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Cost
total variable cost is an increasing function of the level of output. Total cost is the sum of total fixed and total variable cost.
KEY RELATIONSHIPS: AVERAGE TOTAL COST, AVERAGE FIXED COST, AVERAGE VARIABLE COST, AND MARGINAL COST The definitions of average fixed cost, average variable cost, average total cost, and marginal cost are, appropriately, as follows: Average fixed cost: AFC =
TFC Q
Average variable cost: AVC = Average total cost: ATC =
TVC Q
TC TFC + TVC = = AFC + AVC Q Q
Marginal cost: MC =
dTC dTVC = dQ dQ
(6.5) (6.6) (6.7) (6.8)
Average total cost is the total cost of production per unit. It is the total cost of production divided by total output. Average total cost is a short-run production concept if total cost includes fixed cost. It is a long-run production concept if all costs are variable costs. Average fixed cost, which is a short-run production concept, is total fixed cost per unit of output. It is total fixed cost divided by total output. Average variable cost is total variable cost of production per unit of output. Average variable cost is total variable cost divided by total output. Marginal cost is the change in the total cost associated with a change in total output.1 Contrary to conventional belief, this is not the same thing as the cost of producing the “last” unit of output. Since it is total cost that is changing, the cost of producing the last unit of output is the same as the 1 Strictly speaking, it is incorrect to assert that marginal cost is the rate of change in total cost with respect to a change in output unless total cost has been properly specified. The total cost equation TC = PKK + PLL is a function of inputs K and L, and factor prices PK and PL. Mathematically, it is incorrect to differentiate total cost with respect to the nonexistent argument, Q. As we saw from our discussion of isoquants in Chapter 5, it is possible to produce a given level of output with numerous combinations of inputs. For the profit-maximizing firm, however, only the cost-minimizing combination of inputs is of interest. Marginal cost is not, therefore, an arbitrary increase in total cost given an increase in output. Rather, marginal cost is the minimum increase in total cost with respect to an increase in output. The appropriate total cost equation is
TC = PK K * ( PK , PL ,Q) + PL L* ( PK , PL , Q) = TC * ( PK , PL , Q) where L* and K* represent the optimal input levels for a cost-minimizing firm. Once the total cost function has been properly defined, marginal cost is MC = ∂TC*(PK, PL, Q)/∂Q. For a more detailed discussion, see Silberberg (1990, Chapter 10, pp. 226–227).
