Case Study 5

Deriving Cost Curves

Deriving cost curves from total physical product information

A firm's costs depend on the output of its factors. If we want to know precisely what a firm's cost curves will be, we need to know two pieces of information: (a) how its output varies with the amount of each factor it uses; (b) the price of those factors.

Let us take a simple production function and see how cost curves may be derived from it. Assume that a firm uses just two factors: capital and labor.

Assume that capital isfixedin supply at 5 units (column (1)) and costs $60 per unit per week. Thus total fixed costs are $300 (column (4)).

Labor is the variable factor (column (2)). The effects on output (TPP) of employing different amounts of labor are shown in column (3).

It is assumed that workers are paid a wage rate of $100 per week. Total (weekly) variable costs, then, are simply the number of workers employed multiplied by this wage rate: column (5) = column (2) $100.

Total costs are the sum of total fixed and total variable costs:TC= column (4) + column (5).

Capital

(units)

Labor

(Number)

Total physical product

(TPP)(units)

Fixed

(TFC)

($)

(1) x $60

Variable

(TVC)

($)

(2) x $100

(Total)

(TVC)

($)

(4) (5)

Fixed

(AFC)

($)

(4) (3)

Variable

(AVC)

($)

(5) (3)

(Total)

(AC)

($)

(6) (3)

(MC)

($)

(6) (3)

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

5

1

100

300

100

400

3.00

1.00

4.00

5

2

250

300

200

500

1.20

0.80

2.00

0.67

5

3

400

300

300

600

0.75

0.75

1.50

0.67

5

4

500

300

400

700

0.60

0.80

1.40

1.00

5

5

560

300

500

800

0.54

0.89

1.43

1.67

To find the three average costs (AFC, AVCandAC) we have to divide the appropriate total cost column by output (column (3)). ThusAFC = TFC/TPP= column (4) column (3). Similarly,AVC = TVC/TPP= column (5) column (3). Finally,AC = TC/TPP= column (6) column (3). Alternatively,ACcan be found by addingAFCandAVC: i.e. column (7) + column (8). (Check that this gives the same result.)

Marginal cost can be found by using the formulaMC= TC/TPP. In other words, it is the extra cost of producingone moreunit. Thus when the firm employs a fifth worker, for example, its costs have gone up ( TC) by $100 (i.e. the cost of the fifth worker). Its output has increased ( TPP) by 60 units (from 500 to 560). Thus if it is costing the firm an extra $100 to produce an extra 60 units, it is costing it $100/60 = $1.67 to produceonemore unit.

Questions

1. Draw a graph showing theAFC, AVC, ACandMCcurves corresponding to the figures in the above table.

2. Calculate a new set of figures for each of the columns (4) - (10) if (a) the price of capital rose from $60 to $100; (b) the wage rate rose from $100 to $150. Why in the case of (a) is the marginal cost not altered?