Deriving Cost Curves
Deriving cost curves from total physical product information
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) $100.
Total costs are the sum of total fixed and total variable costs: TC = column (4) + column (5).
Inputs / Output / Total costs / Average costs / Marginal costCapital
(units) / Labour
(Number) / Total physical product
(TPP) (units) / Fixed
(TFC)
($)
(1) x $60 / Variable
( TVC )
($)
(2) x $100 / (Total)
( TVC )
($)
(4) ÷ (5) / Fixed
(AFC)
($)
(4) ÷ (3) / Variable
(AVC)
($)
(5) ÷ (3) / (Total)
(AC)
($)
(6) ÷ (3) / ( MC )
($)
Δ(6) ÷ Δ(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, 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 = ΔTC /ΔTPP. 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 (ΔTC) by $100 (i.e. the cost of the fifth worker). Its output has increased (ΔTPP) 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?