Chapter 8: Cost Curves

In this chapter, we do comparative statics based on the cost minimization problem (Chapter 7) and we derive the firm's cost curves. In other words, we find the minimum cost of producing each level of output.

Chapter highlights include:

· The Long Run and Short Run Total Cost Curves

· Total Variable Cost Curve and Total Fixed Cost Curve

· The Long Run and Short Run Average Cost Curves

· Average Variable Cost and Average Fixed Cost

· The Long Run and Short Run Marginal Cost Curves

· Economies and Diseconomies of Scale

· Minimum Efficient Scale

1. Lon-run Total Cost Curve

Given input prices, we can find the minimum cost of producing each level of output by solving the cost minimization problem. We thus can obtain a total cost function LTC(Q).

Changes in input prices cause changes in the total cost curve.

2. Long-run Average Cost and Long-run Marginal Cost

(1) Definitions

LAC = LTC/Q, LMC = ∆LTC/∆Q

(2) Relationship between long-run marginal and average cost curves

· When average cost is decreasing in Q, marginal cost is less than average cost

· When average cost is increasing in Q, marginal cost is larger than average cost

· When average cost is not changing in Q or when AC is at its minimum, marginal cost is equal to average cost

(3) Economies and diseconomies of scale

Economies of scale: average cost decreases as Q increases.

Diseconomies of scale: average cost increases as Q increases.

Minimum Efficient Scale is the smallest output level at which the long-run average cost curve attains its minimum.

(4) Returns to scale and economies of scale

· If a production function exhibits increasing returns to scale (IRS), then the long-run average cost function exhibits economies of scale.

· If a production function exhibits decreasing returns to scale (DRS), then the long-run average cost function exhibits diseconomies of scale.

· If a production function exhibits constant returns to scale (CRS), then the long-run average cost curve is flat.

3. Short-run Cost Curves

(1) Total Variable Cost VC: cost that varies with the quantity of output, Q.

Total Fixed Cost FC: cost that the firm has to incur independent of quantity of output as long as it operates.

Short-run total cost STC: the minimum cost of producing each output Q when at least one input is fixed.

STC = FC(Q) + VC(Q)

(2) Short-run Marginal Cost (SMC) and Short-run Average Cost (SAC)

SAC = STC/Q SMC = ∆STC / ∆Q

Average Fixed Cost: AFC = FC/Q

Average Variable Cost: AVC = VC/ Q

SAC = AFC + AVC

(3) The long-run average cost curve as the envelope curve of short-run average cost curves