Cost Analysis Expansion path and LongRun Total Cost

Cost Analysis

Expansion path and Long-Run Total Cost K*PK + L*PL = Long-Run Total Cost is the least combination of inputs for each production quantity (derives from the expansion path)

LTC = 10 Q-. 6 Q 2+. 02 Q 3

Effect of a Fixed Input on Cost of Production In the short run K is fixed at K 0. n Any input L other than L 0 will result in other than least TC. n If I 1 is required, input L will be reduced to point E, associated with TC much higher than optimal at point A. n

LTC as a Lower Envelope of STC • Every point on LTC represents a least-cost combination. • In the short run one or more inputs are fixed so that only a single point on STC is a least-cost combination of inputs. • STC curves intersect cost axis at the value of the TFC.

STC = TFC + TVC = 1000+80 Q-6 Q 2+. 2 Q 3 SAC = STC / Q = TFC/Q + TVC/Q = AFC + AVC AFC = 1000/Q AVC = 80 -6 Q+. 2 Q 2 SMC = d. STC/d. Q = d. TFC/d. Q + d. TVC/d. Q = 80 -12 Q+. 6 Q 2

Productivity of Variable Input and Short-Run Cost = Q = f(L)

Short-Run Total Cost, Total Variable Cost & Total Fixed Cost = TFC + TVC = PL * L = PK * K

Average Product and Average Variable Cost

Marginal Product and Short-Run Marginal Cost

LAC as a Lower Envelope of SAC • In the long run all total costs represent least-costs. • All average costs must be least cost as well. • Various short-run cost curves for various values of the fixed input. • In the short run only one point represents least cost. Economies of Scale Diseconomies of Scale Economies of scale (minimum SAC of in the smaller facility greater than SAC in the larger facility) exist up to the minimum LAC (downward sloping portion of LAC curve). Beyond minimum LAC diseconomies of scale.

Long-Run Average Cost and Returns to Scale Economies of Scale Diseconomies of Scale Increasing Returns to Scale: Q 1 = f(K = 20, L = 10) = 100 Economies of Scale: PK = 20, PL = 50 LTC 1 = 20*20 + 50*10 = 900 LAC 1 = 900 / 100 = 9 Q 2 = f(K = 40, L = 20) = 300 > 2 Q 1 LTC 2 = 20*40 + 50*20 = 1, 800 LAC 2 = 1, 800 / 300 = 6 < LAC 1

Economies of Scope and Cost Complementarity • Cheaper to produce outputs jointly than separately: C(Q 1, Q 2) < C(Q 1, 0) + C(0, Q 2) • MC of producing good 1 declines as more of good 2 is produced: MC 1 / Q 2 < 0 • Example: Joint processing of deposit accounts and loans in bank Scope: Single financial advisor eliminates duplicate common factors of production (computers, loan production offices) Complementarity: Account and credit information developed for deposits lowers credit check and monitoring cost for loans. Expansion of deposit base lowers cost of providing loans.