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COSTS OF PRODUCTIONCOSTS 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 the firm’s costs at any level of output.

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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 preparation services from the last section, and show how to get to costs of production.

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TOTALLABOR PRODUCT

0 01 32 153 364 485 566 627 668 68

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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.

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TOTAL PL L = LABOR PRODUCT TVC

0 0 01 3 482 15 963 36 1444 48 1925 566 627 668 68 384

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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.

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When output is 56, total variable costs

are $240.

When output is 56, total variable costs

are $240.

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PLOT THE REST OF THE POINTS TOSHOW TVC.

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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

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The total cost curve shows the total cost of producing each output.

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Q

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Here’s another total cost curve that we’ll use to introduce the concepts of average cost and marginal cost.

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Q TC0 50.01 63.02 71.03 76.04 82.45 97.06 130.07 174.08 233.09 314.010 460.011 656.0

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TCTC($)

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

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AVERAGE COSTAVERAGE 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.

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AC = TC/Q = 97/5

Q TC AC0 50.01 63.0 63.02 71.0 35.53 76.0 25.34 82.4 20.65 97.0 19.46 130.07 174.08 233.09 314.0 34.910 460.0 46.011 656.0 59.6

Hidden slide

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AC

AC($/Q)

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PLOT THE REST OF THE AC CURVE. Hidden slide

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AVERAGE VARIABLE COSTS CAN BE SHOWN AT THE SAME TIME.

Q TC AC AVC0 50.01 63.0 63.0 13.02 71.0 35.5 10.53 76.0 25.3 8.74 82.4 20.6 8.15 97.0 19.4 9.46 130.0 21.7 13.37 174.0 24.9 17.78 233.0 29.1 22.99 314.0 34.9 29.310 460.0 46.0 41.011 656.0 59.6 55.1

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MARGINAL 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.

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The marginal costof the 4th unit ofoutput is 6.4 =(82.4-76)/(4-3)

Q TC AC MC0 50.01 63.0 63.0 132 71.0 35.5 83 76.0 25.3 54 82.4 20.6 6.45 97.0 19.4 14.66 130.0 21.7 337 174.0 24.98 233.0 29.19 314.0 34.910 460.0 46.0 14611 656.0 59.6 196

Calculate the missing figures for MC.Hidden slide

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AC, MCMC

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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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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.)

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WHAT WOULD THE AVERAGE VARIABLE COST CURVE LOOK LIKE IF WE WERE TO PUT IT ON THE SAME DIAGRAM?

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$/Q MC

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Two alternative waysof showing information about the firm’s costs.

Two alternative waysof showing information about the firm’s costs.

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COST CURVE SUMMARY:COST CURVE SUMMARY:

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

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CHANGES IN COSTSCHANGES IN COSTS

What are the effects on costs of changes in

a) input prices?

b) the technology of production?

c) taxes on output?

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What are the effects on a firm’s costs of an increase in the price of an input?

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

This has the effect of raising both marginal and average costs.

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Increasing the price of aninput raises both averageand marginal costs.

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TC’ is the total cost curve when the price of a variable input is

increased.

AC’ and MC’ show the effect of higher input

prices.

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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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IMPROVEMENTS IN TECHNOLOGY REDUCE COSTS OF PRODUCTION.

IMPROVEMENTS IN TECHNOLOGY REDUCE COSTS OF PRODUCTION.

Costs fall because the same output can be produced using fewer inputs.

Costs fall because the same output can be produced using fewer inputs.

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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.

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ACAC+3

A per unit tax of $3 willraise average and marginalcost by exactly $3.

A per unit tax of $3 willraise total cost by $3Q, or $3 times the quantity produced.

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What is a SUBSIDY, and howdoes a per unit subsidy affecta firm’s costs?

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SUMMARYSUMMARY

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.

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CHECK UP: WHAT DO THE AC AND MC CURVES LOOK LIKE FOR THE FOLLOWING TOTAL COST CURVES?

$

TC

Q

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$

TC

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$

TC

Q

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