SIGNIFICANCE & MEANING OF ECONOMIC COSTSIGNIFICANCE & MEANING OF ECONOMIC COSTTAXONOMY OF COSTS TAXONOMY OF COSTSTAXONOMY OF COSTSTAXONOMY (cont’d) TAXONOMY (cont’d)TAXONOMY (cont’d)COST MINIMIZATIONCOST MINIMIZATION COST MINIMIZATIONCOMPARATIVE STATICS COMPARATIVE STATICSCOMPARATIVE STATICS COMPARATIVE STATICSOutput Elasticity of Total CostOutput Elasticity of Total CostDuality in Production and CostDuality in Production and Cost (Con’t)SUMMARYSIGNIFICANCE & MEANING OF ECONOMIC COST• Why care about costs?– Should drive business decisions regarding price, production, investment, etc.– Affects which companies and technologies succeed, and which ones fail– Determines the size of firms – Determines the level, structure and trends in prices paid for goods and servicesSIGNIFICANCE & MEANING OF ECONOMIC COST• Meaning of economic cost– Measure the use of resources in the production of goods and services– Accountants measure only explicit expenses (and sometimes not even those)– “Opportunity cost” includes the value of employed resources in their best alternative use• what matters is expenditure affected by a decision• there may also be “external costs” born by those not involved in production (e.g., pollution)TAXONOMY OF COSTSTotal v. Average v. Marginal• AC = TC / Q also referred to as “unit costs”•MC = ΔTC / ΔQ sometimes called “incremental”TAXONOMY OF COSTSTAXONOMY OF COSTSFixed v. Variable• how costs vary with level of output• [total cost] = [variable cost] + [fixed cost]• Example of fixed costs• CA business license: $800 per year (nontransferable)• NYC taxi medallion: $227,000 in perpetuity (transferable)TAXONOMY (cont’d)• Short Run v. Long Run• as before, depends on the time period considered, and hence whether inputs are “fixed” or “variable”• make distinction between “fixed cost” and “fixed factor”TAXONOMY (cont’d)• Sunk v. Avoidable (non-sunk)• difference depends on whether cost can be avoided by some decision• e.g., fixed cost can be avoided by shutting down.• usually treat variable costs as avoidable, fixed costs as sunk• because they are unavoidable, “sunk” costs should be ignored when making decisionsTAXONOMY (cont’d)• Other cost distinctions• production vs. transaction costs• one-time vs. recurring costsCOST MINIMIZATION• The firm’s problem– A profit maximizing firm won’t spend more to produce its output than it has to: MinimizeL,KTC = rK + wLSubject to: f(L,K) = Q0• The solution– in words: find the cheapest input combination that produces the desired level of output– iso-quant curve: input combinations that produce the same quantity of output• Slope of iso-quant = - MRTSL,K •= -MPL/MPK– iso-cost lines: input combinations that cost same amount• wL + rK = C (a constant) => K = (C - wL ) / r• slope of iso-cost = ΔK / ΔL (along an iso-cost line) = - w / r • compare: budget lines– Putting two togetherMRTSL,K= MPL/ MPK= w / rCOST MINIMIZATION• Solution: another viewMPL/ w = MPK/ r• 1/w = the amount of labor that can be purchased for $1•MPL = the amount of output that can be produced with last unit of labor•MPL/w = output derived from last $ spent on labor• similar interpretation for capital• therefore, equate incremental output of last $ spent on each input across inputsCOST MINIMIZATIONCOMPARATIVE STATICSOutput Expansion Path: L(Q) and K(Q) are labor and capital levels that minimizecost• plot optimal cost-minimizing input combinations as output increases (i.e., moves in the northeast direction)• if the cost-minimizing quantity of an input rises (falls) with output, then it is a “normal” (“inferior”) input.• compare: income-consumption curveCOMPARATIVE STATICSCOMPARATIVE STATICSFactor Price Change: L(w; Q) gives labor that minimizes cost for each wage rate. • increase the price of one input (e.g., wage)• factor substitution:– All else equal, an increase in w must decrease labor and increase capital due to diminishing MRTSL,K• compare: price-consumption curveCOMPARATIVE STATICSOutput Elasticity of Total CostOutput Elasticity of Total CostEstimates: (from Indian manufacturing):Iron and Steel 0.553Cotton Textiles 1.211Cement 1.162Electricity and Gas 0.382,Industry TC QEDuality in Production and Cost• Firm’s input decisions have a dual nature.• Optimal choice of K and L– Minimal cost subject to the production function– Maximum output subject to the cost constraint• Formally,–Maximum F(L,K)– Subject to wL + rK = C0Duality in Production and Cost (Con’t)• Solution: from the relevant lagrangian we obtain the necessary conditions• Solving these equations, we have•Or 0kMPrμ−=0LMPwμ−=KLMPr MPw=/LKMPMP wr=SUMMARY• Opportunity cost is the relevant notion of economic cost.• A profit-maximizing firm will minimize the cost of producing its chosen level of output. • Costs are minimized when the MRTS equals the input price ratio. • The input demand functions show how the cost-minimizing quantities of inputs vary with the quantity of the output and the input prices. • The short run cost minimization problem solves the firm’s problem when one or more inputs are fixed. • Returns to scale have a counter part in the shape of the cost function captured by degree of “economies of
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