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Case D6
Deriving Cost Curves
Deriving cost curves from total physical product information
In section 9.3 we argued that 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 labour.
Assume that capital is fixed in supply at 5 units (column (1)) and costs £60 per unit per week.
Thus total fixed costs are £300 (column (4)).
Labour is the variable factor (column (2)). The effects on output (TPP) of employing different
amounts of labour 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).
Inputs
Output
Capital Labour Total physical
(units) (Number)
product
(TPP) (units)
Total costs
Fixed
Variable
(TFC)
(TVC)
(£)
(£)
(1)  £60 (2)  £100
Average costs
Marginal cost
(Total)
(TVC)
(£)
(4)  (5)
Fixed
(AFC)
(£)
(4)  (3)
Variable
(AVC)
(£)
(5)  (3)
(Total)
(AC)
(£)
(6)  (3)
(MC)
(£)
(6)  (3)
(10)
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
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, AVC and AC) we have to divide the appropriate total cost
column by output (column (3)). Thus AFC = TFC/TPP = column (4) ÷ column (3). Similarly, AVC
= TVC/TPP = column (5) ÷ column (3). Finally, AC = TC/TPP = column (6) ÷ column (3).
Alternatively, AC can be found by adding AFC and AVC: i.e. column (7) + column (8). (Check that
this gives the same result.)
Marginal cost can be found by using the formula MC = TC/TPP. In other words, it is the
extra cost of producing one more unit. 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 produce one more unit.
Questions
1. Draw a graph showing the AFC, AVC, AC and MC curves 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?