Chapter 12Definitions of CostsSlide 3Slide 4Slide 5Economic CostTwo Simplifying AssumptionsEconomic ProfitsSlide 9Cost-Minimizing Input ChoicesSlide 11Slide 12Slide 13Slide 14Output MaximizationSlide 16Derived DemandSlide 18The Firm’s Expansion PathSlide 20Slide 21Minimizing Costs for a Cobb-Douglas FunctionSlide 23Slide 24Total Cost FunctionAverage Cost FunctionMarginal Cost FunctionGraphical Analysis of Total CostsSlide 29Slide 30Slide 31Slide 32Shifts in Cost CurvesHomogeneitySlide 35Change in the Price of One InputSlide 37Slide 38Size of Shifts in Costs CurvesCobb-Douglas Cost FunctionSlide 41Slide 42Slide 43Short-Run, Long-Run DistinctionShort-Run Total CostsSlide 46Slide 47Short-Run Marginal and Average CostsShort-Run Average Fixed and Variable CostsRelationship between Short-Run and Long-Run CostsSlide 51Slide 52Important Points to Note:Slide 54Slide 55Slide 56Chapter 12COSTSCopyright ©2002 by South-Western, a division of Thomson Learning. All rights reserved.MICROECONOMIC THEORYBASIC PRINCIPLES AND EXTENSIONSEIGHTH EDITIONWALTER NICHOLSONDefinitions of Costs•It is important to differentiate between accounting cost and economic cost–the accountant’s view of cost stresses out-of-pocket expenses, historical costs, depreciation, and other bookkeeping entries–economists focus more on opportunity costDefinitions of Costs•Labor Costs–to accountants, expenditures on labor are current expenses and hence costs of production–to economists, labor is an explicit cost•labor services are contracted at some hourly wage (w) and it is assumed that this is also what the labor could earn in alternative employmentDefinitions of Costs•Capital Costs–accountants use the historical price of the capital and apply some depreciation rule to determine current costs–economists refer to the capital’s original price as a “sunk cost” and instead regard the implicit cost of the capital to be what someone else would be willing to pay for its use•we will use v to denote the rental rate for capitalDefinitions of Costs•Costs of Entrepreneurial Services–To an accountant, the owner of a firm is entitled to all profits, which are the revenues or losses left over after paying all input costs–Economists consider the opportunity costs of time and funds that owners devote to the operation of their firms•these services are inputs and some cost should be imputed to them•part of accounting profits would be considered as entrepreneurial costs by economistsEconomic Cost•The economic cost of any input is the payment required to keep that input in its present employment–the remuneration the input would receive in its best alternative employmentTwo Simplifying Assumptions•There are only two inputs–homogeneous labor (L), measured in labor-hours–homogeneous capital (K), measured in machine-hours•entrepreneurial costs are included in capital costs•Inputs are hired in perfectly competitive markets–firms are price takers in input marketsEconomic Profits•Total costs for the firm are given bytotal costs = TC = wL + vK•Total revenue for the firm is given bytotal revenue = Pq = Pf(K,L)•Economic profits () are equal to = total revenue - total cost = Pq - wL - vK = Pf(K,L) - wL - vKEconomic Profits•Economic profits are a function of the amount of capital and labor employed–we could examine how a firm would choose K and L to maximize profit•“derived demand” theory of labor and capital inputs (see Chapter 21)•But for now we will assume that the firm has already chosen its output level (q0) and wants to minimize its costsCost-Minimizing Input Choices•To minimize the cost of producing a given level of output, a firm should choose a point on the isoquant at which the RTS is equal to the ratio w/v–it should equate the rate at which K can be traded for L in the productive process to the rate at which they can be traded in the marketplaceCost-Minimizing Input Choices•Mathematically, we seek to minimize total costs given q = f(K,L) = q0•Setting up the LagrangianL = wL + vK + [q0 - f(K,L)]•First order conditions areL/L = w - ( f/L) = 0L/K = v - (f/K) = 0L/ = q0 - f(K,L) = 0Cost-Minimizing Input Choices•Dividing the first two conditions we get) for ( //KLRTSKfLfvw•The cost-minimizing firm should equate the RTS for the two inputs to the ratio of their pricesq0Given output q0, we wish to find the least costly point on the isoquantTC1TC2TC3Costs are represented by parallel lines with a slope of -w/vCost-Minimizing Input ChoicesL per periodK per periodTC1 < TC2 < TC3TC1TC2TC3q0The minimum cost of producing q0 is TC2Cost-Minimizing Input ChoicesL per periodK per periodThis occurs at the tangency between the isoquant and the total cost curveK*L*The optimal choice is L*, K*Output Maximization•The dual formulation of the firm’s cost minimization problem is to maximize output for a given level of cost•The Lagrangian isL = f(K,L) + D(TC1 - wL - vK)•The first-order conditions are identical to those for the primal problemq00The maximum output attainable with total cost TC2 is q0q0q1TC2 = wL + vKOutput MaximizationL per periodK per periodThis occurs at the tangency between the total cost curve and isoquant q0K*L*The optimal choice is L*, K*Derived Demand•In Chapter 5, we considered how the utility-maximizing choice is affected by the change in the price of a good–we used this technique to develop the demand curve for a good•Can we develop a firm’s demand for an input in the same way?Derived Demand•To analyze what happens to K* if v changes, we must know what happens to the output level chosen by the firm•The demand for K is a derived demand–it is based on the level of the firm’s output•We cannot answer questions about K* without looking at the interaction of supply and demand in the output marketThe Firm’s Expansion Path•The firm can determine the cost-minimizing combinations of K and L for every level of output•If input costs remain constant for all amounts of K and L the firm may demand, we can trace the locus of cost-minimizing choices–called the firm’s expansion pathThe Firm’s Expansion PathL per periodK per periodq00The expansion path is the locus of cost-minimizing tangenciesq0q1EThe curve shows how inputs increase as output increasesThe Firm’s Expansion Path•The expansion path does not have to be a straight line–some inputs may increase