Cost Analysis. Expansion path and Long-Run Total Cost. K*P K + L*P L = . Long-Run Total Cost is the least cost combination of inputs for each production quantity (derives from the expansion path). LTC = 10Q-.6Q 2 +.02Q 3. Effect of a Fixed Input on Cost of Production.
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Expansion path and Long-Run Total Cost
K*PK + L*PL =
Long-Run Total Cost is the least cost combination of inputs for each production quantity (derives from the expansion path)
LTC = 10Q-.6Q2+.02Q3
Effect of a Fixed Input on Cost of Production
LTC as a Lower Envelope of STC
STC = TFC + TVC = 1000+80Q-6Q2+.2Q3
SAC = STC / Q
= TFC/Q + TVC/Q
= AFC + AVC
AFC = 1000/Q
AVC = 80-6Q+.2Q2
SMC = dSTC/dQ
= dTFC/dQ + dTVC/dQ
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
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
Increasing Returns to Scale:Economies of Scale:Q1 = f(K = 20, L = 10) = 100PK = 20, PL = 50 LTC1 = 20*20 + 50*10 = 900LAC1 = 900 / 100 = 9Q2 = f(K = 40, L = 20) = 300 > 2Q1 LTC2 = 20*40 + 50*20 = 1,800LAC2 = 1,800 / 300 = 6 < LAC1
C(Q1, Q2) < C(Q1, 0) + C(0, Q2)
ď‚¶MC1 / ď‚¶Q2 < 0
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.