12712 costs-short run

8/6/2019 12712 Costs-short Run

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Short-run costs slide 1

COSTS OF PRODUCTIONCOSTS OF PRODUCTIONGeneral 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 the

firms costs at any level of output.

Put another way:Put another way:Costs are determined by the technology of

production and input prices.


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TOTAL

LABOR PRODUC0 01 32 15

3 364 485 566 627 668 68

Suppose labor costs $48 per day.

If labor is the only variable

input, we can find the total

variable costs at each output

level.


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TOTAL PLL =

LABOR PRODUCT TVC

0 0 01 3 482 15 96

3 36 1444 48 1925 566 62

7 668 68 384

240288

336


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0

100

200

300400

500

600

700

0 20 40 60 80

When output is 56,total variable costs

are $240.

When output is 56,total variable costs

are $240.

$

Q

TVC

HERES THE TVC CURVE.


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If there are fixed costs (costs associated with inputs

that cant 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


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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


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Q TC

0 50.01 63.0

2 71.03 76.0

4 82.45 97.06 130.0

7 174.0

8 233.09 314.0

10 460.0

11 656.0


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0

100

200

300

400

500

600

700

0 2 4 6 8 10 12 14

TCTC($)

Heres the graph of this new total cost curve.


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AVERAGE

COSTAVE

RAGE

COSTAverage 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.


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AC = TC/Q= 97/5

And we can

graph theAC curve.

Q TC AC

0 50.01 63.0 63.0

2 71.0 35.5

3 76.0 25.3

4 82.4 20.6

5 97.0 19.4

6 130.0 21.7

7 174.0 24.9

8 233.0 29.1

9 314.0 34.9

10 460.0 46.0

11 656.0 59.6


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0

20

40

60

80

100

120

0 2 4 6 8 10 12 14

AC

AC($/Q)

Q


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AVERAGEVARIABLECOSTS 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


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MARGIN

ALCOST

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 ofthe total cost curve. (TC / (Q.

Marginal cost curve: The curve that shows marginal

cost as a function of output.


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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


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0

20

40

60

80

100

120

0 2 4 6 8 10 12 14

AC, MCMC

AC

Q


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Of course, the marginal and average cost curves must

conform to the usual rules about marginal and average

curves.

1) When the average is rising, the marginal quantity

must be greater than the average quantity.

2) When the average is falling, the marginal quantity

must be less than the average quantity.

3) When the average is neither rising nor falling (at a

maximum or minimum), average and marginal are

equal.


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0

20

40

60

80

100

120

0 2 4 6 8 10 12 14

$/Q

MC

ACAVC

Q

WHAT WOULD THE AVERAGEVARIABLECOST CURVELOOK LIKE

IF WE WERE TO PUT IT ON THE SAME DIAGRAM?


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Two alternative ways

of showing informationabout the firms costs.

0

20

40

60

80

100

120

0 2 4 6 8 10 12 14

0

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0 2 4 6 8 10 12 14

$

$/Q

TC

Q

MC

AC

Q


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Short-Run Cost FunctionsAverage Total Cost = ATC = TC/Q

Average Fixed Cost = AFC = TFC/QAverage Variable Cost = AVC = TVC/Q

ATC = AFC + AVC

Marginal Cost = (TC/(Q = (TVC/(Q



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COST CURVESUMMARY:COST CURVESUMMARY:

Costs depend output, technology, and input prices.

There are two ways to depict a firms costs:

1) Total cost curves

2) Average and marginal cost curves


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What are the effects on a firms costs of anincrease in the price of an input?

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

This has the effect of raising both marginaland average costs.


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0

50

100

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300

350

0 2 4 6 8 10 12 14

0

10

20

30

40

50

60

0 2 4 6 8 10 12 14

$

$/Q

TC

TC

AC

AC

MC

MC

Q

Increasing the price of aninput raises both averageand marginal costs.

Q

TC is the total costcurve when the priceof a variable input isincreased.

AC and MC show theeffect of higher inputprices.


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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.


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0

50

100

150

200

250

300

350

0 2 4 6 8 10 12 14

0

10

20

30

40

50

60

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 fewerinputs.


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

$

TC

Q


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$/Q

AC

MC

Q


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$

TC

Q


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$/Q

AC=MC

Q


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12712 costs-short run

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