Quản trị kinh doanh - Chapter 7: Costs and cost minimization

1Costs and Cost MinimizationChapter 7Copyright (c)2014 John Wiley & Sons, Inc.2Chapter Seven Overview1. What are Costs?2. Long Run Cost MinimizationThe constraint minimization problemComparative staticsInput demandsShort Run Cost MinimizationChapter SevenCopyright (c)2014 John Wiley & Sons, Inc.3Explicit Costs – Costs that involve a direct monetary outlay.Chapter SevenExplicit Costs and Implicit CostsImplicit Costs – Costs that do not involve outlays of cash.Copyright (c)2014 John Wiley & Sons, Inc.4The relevant concept of cost is opportunity cost: the value of a resource in its best alternative use. The only alternative we consider is the best alternativeChapter SevenOpportunity CostCopyright (c)2014 John Wiley & Sons, Inc.5Economic Costs – Sum of a firm’s explicit costs and implicit Costs.Chapter SevenEconomic Costs and Accounting CostsAccounting Costs – Total of a firm’s explicit costs.Copyright (c)2014 John Wiley & Sons, Inc.6Sunk Costs are costs that must be incurred no matter what the decision. These costs are not part of opportunity costs. Chapter SevenSunk Costs It costs $5M to build and has no alternative uses $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 factoryExample: Bowling Ball FactoryNon-Sunk Costs are costs that must be incurred only if a particular decision is made. Copyright (c)2014 John Wiley & Sons, Inc.7Chapter SevenCost MinimizationCost minimization problem: Finding the input combination that minimizes a firm’s total cost of producing a particular level of output.Cost minimization firm: A firm that seeks to minimize the cost of producing a given amount of output.Long run: A period of time when the quantities of all of the firm’s input can vary.Short run: A period of time when at least one of its inputs’ quantities is fixed.Copyright (c)2014 John Wiley & Sons, Inc.8Chapter SevenLong-Run Cost MinimizationMinimize the firm’s costs, subject to a firm producing a given amount of output.Cost to the Firm: TC = Total Cost w = wage rate L = Quantity of Labor r = price per unit of capital services K = Quantity of Capital Copyright (c)2014 John Wiley & Sons, Inc.9The set of combinations of labor and capital that yield the same total cost for the firm.Chapter SevenIsocost LineCopyright (c)2014 John Wiley & Sons, Inc.10Chapter SevenIsocost Linew = $10/hourr = $20/hour TC = $1 million$1 mil = $10L + $20KK = $1 mil/20-(10/20)LOr more generally:Copyright (c)2014 John Wiley & Sons, Inc.11LKTC0/w TC1/w TC2/wTC2/rTC1/rTC0/rSlope = -w/rDirection of increase in total costChapter SevenIsocost LinesCombinations of labor and capital that yields the same total cost for the firmCopyright (c)2014 John Wiley & Sons, Inc.12Chapter SevenSuppose that a firm’s owners wish to minimize costsLet the desired output be Q0Technology: Q = f(L,K)Owner’s problem: min TC = rK + wL K,L Subject to Q0 = f(L,K)Long-Run Cost MinimizationTC = rK + wL orK = TC/r – (w/r)Lis the isocost lineCopyright (c)2014 John Wiley & Sons, Inc.13Chapter SevenLong-Run Cost Minimization Cost minimization subject to satisfaction of the isoquant equation: Q0 = f(L,K) Note: analogous to expenditure minimization for the consumerTangency Condition: MRTSL,K = -MPL/MPK = -w/r (or) MPL/w = MPK/rConstraint: Q0 = f(K,L)Copyright (c)2014 John Wiley & Sons, Inc.14Chapter SevenLong-Run Cost MinimizationSolution to cost minimization:Point where isoquant is just tangent to isocost line (A)G – Technically InefficientE & F – Technically Efficient but do not minimize costCopyright (c)2014 John Wiley & Sons, Inc.15Chapter SevenLong-Run Cost MinimizationSolution to cost minimization: Slope of isoquant = slope of isocost line (or) Ratio of marginal products = ratio of input pricesCopyright (c)2014 John Wiley & Sons, Inc.16Chapter SevenLong-Run Cost MinimizationAt point EThis implies the firm could spend an additional dollar on labor and save more than a dollar by reducing its employment of capital and keep output constantCopyright (c)2014 John Wiley & Sons, Inc.17Chapter SevenLong-Run Cost MinimizationAt point FThis implies the firm could spend an additional dollar on capital and save more than a dollar by reducing its employment of labor and keep output constantCopyright (c)2014 John Wiley & Sons, Inc.18Chapter SevenInterior SolutionQ = 50L1/2K1/2MPL = 25L-1/2K1/2MPK = 25L1/2K-1/2w = $5r = $20Q0 = 1000MPL/MPK = K/L => K/L = 5/20orL=4K1000 = 50L1/2K1/2 K = 10; L = 40Copyright (c)2014 John Wiley & Sons, Inc.19Chapter SevenCorner SolutionThe cost-minimizing input combination for producing Q0 units of output occurs at point A where the firms uses no capital. At this corner point the isocost line is flatter than the isoquant.Copyright (c)2014 John Wiley & Sons, Inc.20Q = 10L + 2KMPL = 10MPK = 2w = $5r = $2Q0 = 200Chapter SevenCorner SolutionMPL/MPK = 10/2 > w/r = 5/2But the “bang for the buck” in labor larger than the “bang for the buck” in capitalMPL/w = 10/5 > MPK/r = 2/2 K = 0; L = 20Copyright (c)2014 John Wiley & Sons, Inc.21A change in the relative price of inputs changes the slope of the isocost line.All else equal, an increase in w must decrease the cost minimizing quantity of labor and increase the cost minimizing quantity of capital with diminishing MRTSL,K.All else equal, an increase in r must decrease the cost minimizing quantity of capital and increase the cost minimizing quantity of labor.Chapter SevenComparative StaticsCopyright (c)2014 John Wiley & Sons, Inc.22Chapter SevenChange in Relative Prices of InputsPrice of capital r = 1Quantity of output Q0 is constant.When price of labor w = 1 the isocost line is C1, optimal point AWhen price of labor w = 2 isocost line is C2, optimal point BCopyright (c)2014 John Wiley & Sons, Inc.23An increase in Q0 moves the isoquant Northeast. Expansion Path: A line that connects the cost-minimizing input combinations as the quantity of output, Q, varies, holding input prices constant. Normal Inputs: An input whose cost-minimizing quantity increases as the firm produces more output. Inferior Input: An input whose cost-minimizing quantity decreases as the firm produces more output.Chapter SevenSome Key DefinitionsCopyright (c)2014 John Wiley & Sons, Inc.24Chapter SevenAn Expansion PathAs output increases, the cost minimization path moves from point A to B to C when inputs are normalCopyright (c)2014 John Wiley & Sons, Inc.25Chapter SevenAn Expansion PathAs output increases, the cost minimization path moves from point A to B to C when labor is an inferior inputCopyright (c)2014 John Wiley & Sons, Inc.26Chapter SevenInput 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 of labor.Capital demand curve: Shows how the firm’s cost-minimizing quantity of capital varies with the price of capital.Copyright (c)2014 John Wiley & Sons, Inc.27Chapter SevenInput Demand FunctionsCopyright (c)2014 John Wiley & Sons, Inc.28Chapter SevenInput 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 demand curve.Copyright (c)2014 John Wiley & Sons, Inc.29Chapter SevenPrice Elasticity of Demand for InputsPercentage change in the cost-minimizing quantity of labor with respect to a 1% change in the price of labor.Percentage change in the cost-minimizing quantity of capital with respect to a 1% change in the price of capital.Copyright (c)2014 John Wiley & Sons, Inc.30Chapter SevenPrice Elasticity of Demand for InputsCopyright (c)2014 John Wiley & Sons, Inc.31Chapter SevenShort-Run Cost MinimizationTotal Variable Costs – the sum of total expenditures on variable inputs, such as labor and materials, at the short-run cost-minimizing input combinationTotal Fixed Costs – the cost of fixed inputs; it does not vary with output Variable and nonsunk Fixed and nonsunk Fixed and sunkCopyright (c)2014 John Wiley & Sons, Inc.32Chapter SevenShort-Run Cost MinimizationOne fixed Input - CapitalShort run combination is point FIf the firm were free to adjust all of its inputs, the cost-minimizing combination is at Point ACopyright (c)2014 John Wiley & Sons, Inc.33Chapter SevenShort-Run Cost MinimizationLong 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 –F Copyright (c)2014 John Wiley & Sons, Inc.34Chapter SevenShort-Run Cost MinimizationShort run: One input is fixed, capital . Firm can vary the other 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.35Chapter SevenShort-Run Cost MinimizationCapital is fixedCopyright (c)2014 John Wiley & Sons, Inc.36Chapter SevenShort-Run Cost MinimizationMore than one variable input – analysis similar to long-run cost minimization3 inputs – labor (L), capital ( ), raw materials (M)Copyright (c)2014 John Wiley & Sons, Inc.