short run costs.ppt

8/7/2019 short run costs.ppt

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Short-run costs slide 1

COSTS OF PRODUCTION COSTS OF PRODUCTION

General principle: If you know the technology

of production (the production function or total

product curve), and if you know the prices of

the inputs to production, then you can find thefirm¶s costs at any level of output.




Put another way:Put another way:

Costs are determined by the technology of

production and input prices.

Let¶s start with the total product curve for tax preparationservices from the last section, and show how to get tocosts of production.




TOTAL

LABOR PRODUC0 01 32 153 364 485 56

6 627 668 68




Suppose labor costs $48 per day.

PL = $48/day

If labor is the only variable input, we can find the

total variable costs at each output level.




TOTAL PLL =

LABOR PRODUCT TVC

0 0 01 3 482 15 96

3 36 1444 48 1925 566 62

7 668 68 384

Hidden slide




TOTAL PLL =

LABOR PRODUCT TVC

0 0 0

1 3 48

2 15 96

3 36 1444 48 192

5 56 240

6 62 288

7 66 3368 68 384




THE TOTAL VARIABLE COST CURVE shows the

total variable cost at each level of output.

In the total variable cost curve the independent

variable is OUTPUT, and the dependent variable

is TOTAL VARIABLE COSTS.




When output is 56,total variable costs

are $240.

$

Q0

100

200

300

400

500

600

700

0 20 40 60 80

PLOT THE REST OF THE POINTS TO

SHOW TVC.




0

100

200

300400

500

600

700

0 20 40 60 80


are $240.


are $240.

$

Q

TVC

HERE¶S THE TVC CURVE.




If there are fixed costs (costs associated with inputs

that can¶t be changed), then we can add these to

the total variable costs to get total costs.

Total Cost = Fixed Cost + Total Variable Cost

TC = FC + TVC




100

200

300

400

500

600

700

0 20 40 60 80

TVC

TC

The total cost curve shows the total cost of

producing each output.

$

Q




Here¶s another total cost curve that we¶ll use to

introduce the concepts of average cost and

marginal cost.




Q TC

0 50.01 63.0

2 71.03 76.0

4 82.45 97.06 130.0

7 174.0

8 233.09 314.010 460.0

11 656.0




0

100

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300

400

500

600

700

0 2 4 6 8 10 12 14

TCTC($)

Here¶s the graph of this new total cost curve.




AVER

AGE COST

AVER

AGE COST

Average cost: Cost per unit of output. Total cost

divided by output. TC/Q.

Average cost curve: The curve that shows average

cost as a function of output. Output is the

independent variable and average cost is the

dependent variable.




AC = TC/Q= 97/5

Q TC AC

0 50.01 63.0 63.0

2 71.0 35.5

3 76.0 25.3

4 82.4 20.65 97.0 19.4

6 130.0

7 174.0

8 233.09 314.0 34.9

10 460.0 46.0

11 656.0 59.6

Hidden slide






AC

AC($/Q)

Q0

20

40

60

80

100

120

0 2 4 6 8 10 12 14

PLOT THE REST OF THE AC CURVE. Hidden slide




0

20

40

60

80

100

120

0 2 4 6 8 10 12 14

AC

AC($/Q)

Q




AVERAGEVARIABLE COSTS CAN BE

SHOWN AT THE SAME TIME.

Q T C A C A C

0 5 0 .0

1 6 3 .0 6 3 .0 1 3 .0

2 7 1 .0 3 5 .5 1 0 .5

3 7 6 .0 2 5 .3 8 .7

4 8 2 .4 2 0 .6 8 .15 9 7 .0 1 9 .4 9 .4

6 1 3 0 .0 2 1 .7 1 3 .3

7 1 7 4 .0 2 4 .9 1 7 .7

8 2 3 3 .0 2 9 .1 2 2 .9

9 3 1 4 .0 3 4 .9 2 9 .3

1 0 4 6 0 .0 4 6 .0 4 1 .0

1 1 6 5 6 .0 5 9 .6 5 5 .1




0

20

40

60

80

100

120

0 2 4 6 8 10 12 14

$/Q

Q

AVC

AC




M ARG

IN AL

COST Marginal cost: The change in total cost per unit

change in output. The increase in cost due to

producing one more unit of output. The slope of the total cost curve. (TC / (Q.

Marginal cost curve: The curve that shows marginal

cost as a function of output. The independent

variable is output. The dependent variable is

marginal cost.




The marginal costof the 4th unit of

output is 6.4=(82.4-76)/(4-3)

Q TC AC MC

0 50.01 63.0 63.0 132 71.0 35.5 83 76.0 25.3 5

4 82.4 20.6 6.45 97.0 19.4 14.66 130.0 21.7 337 174.0 24.9

8 233.0 29.19 314.0 34.910 460.0 46.0 14611 656.0 59.6 196

Calculate the missing figures for MC.Hidden slide




The marginal costof the 4th unit of

output is 6.4=(82.4-76)/(4-3)

And we can graphthe MC curve.

Q TC AC MC

0 50.01 63.0 63.0 132 71.0 35.5 83 76.0 25.3 5

4 82.4 20.6 6.45 97.0 19.4 14.66 130.0 21.7 33

7 174.0 24.9 44

8 233.0 29.1 599 314.0 34.9 8110 460.0 46.0 14611 656.0 59.6 196




AC, MCMC

AC

Q

0

20

40

60

80

100

120

0 2 4 6 8 10 12 14

AC

Hidden slide




0

20

40

60

80

100

120

0 2 4 6 8 10 12 14

AC, MCMC

AC

Q






Notice that the general shape of the AC and MC

curves can be deduced by looking as the TC curve.

(Review, if necessary, the techniques for finding AP

and MP curves by inspecting TP curves covered in

the last section.)




WHAT WOULD THE AVERAGE V ARI ABLE COST CURVE LOOK LIKE

IF WE WERE TO PUT IT ON THE SAME DIAGRAM?

0

20

40

60

80

100

120

0 2 4 6 8 10 12 14

$/Q MC

AC

Q

Hidden slide




0

20

40

60

80

100

120

0 2 4 6 8 10 12 14

$/Q

MC

ACAVC

Q




Two alternative ways

of showing informationabout the firm¶s costs.

0

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120

0 2 4 6 8 10 12 14

0

100

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300

400

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700

0 2 4 6 8 10 12 14

$

$/Q

TC

Q

MC

AC

Q




COST CURVE SU MM ARY:COST CURVE SU MM ARY:

Costs depend output, technology, and input prices.

There are two ways to depict a firm¶s costs:

1) Total cost curves

2) Average and marginal cost curves




CH A

N G

ES IN COSTS CH A

N G

ES IN COSTS

What are the effects on costs of changes in

a) input prices?

b) the technology of production?

c) taxes on output?




What are the effects on a firm¶s costs of anincrease in the price of an input?

The increase in the price of a variable inputwill raise the total variable costs of production at each output level.

This has the effect of raising both marginaland average costs.






An improvement in technology lowers the cost of

producing each level of output.

Marginal and average costs of production will be

lower as a result.




0

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350

0 2 4 6 8 10 12 14

0

10

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30

40

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0 2 4 6 8 10 12 14

$

$/Q

Q

Q

TC

TC¶

MC

MC¶

ACAC¶

IMPROVEMENTS IN

TECHNOLOGY REDUCECOSTS OF PRODUCTION.

Costs fall because thesame output can beproduced using fewer inputs.




Imposing a tax per unit of output will raise total cost

by tQ, where t is the tax per unit and Q is the

number of units of output sold.

The tax will raise both average and marginal costs by

exactly the amount of the tax per unit of output.




0

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300

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0 2 4 6 8 10 12 14

0

10

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0 2 4 6 8 10 12 14

$

$/Q

Q

Q

TC

TC+3Q

MC

MC+3

ACAC+3

A per unit tax of $3 will

raise average and marginal

cost by exactly $3.

A per unit tax of $3 will

raise total cost by $3Q, or $3 times the quantity

produced.




What is a SU BSIDY , and how

does a per unit subsidy affect

a firm¶s costs?

Hidden slide




A subsidy is a negative tax. It is a payment

from the government to the firm.

A per unit subsidy lowers the firm¶s average

and marginal costs by the amount of the

subsidy per unit of output.




SU MM A

RY SU MM A

RY Increases in the prices of inputs will raise the total,

average, and marginal costs of production.

Improvements in technology lower total, average,

and marginal costs of production.

A per unit tax of t will raise total costs by tQ, and

will raise marginal and average costs by exactly t.




CHECK UP: WHAT DO THE AC AND MCCURVES LOOK LIKE FOR THE FOLLOWINGTOTAL COST CURVES?

$

TC

Q

Hidden slide




$/Q

AC

MC

Q




$

TC

Q

Hidden slide






$

TC

Q

Hidden slide




$/Q

Q

MC

AC

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