

n/a

$70

60

53.33

52.50

56.00

63.33

74.29

0

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

AVC = VC/Q

Q

VC

AVC

0

$0

1

70

2

120

3

160

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

4

210

5

280

6

380

7

520


Example 2 average total cost cost per unit or unit cost

Example 2: Average total cost (cost per unit, or unit cost)

AFC

AVC

n/a

n/a

n/a

$170

$100

$70

110

50

60

86.67

33.33

53.33

77.50

25

52.50

76

20

56.00

80

16.67

63.33

88.57

14.29

74.29

0

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

ATC = TC/Q

Q

TC

ATC

0

$100

1

170

2

220

3

260

Also,

ATC = AFC + AVC

4

310

5

380

6

480

7

620


Example 2 average total cost

Example 2: Average total cost

$200

$175

$150

$125

Costs

$100

$75

$50

$25

$0

0

1

2

3

4

5

6

7

Q

0

Q

TC

ATC

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

0

$100

n/a

1

170

$170

2

220

110

3

260

86.67

4

310

77.50

5

380

76

6

480

80

7

620

88.57


Example 2 the cost curves atc afc avc and mc

Example 2: The cost curves, ATC, AFC, AVC and MC

$200

$175

$150

AFC

$125

AVC

Costs

$100

ATC

$75

MC

$50

$25

$0

0

1

2

3

4

5

6

7

Q

0


Example 2 why atc is usually u shaped

Example 2: Why ATC Is usually u-shaped

$200

$175

$150

$125

Costs

$100

$75

$50

$25

$0

0

1

2

3

4

5

6

7

Q

0

As Q rises:

Initially, falling AFCpulls ATC down.

Eventually, rising AVCpulls ATC up.

Efficient scale:The quantity that minimizes ATC.


Example 2 atc and mc and profit maximization

EXAMPLE 2: ATC and MC and profit maximization

$200

$175

$150

$125

Costs

$100

ATC

$75

MC

$50

$25

$0

0

1

2

3

4

5

6

7

Q

0

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 short and long run

Costs in the short- and long-run

Short-run

Some inputs are fixed (land, capital)

Long-run:

All inputs are variable, as more land can be bought, etc

Fixed costs (FC) do not vary with the quaintly of output produced

The long-run ATC is a succession of short-run ATC curves.

26


A typical lratc curve

A typical LRATC curve

ATC

LRATC

Q

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

So a typical LRATC curve looks like this:


Atc changes as scale of production changes

ATC Changes as scale of production changes

ATC

LRATC

Q

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.


Atc and production scale

ATC and production scale

Economies of scale occur when increasing production allows greater specialization. Workers can be more productive focused on a narrow task.

More common when quantity supplied is low.

Diseconomies of scale develop due to coordination problems in large organizations (stretched management)

More common when output supplied is high

29


Summary and conclusion

Summary and conclusion

Costs are both explicit (in cash) or implicit (no cash outlay but an opportunity cost). Both are important to the firm’s decision making

Accounting profit is revenue less cash outlays; economic profit is revenue less all (explicit and implicit) costs

Production function shows relationship between inputs and output.

Marginal production is the increase in output coming from one additional input. Labor is the most common example.

Marginal product usually diminishes with insensitivity of use. As output rise the production function becomes flatter (the delta declines) and the total cost curve becomes steeper (delta increases)

Variable costs vary with output; fixed costs do not

Marginal costs is the increase in total cost from an extra (incremental) unit of production,. The MC curve is usually upward sloping.

30


Summary and conclusion1

Summary and conclusion

Average variable cost is variable costs divided by output

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

Average total cost (cost per unit or unit cost) is total costs divided by the quantity of output. ATC curve is usually U-shaped.

The MC curve intersects the ATC curve at the minimum average total cost

MC < ATC, ATC fall as Q rises

MC > ATC, ATC rises as Q

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 the same as Q rises

31


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