21 Cost Curves

Types of Cost Curves A total cost curve is the graph of a firm’s total cost function. A variable cost curve is the graph of a firm’s variable cost function. An average total cost curve is the graph of a firm’s average total cost function.

Types of Cost Curves An average variable cost curve is the graph of a firm’s average variable cost function. An average fixed cost curve is the graph of a firm’s average fixed cost function. A marginal cost curve is the graph of a firm’s marginal cost function.

Types of Cost Curves How are these cost curves related to each other? How are a firm’s long-run and short-run cost curves related?

Fixed, Variable & Total Cost Functions F is the total cost to a firm of its short-run fixed inputs. F, the firm’s fixed cost, does not vary with the firm’s output level. cv(y) is the total cost to a firm of its variable inputs when producing y output units. cv(y) is the firm’s variable cost function. cv(y) depends upon the levels of the fixed inputs.

Fixed, Variable & Total Cost Functions c(y) is the total cost of all inputs, fixed and variable, when producing y output units. c(y) is the firm’s total cost function;

Av. Fixed, Av. Variable & Av. Total Cost Curves For y > 0, the firm’s average total cost function, the cost per unit of output, is

Av. Fixed, Av. Variable & Av. Total Cost Curves Average Fixed Costs: As y increases, AFC decrease. Average Variable Costs: In general, AVC increase, as fixed factors will constrain the production (Although, initially AVC may decrease, if production can be organized in a more efficient way as the scale increases).

Av. Fixed, Av. Variable & Av. Total Cost Curves Average Costs: U shaped At first, declining AFC dominate Eventually, rising AVC will increase AC What do these functions look like?  See Varian Figure 21.1 and sketch the curves

AC AC AC y y y

Marginal Cost Function Marginal cost is the rate-of-change of variable production cost as the output level changes. That is,

Marginal Cost Function The firm’s total cost function is and the fixed cost F does not change with the output level y, so MC is the slope of both the variable cost and the total cost functions.

Marginal and Variable Cost Functions Since MC(y) is the derivative of cv(y), cv(y) must be the integral of MC(y). That is,

Marginal and Variable Cost Functions $/output unit MC(y) Area is the variable cost of making y’ units y

Marginal & Average Cost Functions How is marginal cost related to average variable cost? For the first produced unit: MC(1)=AVC(1). If AVC are decreasing at some output level y, MC must be smaller than AVC at that region. If AVC are rising, it must be that MC>AVC. MC curve must cut AVC curve at its minimum point.

Marginal & Average Cost Functions The same argument applies for the average costs as well. Also, this can be seen by writing: When AC-curve rises: MC > AC, When AC-curve decreases: MC < AC When AC’(y)=0: MC = AC.

Cost Curves: See Varian Figure 21.2 and sketch MC-, AC- and AVC-curve

Cost Curves QUESTION 1 Consider a following cost function: 𝑐 𝑦 = 𝑦 2 +1. Write down Variable costs fixed costs Average variable costs Average fixed costs Average costs Marginal costs Draw curves for average, marginal and average variable costs.

Long-Run Costs In the long-run: No fixed factors. Firms are able to adjust all of the factors of production (e.g. plant size, contractual oblications, etc.) Here, say fixed factor is the plant size k, which the firm can optimize in the long-run. This size depends on the level of output y: k(y).

Long-Run Costs Short-run costs are Long-run costs are Thus, for one output level y*, short-run and long-run costs are the same. At y*, the optimal choice of plant size is k*. See Varian Figure 21.7 (Fig. 21.6 in 7th ed.), and sketch SAC and LAC:

AC y The short-run average cost curve must be tangent to the long-run average cost curve.

Long-Run Costs The same analysis can be applied to other levels of outputs and plant sizes The long-run average cost curve is the lower envelope of the short-run average cost curves. See Varian Figure 21.8 (Fig. 21.7 in 7th ed.), and sketch short-run and long-run average costs:

AC y The long-run average cost curve is the envelope of the short-run average cost curves.

Long-Run Marginal Costs The long-run marginal cost at any output y has to equal the short-run marginal cost associated with the optimal level of plant size to produce y. See Varian Figure 21.11 (Fig. 21.10 in 7th ed), and sketch the relationship between the long-run and short-run marginal costs:

AC y