MicroEconomics 5e by besanko braeutigam chapter 07

Copyright (c)2014 John Wiley & Sons, Inc Chapter Costs and Cost Minimization Chapter Seven Overview 1.1.What Whatare areCosts? Costs? 2.2.Long LongRun RunCost CostMinimization Minimization •• •• •• The constraint minimization problem The constraint minimization problem Comparative statics Comparative statics Input demands Input demands Chapter Seven Copyright (c)2014 John Wiley & Sons, Inc 3 Short ShortRun RunCost CostMinimization Minimization Explicit Costs and Implicit Costs Explicit ExplicitCosts Costs––Costs Coststhat thatinvolve involveaadirect directmonetary monetaryoutlay outlay Copyright (c)2014 John Wiley & Sons, Inc Implicit ImplicitCosts Costs––Costs Coststhat thatdo donot notinvolve involveoutlays outlaysofofcash cash Chapter Seven Opportunity Cost The Therelevant relevantconcept conceptofofcost costisisopportunity opportunitycost: cost:the thevalue valueofofaa resource resourceininits itsbest bestalternative alternativeuse use Copyright (c)2014 John Wiley & Sons, Inc •• The Theonly onlyalternative alternativewe weconsider considerisisthe thebest bestalternative alternative Chapter Seven Economic Costs and Accounting Costs Economic EconomicCosts Costs––Sum Sumofofaafirm’s firm’sexplicit explicitcosts costsand andimplicit implicitCosts Costs Copyright (c)2014 John Wiley & Sons, Inc Accounting AccountingCosts Costs––Total Totalofofaafirm’s firm’sexplicit explicitcosts costs Chapter Seven Sunk Costs Sunk SunkCosts Costsare arecosts coststhat thatmust mustbe beincurred incurredno nomatter matterwhat whatthe thedecision decision These Thesecosts costsare arenot notpart partofof opportunity opportunitycosts costs • $5M is not sunk cost for the decision of whether or not to build the factory • $5M is sunk cost for the decision of whether to operate or shut down the factory Copyright (c)2014 John Wiley & Sons, Inc Example: Bowling Ball Factory • It costs $5M to build and has no alternative uses Non-Sunk Non-SunkCosts Costsare arecosts coststhat thatmust mustbe beincurred incurredonly onlyififaaparticular particulardecision decisionisismade made Chapter Seven Cost Minimization Cost Costminimization minimizationproblem: problem: Finding Findingthe theinput inputcombination combinationthat thatminimizes minimizesaafirm’s firm’stotal totalcost costofof producing producingaaparticular particularlevel levelofofoutput output Cost Costminimization minimizationfirm: firm:AAfirm firmthat thatseeks seekstotominimize minimizethe thecost costofofproducing producingaagiven givenamount amountofofoutput output Long Longrun: run: AAperiod periodofoftime timewhen whenthe thequantities quantitiesofofall allofofthe thefirm’s firm’sinput inputcan canvary vary Copyright (c)2014 John Wiley & Sons, Inc Short Shortrun: run: AAperiod periodofoftime timewhen whenatatleast leastone oneofofits itsinputs’ inputs’quantities quantitiesisisfixed fixed Chapter Seven Long-Run Cost Minimization Minimize Minimizethe thefirm’s firm’scosts, costs,subject subjecttotoaafirm firmproducing producingaagiven givenamount amountofofoutput output Cost Costto tothe theFirm: Firm: TC TC==Total TotalCost Cost ww==wage wagerate rate LL==Quantity QuantityofofLabor Labor Copyright (c)2014 John Wiley & Sons, Inc r r==price priceper perunit unitofofcapital capitalservices services KK==Quantity QuantityofofCapital Capital TC = wL + rK Chapter Seven Isocost Line The Theset setof ofcombinations combinationsof oflabor laborand andcapital capitalthat thatyield yieldthe thesame sametotal totalcost cost Copyright (c)2014 John Wiley & Sons, Inc for forthe thefirm firm Chapter Seven Isocost Line w = $10/hour r = $20/hour TC = $1 million Or more generally: TC K= r − (w / r ) L Chapter Seven 10 Copyright (c)2014 John Wiley & Sons, Inc ⇒$1 mil = $10L + $20K ⇒K = $1 mil/20-(10/20)L Change in Relative Prices of Inputs • • • Price of capital r = Quantity of output Q0 is constant When price of labor w = the isocost line is C1, optimal point A • When price of labor w = isocost line is C2, Copyright (c)2014 John Wiley & Sons, Inc optimal point B Chapter Seven 22 Some Key Definitions An Anincrease increaseininQQ00moves movesthe theisoquant isoquantNortheast Northeast •• Expansion ExpansionPath: Path:AAline linethat thatconnects connectsthe thecost-minimizing cost-minimizinginput inputcombinations combinationsasasthe thequantity quantityofofoutput, output,Q, Q,varies, varies, holding holdinginput inputprices pricesconstant constant •• Inferior InferiorInput: Input:An Aninput inputwhose whosecost-minimizing cost-minimizingquantity quantitydecreases decreasesas asthe thefirm firmproduces producesmore moreoutput output Chapter Seven 23 Copyright (c)2014 John Wiley & Sons, Inc •• Normal NormalInputs: Inputs:An Aninput inputwhose whosecost-minimizing cost-minimizingquantity quantityincreases increasesasasthe thefirm firmproduces producesmore moreoutput output An Expansion Path As output increases, the cost minimization path moves from point A to B to C when Copyright (c)2014 John Wiley & Sons, Inc inputs are normal Chapter Seven 24 An Expansion Path As output increases, the cost minimization path moves from point A to B to C when Copyright (c)2014 John Wiley & Sons, Inc labor is an inferior input Chapter Seven 25 Input Demand Definition: A function that shows how the firm’s cost-minimizing quantity of input varies with the price of that input Labor demand curve: Shows how the firm’s cost-minimizing quantity of labor varies with the price Capital demand curve: Shows how the firm’s cost-minimizing quantity of capital varies with the price of capital Chapter Seven 26 Copyright (c)2014 John Wiley & Sons, Inc of labor Copyright (c)2014 John Wiley & Sons, Inc Input Demand Functions Chapter Seven 27 Input Demand • For a fixed quantity, as price of labor increases from $1 to $2, firm moves along its labor demand curve from A to B Increase in output shifts the Copyright (c)2014 John Wiley & Sons, Inc demand curve Chapter Seven 28 Price Elasticity of Demand for Inputs Percentage change in the cost-minimizing quantity of labor with respect to a 1% change in the price of labor ε L,w • ∆L w = ∆w L Percentage change in the cost-minimizing quantity of capital with respect to a 1% change in the price of capital ε K ,r Copyright (c)2014 John Wiley & Sons, Inc • ∆K r = ∆r K Chapter Seven 29 Copyright (c)2014 John Wiley & Sons, Inc Price Elasticity of Demand for Inputs Chapter Seven 30 Short-Run Cost Minimization Total Variable Costs – the sum of total expenditures on variable inputs, such as labor and materials, at the short-run cost-minimizing input combination Total Fixed Costs – the cost of fixed inputs; it does not vary with output Variable and nonsunk Copyright (c)2014 John Wiley & Sons, Inc • • • Fixed and nonsunk Fixed and sunk Chapter Seven 31 Short-Run Cost Minimization K One fixed Input - Capital • • Short run combination is point F If the firm were free to adjust all of its inputs, the cost-minimizing combination Copyright (c)2014 John Wiley & Sons, Inc is at Point A Chapter Seven 32 Short-Run Cost Minimization • Long run-all variables are variable and the expansion path is from A – B – C • Short run-some variables are fixed (capital)-the expansion path is from D –E – Copyright (c)2014 John Wiley & Sons, Inc F Chapter Seven 33 Short-Run Cost Minimization • Short run: One input is fixed, capital Firm can vary the other K input, labor SO demand for labor will be independent of price Short run demand for labor will also depend on quantity produced As quantity increased, labor used increases holding capital fixed Copyright (c)2014 John Wiley & Sons, Inc • Chapter Seven 34 Short-Run Cost Minimization Q = 50 LK = 1000 • Capital is fixed K Copyright (c)2014 John Wiley & Sons, Inc Q L= 2500 K Chapter Seven 35 Short-Run Cost Minimization More than one variable input – analysis similar to long-run cost minimization inputs – labor (L), capital ( ), raw materials (M) K − MRTS L , M w = m MPL w = MPM m Chapter Seven 36 Copyright (c)2014 John Wiley & Sons, Inc • • ... Wiley & Sons, Inc for forthe thefirm firm Chapter Seven Isocost Line w = $10/hour r = $20/hour TC = $1 million Or more generally: TC K= r − (w / r ) L Chapter Seven 10 Copyright (c)2014 John Wiley... w r Chapter Seven 15 Long-Run Cost Minimization MPL w > MPK r • At point E • This implies the firm could spend an additional MPL MPK (or ) > w r dollar on labor and save more than a dollar by. .. constant Chapter Seven 16 Long-Run Cost Minimization MPL w < MPK r • At point F • This implies the firm could spend an additional MPL MPK (or ) < w r dollar on capital and save more than a dollar by