**Cost & Production Theory** Firms seek to produce any given quantity of output (Q) at lowest cost. Firms are cost minimizers.

**Costs** • C = rK + wL • r is the price of capital, w is the wage • Cost is the sum of each input quantity multiplied by its price • when input prices reflect all costs • including opportunity costs

**Economic Costs are Opportunity Costs** • Economic Cost includes both implicit and explicit costs • Explicit Costs – payment to others • Implicit Costs – cost of owned inputs, or other costs that do not generate explicit payments

**Costs and Output** • Long-Run Total Cost or LTC • Combinations of Cost and Output Q • (C1,Q1), (C2,Q2), (C3,Q3) • Long-run average cost • LAC = (LTC/Q) • Long-run marginal cost • LMC = ΔLTC/ΔQ

**Short-run vs. Long-run** • Long-run: all inputs variable • Short-run: one or more inputs fixed • Total Product: Q = f(K0,L) • Average Product of Labor: APL = Q/L • Marginal Product of Labor: MPL = ΔQ/ΔL • Law of diminishing marginal product • As more labor is employed with a fixed amount of capital, labor’s marginal product (MPL) eventually declines

**Short-run Costs** • Total Cost = rK0 + wL = TC • Total Fixed Cost = rK0 = TFC • Total Variable Cost = wL = TVC • TC = TFC + TVC • Average Fixed Cost: AFC = TFC/Q • Average Variable Cost: AVC = TVC/Q • Average Total Cost: ATC = TC/Q

**Short-run Marginal Cost** • SMC = ΔTC/ΔQ • ΔTFC/ΔQ = 0 • SMC = ΔTVC/ΔQ = ΔTC/ΔQ • SMC = AVC at its minimum • SMC = ATC at its minimum

**Short-run Cost & Product** • AVC and MC are inversely related to APL and MPL • MPL > APL implies MC < AVC • Max MPL corresponds to Min MC • MPL = APL implies MC = AVC • MPL < APL implies MC > AVC

**Short-run and Long-run Cost** • Short-run and long-run costs are equal ONLY at a long-run optimum • The quantity where short-run fixed K0 minimizes long run cost • ATC = LAC • Only at the minimum of LAC are all average and marginal costs equal • LAC = LMC = ATC = SMC

**Economies of Scale** • Economies of scale: LAC is decreasing • Costs increase less than proportionately with output • Diseconomies of scale: LAC increasing • Costs increase more than proportionately with output • Constant returns to scale: LAC = LMC • Costs increase exactly in proportion to output • Minimum Efficient Scale or MES • The quantity at which economies of scale end and constant returns begin

**Economies of Scope** • A firm can produce two products together more cheaply than producing each product separately • C(X,Y) < C(X) + C(Y)

**Estimating Short Run Costs** • General Form: TVC = V(Q, P, K) • Q = Output quantity • P = price of variable input(s) • K = quantity of capital or fixed input(s)

**Linear Short Run Costs** • Linear: TVC = a + bQ • MC=b, a constant • AVC declines as Q increases • Cannot represent • U-shaped AVC • Upward sloping MC

**Cubic Short Run Costs** • Cubic: TVC = aQ + bQ2 + cQ3 • AVC = a + bQ + cQ2 • For U-shaped AVC: a > 0, b < 0, c > 0 • MC = a + 2bQ + 3cQ2 • Can be upward sloping • Q for minimum AVC: Qmin = -b/(2c)

**Cost Project** COST REGRESSION PROJECT Econ 4570 DATA: TVACostData.xls under Cost Project Data on D2L • The data file contains actual cost and output data for TVA non-hydroelectric plants in 2003. Use this data file to run a linear regression as specified below. Have the computer program plot the actual vs. predicted values of the dependent variable (in Excel, check the box marked “Line Fit Plots”). Dependent Variable: AVC Explanatory Variables: Q, QSQ. a. Which coefficients (including the constant) are statistically significant at the 10% level or better? Which are not significant? b. How much of the variation in the dependent variable is explained by the estimated equation? c. Is the equation as a whole statistically significant? At what level? d. Is the estimated average variable cost curve U-shaped? Why?