Costs Costs: Introduction Managerial Problem Technology choice at home versus abroad: In western countries, firms use relatively capital-intensive technology. Will that same technology be cost minimizing if they move their production abroad? Solution Approach First, a firm must determine which production processes are technically efficient so that it can produce the desired level of output without waste. Second, a firm should pick from these technically efficient processes the one that is also economically efficient (minimum cost). By minimizing costs, a firm can increase its profit. Take-away When considering costs, a good manager includes opportunity costs or foregone alternatives. To minimize costs, a manager should distinguish short-run costs from long-run costs. Firms may reduce costs over time based on experience or its learning curve. If a firm produces several goods, individual cost may depend on the cost of producing multiple goods. 1
The Nature of Costs: Opportunity Costs Explicit and Implicit Costs Explicit costs are direct, out-of-pocket payments for labor, capital, energy, and materials. Implicit costs reflect only a foregone opportunity rather than explicit, current expenditure. Opportunity Costs The opportunity cost of a resource is the value of the best alternative use of that resource. Value of Manager s Time example: Peter owns and manages a firm. He pays himself only $1k per month but could work for another firm and make $11k per month. Working for another firm is the best alternative use of his time, so his opportunity cost of time is $11k. Relevance of Considering Opportunity Cost Peter example: Assume monthly revenue is $49k and explicit costs are $40k, including Peter s monthly wage. The accounting profit is $9k and Peter collects $10k per month (profit + wage). However, his opportunity cost is $11k. So, he incurs an economic loss of $1k. The Nature of Costs: durable inputs Costs of Durable Inputs Durable inputs are usable for a long period, perhaps for many years. Capital such as land, buildings, or equipment are durable inputs. Costs of Durable Inputs (for example, a truck) There are two problems. First, how to allocate the initial purchase cost over time. Second, what to do if the value of the capital changes over time. Solution if there is a rental market: The accountant could expense the truck s purchase price or may amortize it over the life of the truck, following tax rules (poor choice). The firm s opportunity cost of using the truck is the amount that the firm would earn if it rented the truck to others. if there is no rental market: The opportunity cost of capital of using the truck a year would be the market depreciation + the interest forgone in a year. 2
The Nature of Costs: Sunk Costs Sunk Costs Sunk cost is a past expenditure that cannot be recovered. If an expenditure is sunk, it is not an opportunity cost. So we should not consider it for managerial decisions. However, sunk costs appear in financial accounts. Managers Should Ignore Sunk Costs!! A firm paid $300k for a parcel of land but the market value is now $200k. If the firm builds a plant on this land, the value for the firm becomes $240k. Is it worth carrying out production on this land or should the land be sold for its market value of $200k? The land s opportunity cost is $200k and the market value loss of $100k is a sunk cost. The sunk cost cannot be recovered and should not be considered in the decision. The values to compare are $240 versus $200. Certainly, the firm should carry out production on this land. Common Measures of Short-Run Costs Fixed Cost F Variable Cost VC Total Cost C = F + VC Fixed Cost (F) does not vary with the level of output; includes expenditures on land, office space, production facilities, and other overhead expenses; are often sunk costs, but not always. Variable Cost(VC) changes as the quantity of output changes; refers to the costs of variable inputs. Total Cost (C) is the sum of fixed and variable costs. F and VC should be based on inputs opportunity costs. F may (or may not) be sunk 3
Common Measures of Short-Run Costs Average Fixed Cost AFC = F/q Average Variable Cost AVC= VC/q Average Cost AC = C/q = AFC + AVC Average Fixed Cost (AFC) falls as output rises because the fixed cost is spread over more units. Average Variable Cost (AVC) or variable cost per unit of output may either increase or decrease as output rises. Average Cost (AC) or average total cost may either increase or decrease as output rises. Short-Run Costs Marginal Cost: Marginal cost (MC) is the amount by which a firm s cost changes if the firm produces one more unit of output; C is the change in cost when the change in output, q, is 1 unit. Marginal cost also equals the change in variable cost from a one-unit increase in output. MC = ΔC/Δq = ΔVC/Δq Marginal Cost using Calculus: Marginal cost is the rate of change of cost as we make an infinitesimally small change in output. MC=dVC/dq because df/q=0. MC = dc/dq = dvc/dq 4
Total, Variable and Fixed Short-Run Costs The fixed cost curve, F, is a horizontal line at $48. The variable cost curve, VC, is zero at zero units of output and rises with output. The total cost curve, C, is the vertical sum of the VC and F curves, so it is $48 higher than the VC curve at every output level. VC and C curves are parallel. Average and Marginal Short-Run Costs The marginal cost curve, MC, cuts the average variable cost, AVC, and average cost, AC, curves at their minimums. The height of the AC curve at point a equals the slope of the line from the origin to the cost curve at A. The height of the AVC at b equals the slope of the line from the origin to the variable cost curve at B. The height of the marginal cost is the slope of either the C or VC curve at that quantity. 5
Production Functions and the Short-Run Costs Curves The production function determines the cost curves. In the short run, the firm increases output by using more labor. However, each extra worker increases output by a smaller amount. Diminishing marginal returns to labor determine the shape of the production function. The production function determines the shape of the variable cost curve. As output increases, variable cost increases more than proportionally because of diminishing marginal returns. Long Run Costs Input Choice In the long run, the firm adjusts all its inputs so that its cost of production is as low as possible. The firm can change its plant size, design, build new machines, and otherwise adjust inputs that were fixed in the short run. Technically and Economically Efficient From among the technically efficient combinations of inputs that can be used to produce a given level of output, a firm wants to choose that bundle of inputs with the lowest cost of production, which is the economically efficient combination of inputs. To do so, the firm combines information about technology from the isoquant with information about the cost of production. 6
Long Run Costs An isocost represents all the combinations of inputs that have the same (iso-) total cost. In general, C = w L + r K In the Figure, the $200 isocost line represents all the combinations of labor and capital that the firm can buy for $200. Long Run Costs Properties of isocost lines The points at which the isocost lines hit the capital and labor axes depends on the firm s cost, and on the input prices. Isocost lines that are farther from the origin have higher costs than those closer to the origin. The slope of each isocost line is the same: K/ L = w/r, the rate at which the firm can trade capital for labor in input markets 7
Long Run Costs Isocost and Isoquant Combined The firm minimizes its cost by using the combination of inputs on the isoquant that is on the lowest isocost line that touches the isoquant. Long Run Costs The lowest possible isoquant that will allow the beer manufacturer to produce 100 units of output is tangent to the $2,000 isocost line. At x, the bundle of inputs are L = 50 workers and K = 100 units of capital. At x, the isocost is tangent to the isoquant, so the slope of the isocost, w/r = 3, equals the slope of the isoquant, which is the negative of the marginal rate of technical of substitution. Notice, y and z also produce 100 units of output but at a cost of $3,000. The x input combination is economically efficient. 8
Three Equivalent Rules to Minimize Costs in the Long-Run The Lowest Isocost Rule The firm minimizes its cost by using the combination of inputs on the isoquant that is on the lowest isocost line that touches the isoquant. The Tangency Rule: MRTS = - w/r At the minimum-cost bundle, x, the isoquant is tangent to the isocost line. The slope of the isoquant (MRTS) and the slope of the isocost are equal. The Last-Dollar Rule: (MP L /w) = (MP K /r) Cost is minimized if inputs are chosen so that the last dollar spent on labor adds as much extra output as the last dollar spent on capital. Thus, spending one more dollar on labor at x gets the firm as much extra output as spending the same amount on capital. Factor Price Changes How should the firm change its behavior if the cost of one of the factors changes? If one factor becomes relatively cheaper, the firm should substitute factors considering the slopes of the isoquant and isocost curves. 9
Factor Price Changes In the Figure, initial wage = $24 and rental rate of capital = $8. lowest isocost line ($2,000) tangent to the q = 100 isoquant at x(l = 50, K = 100). When the wage falls from $24 to $8, the isocost lines become flatter: Labor is relatively less expensive than capital now. The slope of the isocost lines falls The new lowest isocost line ($1,032) is tangent at v (L = 77, K = 52). Thus, when the wage falls, the firm uses more labor and less capital to produce a given level of output, and the cost of production falls from $2,000 to $1,032. Production Functions and the Shapes of Long-Run Costs Curves In the long run, returns to scale determine the shape of the production function, and the production function, in turn, determines the shape of the AC curve and other cost curves. If a production function has increasing returns to scale at low levels of output, constant returns to scale at intermediate levels of output, and decreasing returns to scale at high levels of output, the LRAC curve must be U-shaped. LRAC curves can have many different shapes depending whether the production process has economies or diseconomies of scale. Perfectly competitive firms typically have U-shaped AC curves. Noncompetitive markets may be U-shaped, L-shaped, everywhere downward sloping, everywhere upward sloping or have other shapes. 10
LRAC as the Envelope of SRAC Curves LRAC as the Envelope of SRAC Curves The long-run average cost is always equal to or below the short-run average cost. Any input combination in the short run is also available in the long run. However, changing capital levels to reduce costs are only available in the long run. In the long run, the firm chooses the plant size that minimizes its cost of production, so it picks the plant size that has the lowest average cost for each possible output level. LRAC as the Envelope of SRAC Curves At q 1, in Figure 6.7, the firm opts for the small plant size, whereas at q 2, it uses the medium plant size. If there are only three possible plant sizes, with short-run average costs SRAC 1, SRAC 2, and SRAC 3, the long-run average cost curve is the solid, scalloped portion of the three short-run curves (envelope curve). LRAC is the smooth and U-shaped long-run average cost curve. 11
The Learning Curve Learning by Doing Learning by doing refers to the productive skills and knowledge that workers and managers gain from experience. Workers add speed with practice. Managers learn how to organize production more efficiently, assign tasks based on worker s skills, and reduce inventory costs. Engineers optimize product designs with experimentation. For these and other reasons, the average cost of production tends to fall over time, and the effect is particularly strong with new products. Learning Curve and Costs The learning curve is the relationship between average costs and cumulative output. The cumulative output is the total number of units of output produced since the product was introduced. If a firm is operating in the economies of scale section of its average cost curve, expanding output lowers its cost for two reasons. Its average cost falls today because of economies of scale, and also because of learning by doing. Costs of Producing Multiple Goods Joint Production is Less Costly If a firm produces two or more goods that are linked by a single input, the cost of one good may depend on the output level of another. For example, cattle provide beef and hides. A firm enjoys economies of scope if it is less expensive to produce goods jointly than separately. It is less expensive to produce beef and hides together than separately, so there are economies of scope. Economies of Scope: SC = [C(q 1,0) + C(0,q 2 ) - C(q 1, q 2 )]/C(q 1, q 2 ) C(q 1, 0) is the cost of producing q 1 of the first good, C(0, q 2 ) is the cost of producing q 2 of the second good, and C(q 1, q 2 ) is the cost of producing both goods together. If SC is zero, there are no economies of scope: the cost of producing the two goods separately, C(q 1,0) + C(0,q 2 ), is the same as producing them together, C(q 1, q 2 ). If SC is positive, there are economies of scope: it is less expensive to produce goods jointly than separately. If SC is negative, there are diseconomies of scope: and the two goods should be produced separately. 12
Managerial Solution Managerial Problem Technology choice at home versus abroad: In the United States, firms use a relatively capital-intensive technology Will that same technology be cost minimizing if they move their production abroad? Solution The answer depends on relative factor prices and whether the firm s isoquant is smooth. If the isoquant is smooth, even a slight difference in relative factor prices will induce the firm to shift along the isoquant and use a different technology with a different capital-labor ratio. If the isoquant has kinks, the firm will use a different technology only if the relative factor prices differ substantially. Assignment Chapter 6 Exercise 2.4 Exercise 3.5 Exercise 4.3 13