1Chapter 7Minimizing CostsKey issues1. measuring costs2. short-run cost minimization3. long-run cost minimization4. costs are lower in long run5. costs of producing multiple goods simultaneouslyTwo-step procedure to choose technology1. pick all technologically efficient production processes2. from these technologically efficient production processes, pick the one that is economically efficient (minimizes cost)2Two reasons to study costs1. understanding relationship between costs of inputs and production helps us determine least costly way to produce2. relationship between output and costs determines nature of an industry• how many firms are in the industry• how high price is relative to costBusiness vs. economic costs• business costs: only explicit costs (out of pocket)• economic costs: explicit cost + implicit cost = opportunity cost• opportunity cost• value of best alternative use of the resource• classic example: "There's no such thing as a free lunch" • “What have you given up to study opportunity costs”Cost of running your own firm• explicit cost: $40,000 per year (rent, materials, wage payments)• instead of paying yourself a salary, you keep any profit at year's end• your labor opportunity cost = $25,000/year you could have earned working for another firm• business cost = $40,000• economic cost = $65,000 = $40,000 + $25,0003Capital costs• capital is a durable good: a product that is usable for years • capital may be rented or purchasedIf capital is rented • rental payment is the opportunity cost• using the rental rate avoids 2 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 rateIf capital is purchased• firm's bookkeeper may • expense cost by recording purchase price when it's made, or• amortize cost by spreading it over life of capital according to IRS's arbitrary rules• economists amortize capital cost based on its opportunity cost at each moment of time:• amount that firm could charge others to rent capital• thus, economists always use rental rate4Depreciate a business vehicle• Toyota Land Cruiser (sports utility vehicle) and Cadillac Seville (car) both cost $45,000• tax law let’s you depreciate Land Cruiser in 6 years vs. 23 for Seville• after 5 years depreciated $42,408 for Land Cruiser vs. $14,460 for Seville• “reason“• Land Cruiser weighs more than 6,000 pounds and Seville doesn't• Congress uses 6,000 pounds as a criterion to distinguish between trucks and carsShort-run cost measures• fixed cost (F): production expense that does not vary with output• variable cost (VC): production expense that changes with quantity of output produced • Total cost (C):C = VC + FSunk fixed cost• usually assume fixed cost is sunk: expenditure that you cannot be recovered • opportunity cost of capital is zero• because you can't get this expenditure back no matter what you do, so ignore it when making decisions• example: walk out of a bad movie early, regardless of what you paid to attend• otherwise, fixed cost is called avoidable5Marginal cost (MC)• cost of producing the last unit• change in cost, DC, when output changes by Dq• DC/Dq (or dC/dq)Average cost concepts• average fixed cost:AFC = F /q• average variable cost:AVC = VC /q• average (total) cost: AC = C/q = AFC + AVC6Figure 7.1 Short-Run Cost Curves120216400480 6 101042 8Quantity, q, Units per dayQuantity, q, Units per day6baBA42 8CF112720VCMCACAVCAFCCost, $Cost per unit, $(a)(b)6028272080MC curve cuts AC and AVC at their minimum points• AC and AVC curves fall when MC is below them, and rise when MC is above them• therefore, MC cuts AC and AVC curves at their minimum points Production function determines shape of cost curve• production function shows how many inputs needed to produce a given level of output• firm's cost: multiply quantity of each input by its price and sum7Norwegian printing firm• short-run AC curve is U-shaped even though AVC is strictly upward sloping• firm's capital is fixed at 100 Application Short-Run Cost Curves for a Printing FirmCost, kroner100 200 300q, Units per yearAFCAVCACMC02030405010Cost effects of $10 specific tax• affects variable but not fixed cost• after-tax (a) cost = before-tax (b) cost + 10q:Ca= Cb+ 10q• at every quantity, AVC, AC, and MC curves shift up by $10:AVCa= AVCb+ $10ACa= ACb+ $10MCa= MCb+ $108Figure 7.3 Effects of a Specific Tax on Cost CurvesCosts perunit, $155 8 100q, Units per day803727$10ACa= ACb+ 10ACbMCbMCa= MCb+ 10$10Cost effects of lump-sum tax• affects fixed cost but not variable cost• after-tax (a) cost = before-tax (b) cost plus lump-sum tax (L):Ca= Cb+ L• thusACa= ACb+ L/qMCz= MCbSolved Problem 7.1Costs per unit, $/qq, Units per dayACbqaCqbACa=ACb+ /qM9Lump-sum taxes• $800-per-year tax is levied “for the privilege of doing business in California”• $900,600 for three-year license to sell hot dogs in front of NY City's Metropolitan Museum of ArtLong-run costs• firm adjusts all its inputs so its cost of production is as low as possible• if capital and other variable can be varied, no LR fixed costs (F = 0)• then LR total cost = LR variable cost:C = VCInput choicechoose from all technologically efficient combinations of inputs, the economically efficient combination of inputs10Costs of input bundles• isocost: all combinations of inputs that require the same (iso) total expenditure (cost)• if cost is C = wL + rK• then isocost is• where is a fixed level of cost,CwLrK=+CFigure 7.4 A Family of Isocost LinesK, Units ofcapital per yearabdec$150 isocost$100 isocost$50 isocost$100———$5=20$150———$5=30$50———$5=10$100———$1010 =$50———$105 =$150———$1015 =L, Units of labor per yearProperties of isocost lines1. where isocost line hits axes depends on and factor prices• intersects capital axis at • intersects labor axis at 2. isocosts farther from origin have higher costs:3. slope of each isocost line is the same:DK/DL = -w/r/Cr/CwCwKLrr=−11Figure 7.5 Cost minimization for Norweigian printing firmK, Units ofcapital per yearyxz11650240L , Units of labor per year10030328q = 100 isoquant3,000-krisocost2,000-krisocost1,000-krisocostEquivalent cost-minimizing rulesto pick lowest-cost combination of inputs to produce a given level of output when isoquants are smooth:• lowest-isocost
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