bài giảng kinh tế vi mô tiếng anh ch7 minimising cost

1 Chapter 7 Minimizing Costs 1. measuring costs 2. short-run cost minimization 3. long-run cost minimization 4. costs are lower in long run 5. costs of producing multiple goods simultaneously Key issues Applications & problems • taxes and depreciation • labor only firm • allocating time on an exam • demolishing buildings • agricultural subsidies and land restrictions • tomato harvester Two-step procedure to choose technology 1. pick all technologically efficient production processes 2. from these technologically efficient production processes, pick the one that is economically efficient (minimizes cost) Two reasons to study costs 1. understanding relationship between costs of inputs and production helps us determine least costly way to produce 2. relationship between output and costs determines nature of an industry • how many firms are in the industry • how high price is relative to cost Business 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” 2 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 + $25,000 Capital costs • capital is a durable good: a product that is usable for years • capital may be rented or purchased If 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 rate If 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 rate Depreciate 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 cars Short-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 + F 3 Sunk 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 avoidable Marginal cost (MC) • cost of producing the last unit • change in cost, ∆C, when output changes by ∆q • ∆C/∆q (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 + AVC Figure 7.1 Short-Run Cost Curves 120 216 400 48 0610 10 428 Quantity, q, Units per day Quantity, q, Units per day 6 b a B A 428 C F 1 1 27 20 VC MC AC AVC AFC Cost, $ Cost per unit, $ (a) (b) 60 28 27 20 8 0 MC 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 4 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 sum Norwegian 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 Firm Cost, kroner 100 200 300 q, Units per year AFC AVC AC MC 0 20 30 40 50 10 Cost effects of $10 specific tax • affects variable but not fixed cost • after-tax (a) cost = before-tax (b) cost + 10q: C a = C b + 10q • at every quantity, AVC, AC, and MC curves shift up by $10: AVC a = AVC b + $10 AC a = AC b + $10 MC a = MC b + $10 Figure 7.3 Effects of a Specific Tax on Cost Curves Costs per unit, $ 1558100 q, Units per day 80 37 27 $10 AC a = AC b + 10 AC b MC b MC a = MC b + 10 $10 Cost 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 ): C a = C b + L • thus AC a = AC b + L /q MC a = MC b 5 Solved Problem 7.1 Costs per unit, $ /q q, Units per day AC b q a C q b AC a = AC b + / q M Lump-sum tax: California $800-per-year tax is levied “for the privilege of doing business in California” Lump-sum tax: New York $900,600 for three-year license to sell hot dogs in front of NY City's Metropolitan Museum of Art Long-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 = VC Input choice choose from all technologically efficient combinations of inputs, the economically efficient combination of inputs Costs 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=+ C 6 Figure 7.4 A Family of Isocost Lines K, Units of capital per year a b d e c $150 isocost$100 isocost$50 isocost $100 ——— $5 = 20 $150 ——— $5 = 30 $50 ——— $5 = 10 $100 ——— $10 10 = $50 ——— $10 5 = $150 ——— $10 15 = L, Units of labor per year Properties of isocost lines 1. 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: ∆K/∆L = -w/r /Cr /Cw Cw K L rr =− Figure 7.5 Cost minimization for Norweigian printing firm K, Units of capital per year y x z 11650240 L , Units of labor per year 100 303 28 q = 100 isoquant 3,000-kr isocost 2,000-kr isocost 1,000-kr isocost Equivalent cost-minimizing rules to pick lowest-cost combination of inputs to produce a given level of output when isoquants are smooth: • lowest-isocost rule: pick bundle of inputs where lowest isocost line touches isoquant • tangency rule: isoquant is tangent to isocost line: MRTS = |ratio of the input prices| = w/r • last-dollar rule: last dollar spent on one input produces as much extra output as last dollar spent on any other input Derivation of last dollar rule L K M Pw MRTS M Pr == L K M PMP wr = Cost minimizing vs. output maximizing with smooth isoquants: firm determines best factor proportions by either • cost minimizing: what is the lowest cost, C*, at which the firm can produce output q*? • output maximizing: What is the most output, q*, that can be produced at cost C*? 7 Relative factor price changes • cause firm to change the mix of inputs used • firm substitutes relatively less expensive inputs for more expensive ones • In Figure 7.6, r = 8 kr • original wage = 24 kr, so w/r = 3 • new wage = 8 kr, so w/r = 1 Figure 7.6 Change in Factor Price K, Units of capital per year v x 77500 L, Workers per year 100 52 q = 100 isoquant Original isocost, 2,000 kr New isocost, 1,032 kr LR cost varies with output • examine lowest-cost factor combination for various levels of output • expansion path: • cost-minimizing combination of labor and capital for each output level • curve through tangency points is LR expansion path • expansion path shows same relationship between LR cost and output as the LR cost curve Figure 7.7a Expansion Path and Long-Run cost Curve K, Units of capital per year x y z 10075500 L, Workers per year 150 200 100 Expansion path (a) Expansion Path 3,000-kr isocost 2,000-kr isocost 4,000-kr isocost 100 isoquant 150 isoquant 200 isoquant Figure 7.7b Expansion Path and Long-Run cost Curve C, Cost, kroner X Y Z 0 q, Units per year 4,000 3,000 2,000 Long-run cost curve (b) Long-Run Cost Curve 200100 150 Solved Problem • suppose that the wage rate falls (while the rental rate of capital remains unchanged) • what happens to the expansion path? 8 Shape of LR cost curves • reason why LR AC is U-shaped different than SR •SR: •SR AC initially downward sloping because AFC is downward sloping •SR AC later upward sloping because of diminishing returns •LR • no fixed cost in LR (usually) • production function returns to scale determine shape Figure 7.8 Long-Run Cost Curves Cost, $ q* q, Quantity per day (a) Cost Curve C Cost per unit, $ q* q, Quantity per day MC AC (b) Marginal and Average Cost Curves Economies of scale AC rises when output increasesdiseconomies of scale AC does not change as output increases no economies of scale AC falls as output expandseconomies of scale Causes of economies of scale • returns to scale in production function • sufficient condition for AC economies of scale • not necessary condition • in LR, firm may change ratio of K/L as it expands output, so could have economies of scale in costs without increasing returns to scale in production Costs lower in long run • in LR, firm chooses optimal plant size level to minimize its LR cost given q • because the firm cannot vary its capital in SR but can in LR • SR cost ≥ LR cost • SR cost > LR cost if the "wrong" level of capital is used in SR 9 Figure 7.9 Long-Run Average Cost as the Envelope of Short-Run Average Cost Curves Average cost, $ a b d e SRAC 1 SRAC 2 SRAC 3 SRAC 3 LRAC c q 2 q 1 q, Output per day 10 0 12 Long-Run Cost Curves in Printing and Oil Pipelines (a) Norwegian Printing Firm Cost, kroner 200 600 1,200 q, Output per year 0 20 30 40 10 SRAC 1 SRMC 1 SRAC 2 SRMC 2 LRAC = LRMC Long-Run Cost Curves in Printing and Oil Pipelines (b) Oil Pipelines 2000100040020010 20 40 1000 Thousand barrels per day Cost per barrel-mile 150 100 50 10 8"SRAC 10"SRAC 16"SRAC 12"SRAC 26"SRAC 20 " SRAC 40 " SRAC LRAC Why LR cost ≤ SR cost • firms have more flexibility in long run • technical progress may lower cost over time • learning by doing: productive skills and knowledge of better ways to produce that workers and managers gain from experience Figure 7.11a Learning by Doing Labor costs per plane, $ 250100 150 200500 C-141 planes (a) Learning by Doing on C-141 Aircraft 500 400 300 200 100 Average labor cost Figure 7.11b Learning by Doing Average cost A B C b c q, Output per period (b) Economies of Scale and Learning by Doing Learning by doing Economies of scale q 2 q 3 AC 3 AC 2 AC 1 q 1 10 Cost of producing multiple goods • outputs are linked if a single input is used to produce all of them • mutton and wool both come from sheep • beef and hides come from cattle • heating fuel and gasoline come from oil • it is less expensive to produce goods jointly than separately (beef & hides) Joint production • Laura spends one day collecting mushrooms and wild strawberries in the wood • economies of scope (PPF 1 ) • picking only mushrooms: 8 pints • pick only strawberries: 6 pints • pick some of each: 6 pints of mushrooms and 4 pints of strawberries • no economies of scope (PPF 2 ) • mushrooms grow in one section and strawberries in another •PPF 2 is a straight line Figure 7.12 Joint Production Mushrooms, Pints per day PPF 2 PPF 1 64 Wild strawberries, Pints per day 8 6 0 Measuring scope (SC) • C(q 1 , 0) = cost of producing q 1 units of first good by itself • C(0, q 2 ) = cost of producing only q 2 units of second good • C(q 1 , q 2 ) = cost of producing both goods together 1212 12 (,0) (0, ) (, ) (, ) Cq C q Cq q SC Cq q +− = Scope cheaper to produce separately SC < 0 diseconomies of scope cost same either waySC = 0 no economies of scope cheaper to produce goods jointly SC > 0 economies of scope Economies of scope • refining: cheaper to produce motor gasoline, distillate fuels, and other refined products together • auto manufacturing: four automobile manufacturers • 25% less expensive (SC = 0.25) to produce large cars together with small cars and trucks than to produce large cars separately and small cars and trucks together • no economies of scope from producing trucks together with small and large cars [...]... passenger service was transferred from the private railroad companies to Amtrak, and services are separate cost minimization from all technologically efficient production processes, choose one that is economically efficient 1 Measuring costs 2 Short-run costs • use economic cost: explicit + implicit costs • opportunity cost: value of next best alternative use includes both explicit and implicit costs 3... costs 3 Long-run costs • all factors can be varied, so all costs are variable • AC = AVC • costs minimized where • lowest isocost touches the relevant isoquant • isocost is tangent to the isoquant • last dollar spent on any input increases output by as much as last dollar spent on any other input • some factors are fixed in the SR • costs vary with only variable (nonfixed) inputs 4 Costs are lower in... other input • some factors are fixed in the SR • costs vary with only variable (nonfixed) inputs 4 Costs are lower in long run • more flexibility in LR • technological progress • learning by doing 11 5 Costs of producing multiple goods • economies of scope: less expensive to produce goods jointly rather than separately • diseconomies of scope: less expensive to produce separately 12 . relative to cost Business vs. economic costs • business costs: only explicit costs (out of pocket) • economic costs: explicit cost + implicit cost = opportunity cost • opportunity cost • value. (cost) •if cost is C = wL + rK • then isocost is • where is a fixed level of cost ,CwLrK=+ C 6 Figure 7.4 A Family of Isocost Lines K, Units of capital per year a b d e c $150 isocost$100 isocost$50. cost ≥ LR cost • SR cost > LR cost if the "wrong" level of capital is used in SR 9 Figure 7.9 Long-Run Average Cost as the Envelope of Short-Run Average Cost Curves Average cost,