Econ 100AChapter 7Minimizing Costs*Key issues:1. Measuring costs2. Short-run cost minimization3. Long-run cost minimization4. Costs are lower in the Long Run5. Costs of producing multiple goods simultaneouslyA water heater manufacturer can produce using• a lot of equipment and relatively little labor• many workers and relatively few machines.How does it decide which technology to use?The firm uses a two-step procedure.• Pickstechnologically efficientproduction process• From these technologically efficient production processes, it picks the one that iseconomically efficient(minimum cost)Two reasons to study costs:• Understanding the relationship between costs of inputs and production helps usdetermine the least costly way to produce.• The relationship between output and costs determines the nature of an industry:• how many firms are in the industry• how high price is relative to costMeasuring CostsBusiness people and economists measure costs differently.Economic Cost• Includes all costs• explicit costs (out of pocket)• implicit costs• Is theopportunity cost: the value of the best alternative use of the resource.• Classic Example: "There’s no such thing as a free lunch."Suppose your run your own firmYour explicit cost is• $40,000 per year• rent, cost of materials, wage paymentsInstead of paying yourself a salary, you keep any profit at year’s endIf you worked for someone else, you could earn $25,000 per year*Based on Jeffrey M. Perloff,Microeconomics(© Addison Wesley Longman, 1999). Thesenotes are © Jeffrey M. Perloff.Your costs are:• business (explicit) cost = $40,000• economic (opportunity) cost = $65,000Capital CostsCapital is adurable good: a product that is usable for years.Capital may be rented or purchased.If Capital is RentedThe rental payment is the opportunity cost.Using the rental rate avoids two measurement problems:• Don’t have to worry how to allocate the initial purchase cost over time.• Any adjustment in the cost of capital over time is reflected in the rental rate.If Capital is PurchasedThe firm’s bookkeeper may•expensethe cost by recording the purchase price when it’s made, or•amortizethe cost by spreading it over the life of the capital according to the IRS’sarbitrary rulesEconomists amortize capital cost based on itsopportunity costat each moment of time:the amount that the firm could charge others to rent the truck.Thus, economists always use the rental rate (whether the capital is purchased or rented).Tax Rules: One reason why business cost ≠ economic costYou can depreciate a business vehicle• A Toyota Land Cruiser (sports utility vehicle) and a Cadillac Seville (car) both cost$45,000.• You can depreciate the Land Cruiser in 6 years but the Seville takes 23.• After 5 years: you have depreciated• $42,408 of the Land Cruiser• $14,460 for the Seville.• "Reason": the Land Cruiser weighs more than 6,000 pounds and the Seville doesn’t.• Congress uses 6,000 pounds as a criterion to distinguish between trucks and cars.[Don’t ask me why.]Swarthmore College’s Cost of CapitalSwarthmore College (PA) estimates its annual cost at $40,000 per student, based on:• salaries• academic and general institutional support• food• maintenance• additions to the physical plant• other annual expenses such as student aid.Gross underestimate annual cost per student:• Opportunity cost of its land and buildings = $10,000• True total economic cost = $50,0002Short-Run CostsSR Cost Measures:•Fixed cost(F): production expense that does not vary with output.•Variable cost(VC): production expense that changes with the quantity of outputproduced.Cost(ortotal cost,C):C=VC+F.Fixed Costs are SunkWe usually assume that fixed costs aresunk: a expenditure that you cannot avoid.You can’t get this expenditure back no matter what you do, so you should ignore it in makingdecisions.Examples:• Walk out of a bad movie, regardless of what you paid.• Close a plant or firm if you can’t cover your variable expenses (we’ll examine this issuein more detail in Ch 8).Table 7.1q F VC C MC AFC=F/q AVC=VC/q AC=C/q048 0 4814825 73 25 48 25 7324846 94 21 24 23 473 48 66 114 20 16 22 384 48 82 130 16 12 20.5 32.55 48 100 148 18 9.6 20 29.66 48 120 16820820287 48 141 189 21 6.9 20.1 278 48 168 21627621279 48 198 246 30 5.3 22 27.310 48 230 278 32 4.8 23 27.811 48 272 320 42 4.4 24.7 29.112 48 321 369 49 4.0 26.8 30.8Marginal Cost (MC)MC∆C∆q∆VC∆q.∆C= change in cost when output changes by ∆q.See Table 7.1.3Average CostsFirms use three average cost measures:Average fixed cost:AFC=F/q.Average variable cost:AVC=VC/q.Average cost(average total cost):AC=C/q=AFC+AVC.SR Cost CurvesFigure 7.1 illustrates the relationship between output and the various cost measuresSolved Problem: The short-run cost function isC= 125 +q+ .05q2.What are the:• fixed cost• variable cost• average cost• average fixed cost• average variable cost?What is the relationship between theMCcurve and theACandAVCcurves?Note: The marginal cost curve isMC=1+.1q.C= 125 +q+ .05q2.Answer:F= 125VC=q+ .05q2.AC=C/q= 125/q+1+.05qAFC=F/q= 125/qAVC=VC/q=1+.05qRelationships:•MCcutsACat its minimum of $6 atq= 50.•MCandAVCare at their minimum, $1, atq=0.•MCalways rises, so it is everywhere aboveAVC.Production Function Determines the Shape of a Cost Curve• Production function shows the amount of inputs needed to produce a given level ofoutput.• Firm’s cost: Multiply the quantity of each input by its price and sum.Solved Problem:A janitorial service firm’s only variable cost is wages:Wage,w, is $8 per worker per an hour.Each worker cleans 4 offices per hour.What are the• variable cost4• average variable cost• marginal costof cleaning one more office?Answer:1)Use the production function to derive the variable cost function:• Each worker cleans 4 offices an hour, so the production function is:q=4Lwhereq= office cleaned per hourL= number of workers,• Equivalently:L=¼q• Thus, the variable cost isVC(q)=wL(q)=$8×¼q=$2q.2) Calculate the average variable cost by dividing the variable cost byq:AVC=VC(q)/q=$2q/q= $2.3) Calculate the marginal cost:• Each worker cleans 4 offices an hour, so cleaning one more office, ∆q= 1, takes ∆L=¼ of an hour of work•MC=w∆L/∆q= $8/4 = $2.Note: BecauseMPL= ∆q/∆L,MC=w/MPL.Application:For a typical Norwegianprinting firm:• SR AC curve is ∪-shaped• even though AVC is strictly upward
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