The Costs of Production in the long run M. En C. Eduardo Bustos Farías
Costs in the Long Run For many firms, the division of total costs between fixed and variable costs depends on the time horizon being considered. In the short run some costs are fixed. In the long run fixed costs become variable costs. Economía M. En C. Eduardo Bustos Farías 2
Costs in the Long Run Because many costs are fixed in the short run but variable in the long run, a firm s long-run cost curves differ from its short-run cost curves. Economía M. En C. Eduardo Bustos Farías 3
Production And Cost in the Long Run In the long run, costs behave differently Firm can adjust all of its inputs in any way it wants In the long run, there are no fixed inputs or fixed costs All inputs and all costs are variable Firm must decide what combination of inputs to use in producing any level of output The firm s goal is to earn the highest possible profit To do this, it must follow the least cost rule To produce any given level of output the firm will choose the input mix with the lowest cost Economía M. En C. Eduardo Bustos Farías 4
Production And Cost in the Long Run Long-run total cost The cost of producing each quantity of output when the leastcost input mix is chosen in the long run Long-run average total cost The cost per unit of output in the long run, when all inputs are variable The long-run average total cost (LRATC) Cost per unit of output in the long-run LRATC = LRTC Q Economía M. En C. Eduardo Bustos Farías 5
The Relationship Between Long-Run And Short-Run Costs For some output levels, LRTC is smaller than TC Long-run total cost of producing a given level of output can be less than or equal to, but never greater than, short-run total cost (LRTC TC) Long-run average cost of producing a given level of output can be less than or equal to, but never greater than, short run average total cost (LRATC ATC) Economía M. En C. Eduardo Bustos Farías 6
Average Cost And Plant Size Plant Collection of fixed inputs at a firm s disposal Can distinguish between the long run and the short run In the long run, the firm can change the size of its plant In the short run, it is stuck with its current plant size ATC curve tells us how average cost behaves in the short run, when the firm uses a plant of a given size To produce any level of output, it will always choose that ATC curve among all of the ATC curves available that enables it to produce at lowest possible average total cost This insight tells us how we can graph the firm s LRATC curve Economía M. En C. Eduardo Bustos Farías 7
Graphing the LRATC Curve A firm s LRATC curve combines portions of each ATC curve available to firm in the long run For each output level, firm will always choose to operate on the ATC curve with the lowest possible cost In the short run, a firm can only move along its current ATC curve However, in the long run it can move from one ATC curve to another by varying the size of its plant Will also be moving along its LRATC curve Economía M. En C. Eduardo Bustos Farías 8
Average Total Cost in the Short and Long Runs... Average Total Cost ATC in short run with small factory ATC in short run with medium factory ATC in short run with large factory ATC in long run Economía M. En C. Eduardo Bustos Farías 9 0 Quantity of Cars per Day
Economies and Diseconomies of Scale Economies of scale occur when long-run average total cost declines as output increases. Diseconomies of scale occur when longrun average total cost rises as output increases. Constant returns to scale occur when long-run average total cost does not vary as output increases. Economía M. En C. Eduardo Bustos Farías 10
Economics of Scale Economics of scale Long-run average age total cost decreases as output increases When an increase in output causes LRATC to decrease, we say that the firm is enjoying economics of scale The more output produced, the lower the cost per unit When long-run total cost rises proportionately less than output, production is characterized by economies of scale LRATC curve slopes downward Economía M. En C. Eduardo Bustos Farías 11
Gains From Specialization One reason for economies of scale is gains from specialization The greatest opportunities for increased specialization occur when a firm is producing at a relatively low level of output With a relatively small plant and small workforce Thus, economies of scale are more likely to occur at lower levels of output Economía M. En C. Eduardo Bustos Farías 12
More Efficient Use of Lumpy Inputs Another explanation for economies of scale involves the lumpy nature of many types of plant and equipment Some types of inputs cannot be increased in tiny increments, but rather must be increased in large jumps Plant and equipment must be purchased in large lumps Low cost per unit is achieved only at high levels of output Making more efficient use of lumpy inputs will have more impact on LRATC at low levels of output When these inputs make up a greater proportion of the firm s total costs At high levels of output, the impact is smaller Economía M. En C. Eduardo Bustos Farías 13
Diseconomies of Scale Long-run average total cost increases as output increases As output continues to increase, most firms will reach a point where bigness begins to cause problems True even in the long run, when the firm is free to increase its plant size as well as its workforce When long-run total cost rises more than in proportion to output, there are diseconomies of scale LRATC curve slopes upward While economies of scale are more likely at low levels of output Diseconomies of scale are more likely at higher output levels Economía M. En C. Eduardo Bustos Farías 14
Constant Returns To Scale Long-run average total cost is unchanged as output increases When both output and long-run total cost rise by the same proportion, production is characterized by constant returns to scale LRATC curve is flat In sum, when we look at the behavior of LRATC, we often expect a pattern like the following Economies of scale (decreasing LRATC) at relatively low levels of output Constant returns to scale (constant LRATC) at some intermediate levels of output Diseconomies of scale (increasing LRATC) at relatively high levels of output This is why LRATC curves are typically U-shaped Economía M. En C. Eduardo Bustos Farías 15
Economies and Diseconomies of Scale Average Total Cost ATC in long run Economies of scale Constant Returns to scale Diseconomies of scale 0 Quantity of Cars per Day Economía M. En C. Eduardo Bustos Farías 16
Using the Theory: Long Run Costs, Market Structure and Mergers The number of firms in a market is an important aspect of market structure a general term for the environment in which trading takes place What accounts for these differences in the number of sellers in the market? Shape of the LRATC curve plays an important role in the answer Economía M. En C. Eduardo Bustos Farías 17
LRATC and the Size of Firms The output level at which the LRATC first hits bottom is known as the minimum efficient scale (MES) for the firm Lowest level of output at which it can achieve minimum cost per unit Can also determine the maximum possible total quantity demanded by using market demand curve Applying these two curves the LRATC for the typical firm, and the demand curve for the entire market to market structure When the MES is small relative to the maximum potential market Firms that are relatively small will have a cost advantage over relatively large firms Market should be populated by many small firms, each producing for only a tiny share of the market Economía M. En C. Eduardo Bustos Farías 18
LRATC and the Size of Firms There are significant economies of scale that continue as output increases Even to the point where a typical firm is supplying the maximum possible quantity demanded This market will gravitate naturally toward monopoly In some cases the MES occurs at 25% of the maximum potential market In this type of market, expect to see a few large competitors There are significant lumpy inputs that create economies of scale Until each firm has expanded to produce for a large share of the market Economía M. En C. Eduardo Bustos Farías 19
How LRATC Helps Explain Market Structure Dollars LRATC Typical Firm $160 F 80 E D Market 0 1,000 3,000 100,000 Units per Month Economía M. En C. Eduardo Bustos Farías 20
How LRATC Helps Explain Market Structure Dollars LRATC Typical Firm $160 80 D Market 0 100,000 Units per Month Economía M. En C. Eduardo Bustos Farías 21
How LRATC Helps Explain Market Structure Dollars $200 H LRATC Typical Firm F 80 E D Market 0 25,000 100,000 Units per Month Economía M. En C. Eduardo Bustos Farías 22
How LRATC Helps Explain Market Structure Dollars LRATC Typical Firm $160 80 E F D Market 0 1,000 10,000 100,000 Units per Month Economía M. En C. Eduardo Bustos Farías 23
LRATC and the Size of Firms The MES of the typical firm in this market is 1,000 units Lowest output level at which it reaches minimum cost per unit For firms in this market, diseconomies of scale don t set in until output exceeds 10,000 units Since both small and large firms can have equally low average costs with neither having any advantage over the other Firms of varying sizes can coexist Economía M. En C. Eduardo Bustos Farías 24
The Urge To Merge If by doubling their output, firms could slide down the LRATC curve in Figure, and enjoy a significant cost advantage over any other, still-smaller firm, they would This is a market that is ripe for a merger wave A sudden merger wave is usually set off by some change in the market Market structure in general and mergers and acquisitions in particular raise many important issues for public policy Low-cost production can benefit consumers if it results in lower prices Economía M. En C. Eduardo Bustos Farías 25
Production & Cost Estimation Economía M. En C. Eduardo Bustos Farías 26
Empirical Production Function Cubic empirical specification for a short-run production function is derived from a longrun cubic production function Cubic form of the long-run production function is expressed as Q = ak 3 L 3 + bk 2 L 2 Economía M. En C. Eduardo Bustos Farías 27
Properties of a Short-Run Cubic Production Function 3 2 Q = AL + BL Holding capital constant, short-run cubic production function is derived as follows: Q = ak 3 L 3 + bk 2 L 2 = AL + 3 2 BL A = ak B = bk Where and 3 2 Economía M. En C. Eduardo Bustos Farías 28
Properties of a Short-Run Cubic Production Function 3 2 Q = AL + BL The average & marginal products of labor are, respectively: AP = Q L= AL 2 + BL MP =ΔQ Δ L= 3AL 2 + 2BL Economía M. En C. Eduardo Bustos Farías 29
Properties of a Short-Run Cubic Production Function 3 2 Q = AL + BL Marginal product of labor begins to diminish beyond L m units of labor Average product of labor begins to diminish beyond units of labor L a L m B = and L = 3A a B 2A Economía M. En C. Eduardo Bustos Farías 30
MP & AP Curves for the Short-Run Cubic Production Function Q = AL 3 + BL 2 Economía M. En C. Eduardo Bustos Farías 31
Properties of a Short-Run Cubic Production Function 3 2 Q = AL + BL To have necessary properties of a production function, parameters must satisfy the following restrictions: A < 0 and B > 0 Economía M. En C. Eduardo Bustos Farías 32
Estimation of a Short-Run Production Function To use linear regression analysis, the cubic equation must be transformed into linear form Q = AX + BW Where X = L 3 and W = L 2 Estimated regression line must pass through the origin Specify in computer routine Economía M. En C. Eduardo Bustos Farías 33
Estimation of a Short-Run Cost Function Estimate using data for which the level of usage of one or more inputs is fixed Usually time series data are used Data collection may be complicated by the fact that accounting data do not include firm s opportunity costs Capital costs should reflect not only acquisition cost but any foregone rental income, depreciation, & capital gains/losses Must eliminate effects of inflation Divide by appropriate price index Economía M. En C. Eduardo Bustos Farías 34
Properties of a Short-Run Cubic Cost Function TVC = aq + bq + cq 2 3 Average variable cost & marginal cost functions are, respectively: AVC = a + bq + cq SMC = a + 2bQ + 3cQ 2 2 Economía M. En C. Eduardo Bustos Farías 35
Properties of a Short-Run Cubic Cost Function TVC = aq + bq + cq 2 3 Average variable cost reaches its minimum value at: Qm = b 2c To conform to theoretical properties, parameters must satisfy the following restrictions: a > 0, b < 0, and c > 0 Economía M. En C. Eduardo Bustos Farías 36
Properties of a Short-Run Cost Function Cubic specification produces S-shaped TVC curve & ²-shaped AVC & SMC curves All three cost curves employ the same parameters Only necessary to estimate one of these functions to obtain estimates of all three In the short-run cubic specification, input prices are assumed constant Not explicitly included in cost equation Economía M. En C. Eduardo Bustos Farías 37
Summary of Short-Run Empirical Production Functions Short-run cubic production equations Total product Average product of labor Marginal product of labor Diminishing marginal returns Restrictions on parameters 3 2 Q = AL + BL 2 AP = AL + BL MP = 3AL 2 + 2BL begin at L m B = 3 A A< 0 and B > 0 Economía M. En C. Eduardo Bustos Farías 38
Summary of Short-Run Empirical Cost Functions Short-run cubic cost equations Total variable cost Average variable cost Marginal cost Average variable cost reaches minimum at Restrictions on parameters 2 3 TVC = aq + bq + cq AVC = a + bq + cq SMC = a + 2bQ + 3cQ b Qm = 2 c a > 0, b < 0, c > 0 2 2 Economía M. En C. Eduardo Bustos Farías 39