costs of production chapters 11. short-run vs. long run firms typically have several types of inputs...

COSTS OF PRODUCTIONChapters 11

Short-Run vs. Long Run• Firms typically have several types of inputs that they can

adjust to adjust production.• Long-run - When firms are able to adjust all of their inputs

including physical plant.• Short-run – When firms are able to adjust only some of

their inputs (usually energy, labor, and raw material costs).

Productivity• Average Productivity of Labor is output per work.

• Marginal Productivity of Labor is the extra production that is obtained from an extra unit of labor.

Total ProductAPL

Labor

TPMPL

Labor

Short Run Production Function

TPMPL

Labor

ΔLabor

ΔTP

ΔLaborΔTP

Total

Product

Production in the Short-Run• Given a set of fixed inputs (like plant and capital equipment),

a firm can vary other inputs (typically labor) and to vary production.

• Typically, as you add workers, you get more output.

• Up to a point each additional worker adds synergy and adding more workers leads to more and more extra pay-off.

• But at some point, capacity constraints bind, diminishing returns sets in, and the addition of extra workers will generate less and less extra production.

0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88 92 96 100

0

5

10

15

20

25

30

35

Bakery

Hours

Lo

av

es

Productivity• Labor productivity depends on the number of workers

• First, increasing, then, decreasing• Average product of labor begins decreasing when

marginal product of labor drops below average.

Note: Marginal Product crosses through average product at the peak of average product.

As long as the next worker adds more product than the average worker, they will increase the average.

Once diminishing returns set in, additional workers may add less to output than the average worker, reducing the overall average.

MPL, APL

L

MPLAPL

Small Scale Schedule

Average MarginalHours Loaves Product Product

0 00.10

2 0.20 0.100.32

4 0.83 0.210.58

6 2 0.331

8 4 0.53

10 10 1

Large Scale ScheduleAverage Marginal

Hours Output Product Product0 0

110 10 1

0.33333340 20 0.5

0.290 30 0.333333

0.142857160 40 0.25

0.111111250 50 0.2

0.090909360 60 0.166667

Fixed Costs vs. Variable Costs• In short-run, we distinguish between the costs that are

adjustable as production is adjusted (variable costs) and costs that are unchanged regardless of production (fixed costs).• Variable costs (Wages of production workers, supply and raw

materials costs)• Fixed costs (Depreciation costs, Financial costs, wages of non-

production workers).

Types of Costs• Total Fixed Costs – Invariant to the number of goods

produced (in the short-run)• Average Fixed Costs – Decreasing in the number of goods

produced.

• Total Variable Costs- Increasing in the number of goods produced.

• Total Costs: Fixed Costs + Variable Costs

Bakery: Wages $10 per Worker, $5 Wheat per Loaf

Output Fixed Workers Bakers Wheat Variable Total(Loaves) Costs Wages Costs Costs

2.00 1000 6 60 10.00 70.00 1070.00

10.00 1000 10 100 50.00 150.00 1150.00

20.00 1000 40 400 100.00 500.00 1500.00

30.00 1000 90 900 150.00 1050.00 2050.00

40.00 1000 160 1600 200.00 1800.00 2800.00

50.00 1000 250 2500 250.00 2750.00 3750.00

60.00 1000 360 3600 300.00 3900.00 4900.00

Total Variable Costs are increasing at an accelerating rate.

Reason: Diminishing returns to variable inputs.

2.00 10.00 20.00 30.00 40.00 50.00 60.000

1000

2000

3000

4000

5000

6000

Cost Schedule

Fixed Costs Variable Costs Total Costs

Costs: Average vs. Marginal• Total Costs are the sum of all relevant costs for a firm.• Average Costs: Costs per unit of output.• Marginal Cost: Extra Cost per Extra Unit of Output.

Cost SchedulesOutput Average Average Average

Total Fixed Variable Total Marginal(Loaves) Costs Costs Costs Costs Costs

2.00 1070.00 500 35 53510.00

10.00 1150.00 100 15 11535.00

20.00 1500.00 50 25 7555.00

30.00 2050.00 33.33333 35 6875.00

40.00 2800.00 25 45 7095.00

50.00 3750.00 20 55 75115.00

60.00 4900.00 16.66667 65 82

Average and Marginal CostsAverage Fixed Costs decreases as production increases

AVC, ATC, MC all increase as diminishing returns kick in

2.00 10.00 20.00 30.00 40.00 50.00 60.00

AFC NaN 100 50 33.33333333333

33

25 20 16.66666666666

67

AVC 35 15 25 35 45 55 65

ATC NaN 115 75 68.33333333333

33

70 75 81.66666666666

67

MC 35 10 35 55 75 95 115

10

30

50

70

90

110

130

Cost Curve

$

MC equals AVC and ATC when each of the latter are at their minimum level.

Long Run Costs• In the short-run, the size of a firms physical plant is a fixed

factor. • Over-time, the plant size can adjust. • In the bakery example, extra ovens can be added.

Minimizing Costs in the Long Run• Consider average total cost schedules at different

numbers of ovens. • Each oven will have a production level that generates the

minimum average total cost. • To minimize average costs in the long-run, choose the

number of ovens which will have the lowest, minimum average total cost.

Average Total Cost Schedules at Different Scales of Production

10

20

30

40

50

60

70

80

90

10

0

11

0

12

0

48

68

88

108

128

148

168

188

208

228

1 Oven

2 Ovens

3 Ovens

4 Ovens

5 Ovens

6 Ovens

7 Ovens

8 Ovens

Output

Minimum of the different cost Schedules

10

20

30

40

50

60

70

80

90

10

0

11

0

12

0

48

68

88

108

128

148

168

188

208

228

1 Oven

2 Ovens

3 Ovens

4 Ovens

5 Ovens

6 Ovens

7 Ovens

8 Ovens

Output

Connect the DotsLong Run Average Total Costs

10

20

30

40

50

60

70

80

90

10

0

11

0

12

048

68

88

108

128

148

168

188

208

228

1 Oven

2 Ovens

3 Ovens

4 Ovens

5 Ovens

6 Ovens

7 Ovens

8 Ovens

Output

If we adjust capital scale continuously, the collection of minimum points is the Long Run Average Total cost cuve

LR ATC

Short-run ATC

Economies of Scale• When firms are able to adjust all of their inputs, they can choose a size that will minimize costs.

• If a firm is able to achieve some economies of scale, increasing size will reduce the average total cost.

• Sources of Economies of Scale• Production requires major expenditure on items needed to

produce even zero products• Ex. Software, pharmaceuticals

• Production requires many specific steps which can be most efficiently done through specialization• Ex. Airplanes, automobiles

Long Run ATC increasing returns to scale.

Output

Costs

LR ATC

Economies of Scale

Returns to Scale• Scale Economies is not always likely to characterize production.

• If each production unit can act autonomously with identical costs then we may experience constant returns to scale.

• Firms at some point experience diseconomies of scale or increasing long run average total costs.

• Sources of diseconomies of scale• Limits of managerial attention. • Limits of some other fixed resource.

Long Run ATC decreasing returns to scale.

Output

Costs

LR ATC

Constant Returns Scale

Diseconomies

Overall Cost Function

LR ATC

Minimum Efficient Scale

MES and Market Structure• If MES is relatively large in comparison with the market

demand:

$

Q

D

LRAC

The market is most efficiently served by a single firm---natural monopoly!

MES and Market Structure• If MES is relatively small in comparison with market

demand:

$

Q

Many “small” firms in the market.

Learning OutcomesStudents should be able to • Define and calculate various types of economic costs.• Fixed, variable, total, average, marginal.

• Describe the shape of various relevant cost curves• Average Total (in LR and SR), Average Fixed, Marginal Costs

• Describe the relationship between production, productivity (marginal and average) and the law of diminishing returns.