13生产成本

nullnullChapter 13 The Costs of Productionnullnull13.1 What Are Costs?According to the Law of Supply: Firms are willing to produce and sell a greater quantity of a good when the price of the good is high. This results in a supply curve that slopes upward. The Firm’s Objective: The economic goal of the firm is to maximize profits. null13.1.1 Total Revenue, Total Cost, and ProfitTotal Revenue The amount a firm receives for the sale of its output. Total Cost The market value of the inputs a firm uses in production. Profit is the firm’s total revenue minus its cost. Profit = Total revenue – Total cost null13.1.2 Costs as Opportunity CostsThe opportunity cost of an item refers to all those things that must be forgone to acquire that item. When economists speak of a firm’s cost of production, they includes all the opportunity costs of making its output of goods and services. Explicit and Implicit Costs A firm’s cost of production include explicit costs and implicit costs. Explicit cost are input costs that require a direct outlay of money by the firm. Implicit cost are input costs that do not require an outlay of money by the firm.null13.1.2 Costs as Opportunity CostsThis distinction between explicit and implicit costs highlights an important difference between how economists and accountants analyze a business. Economists are interested in studying how firms make production and pricing decisions. Because these decisions are based on both explicit and implicit costs, economists include both when measuring a firm’s cost. By contrast, accountants have the job of keeping track of the money that flows into and out of firms. As a result, they measure the explicit costs but often ignore the implicit cost. null13.1.4 Economic Profit versus Accounting ProfitEconomists measure a firm’s economic profit as total revenue minus total cost, including both explicit and implicit costs. Accountants measure a firm’s accounting profit as the firm’s total revenue minus only the firm’s explicit costs. When total revenue exceeds both explicit and implicit costs, the firm earns economic profit. Economists profit is smaller than accounting profit. Figure 1 Economic versus AccountantsFigure 1 Economic versus AccountantsCopyright © 2004 South-WesternHow an EconomistViews a FirmHow an AccountantViews a FirmnullEconomists include all opportunity costs when analyzing a firm, whereas accountant measure only explicit costs. Therefore, economic profit is smaller than accounting profit.Figure 1 Economists versus Accountantsnullnull13.2 Production and CostsThe Production Function The Production function shows the relationship between quantity of inputs used to make a good and the quantity of output of that good. Marginal Product The Marginal product of any input in the production process is the increase in output that arises from an additional unit of that input. null13.2 The Production FunctionDiminishing Marginal Product Diminishing marginal product is the property whereby the marginal product of an input declines as the quantity of the input increases. Example: As more and more workers are hired at a firm, each additional worker contributes less and less to production because the firm has a limited amount of equipment. nullA production function shows the relationship between the number of workers hired and the quantity of output produced. Here the number of workers hired (on the horizontal axis) is from the first column in Table 13-1, and the quantity of output produced (on the vertical axis) is from the second column. The production function gets flatter as the number of workers increase, which reflects diminishing marginal product.Figure 2 Hungry Helen’s Production Functionnull13.2.1 The Production FunctionDiminishing Marginal Product The slope of the production function measures the marginal product of an input, such as a worker. When the marginal product declines, the production function becomes flatter. null13.2.2 From the Production Function to the Total-Cost CurveThe relationship between the quantity a firm can produce and its costs determines pricing decisions. The total-cost curve shows this relationship graphically. nullTable 1 A Production Function and Total Cost: Hungry Helen’s Cookies FactoryNumber of WorkersOutput (quantity of cookies produced per hour)Marginal Product of LaborCost of FactoryTotal Cost of Inputs (cost of factory + cost of workers)Cost of Workers0 0 $30 $ 0 $30 1 50 30 10 40 2 90 30 20 50 3 120 30 30 60 4 140 30 40 70 5 150 30 50 80 5040302010nullA total-cost curve shows the relationship between the quantity of output produced and total cost of production. Here the quantity of output produced (on the horizontal axis) is from the second column in Table 13-1, and the total cost (on the vertical axis) is from the sixth column. The total-cost curve gets steeper as the quantity of output increases because of diminishing marginal product.Figure 3 Hungry Helen’s Total-Cost CurvenullFrom the Production Function to the Total-Cost CurveNow compare the total-cost curve in Figure 3 with the production function in Figure 2. These two curves are opposite sides of the same coin. The total-cost curve gets steeper as the amount produced rises, whereas the production function gets flatter as production rises. These changes in slope occur for the same reason. High production of cookies means that Helen’s kitchen is crowded with many workers. Because the kitchen is crowded, each additional worker adds less to production, reflecting diminishing marginal product. Therefore, the production function is relatively flat. But now turn this logic around: When the kitchen is crowded, producing an additional cookie requires a lot of additional labor and is thus very costly. Therefore, when the quantity produced is large, the total-cost curve is relatively steep. (Mankiw, third edition, p274)nullCosts of production may be divided into fixed costs and variable costs. Fixed costs are those costs that do not vary with the quantity of output produced. Variable costs are those costs that do vary with the quantity of output produced. Total costs Total Fixed costs (TFC) Total Variable costs (TVC) Total costs (TC) TC = TFC + TVC13.3.1 Fixed and Variable CostsnullTable 2 The Various Measures of Cost: Thirsty Thelma’s Lemonade StandnullAverage costs Average costs can be determined by dividing the firm’s costs by the quantity of output it produces. The average cost is the cost of each typical unit of product. 13.3.2 Average and Marginal CostsnullAverage costs Average Fixed costs (AFC) Average Variable costs (AVC) Average Total costs (ATC) ATC = AFC + AVC 13.3.2 Average and Marginal CostsnullAverage CostsnullTable 2 The Various Measures of Cost: Thirsty Thelma’s Lemonade StandnullMarginal costs Marginal costs (MC) measures the increases in total cost that arises from an extra unit of production. Marginal cost helps answer the following question: How much does it cost to produce an additional unit of output? 13.3.2 Average and Marginal CostsnullMarginal Costs Relationships Among Cost & Production Functions Relationships Among Cost & Production FunctionsAP & AVC are inversely related. (ex: one input) AVC = (WL) /Q = W/ (Q/L) = W/ APL As APL rises, AVC fallsMP and MC are inversely related MC = dTC/dQ = (WdL)/dQ = W / (dQ/dL) = W / MPL As MPL declines, MC risesprod. functionscost functionsMPLLMCAP AVC(Figure 8.3 on page 358)QQcostMarginal Cost Thirsty Thelma’s Lemonade StandMarginal Cost Thirsty Thelma’s Lemonade StandFigure 4 Thirsty Thelma’s Total-Cost CurvesFigure 4 Thirsty Thelma’s Total-Cost CurvesCopyright © 2004 South-WesternTotal Cost$15.0014.0013.0012.0011.0010.009.008.007.006.005.004.003.002.001.00Quantityof Output(glasses of lemonade per hour)014327659810Total-cost curvenullHere the quantity of output produced (on the horizontal axis) is from the first column in Table 13-2, and the total cost (on the vertical axis) is from the second column. As the Figure 13-3, the total-cost curve gets steeper as the quantity of output increases because of diminishing marginal product.Figure 4 Thirty Thelma’s Total-Cost CurvesFigure 5 Thirsty Thelma’s Average-Cost and Marginal-Cost CurvesFigure 5 Thirsty Thelma’s Average-Cost and Marginal-Cost CurvesCopyright © 2004 South-WesternCosts$3.503.253.002.752.502.252.001.751.501.251.000.750.500.25Quantityof Output(glasses of lemonade per hour)014327659810MCATCAVCAFCnullFigure 5 Thirsty Thelma’s Average-Cost and Marginal-Cost CurvesnullFigure 5 Thirsty Thelma’s Average-Cost and Marginal-Cost Curve This figure shows the average total cost (ATC), average fixed cost (AFC), average variable curve (AVC), and marginal cost (MC) for Thirsty Thelma’s Lemonade Stand. All of these curves are obtained by graphing the data in Table 13-2. These cost curves show three features that are typical of many firms: (1) Marginal cost rises with the quantity of output. (2) The average-total-cost curve is U-shaped. (3) The marginal-cost curve crosses the average-total-cost curve at the minimum of average total cost. nullMarginal cost rises with the amount of output produced. This reflects the property of diminishing marginal product. 13.3.3 Cost Curves and Their ShapesnullFigure 5 Thirsty Thelma’s Average-Cost and Marginal-Cost CurvesnullThe average total-cost curve is U-shaped. At very low levels of output average total cost is high because fixed cost is spread over only a few units. Average total cost declines as output increase. Average total cost starts rising because average variable cost rises substantially. 13.3.3 Cost Curves and Their ShapesnullThe bottom of the U-shaped ATC curve occurs at the quantity that minimizes average total cost. This quantity is sometimes called the efficient scale of the firm. 13.3.3 Cost Curves and Their ShapesnullFigure 5 Thirsty Thelma’s Average-Cost and Marginal-Cost CurvesnullRelationship between Marginal cost and Average Total Cost. Whenever marginal cost is less than average total cost, average total cost is falling. Whenever marginal cost is greater than average total cost, average total cost is rising. 13.3.3 Cost Curves and Their ShapesnullRelationship between Marginal cost and Average Total Cost. The marginal-cost curve crossed the average-total-cost curve at the efficient scale. Efficient scale is the quantity that minimizes average total cost. 13.3.3 Cost Curves and Their ShapesnullFigure 5 Thirsty Thelma’s Average-Cost and Marginal-Cost CurvesnullIt is now time to examine the relationships that exist between the different measures of cost. 13.3.4 Typical Cost CurvesnullBig Bob’s Cost CurvesFigure 6 Big Bob’s Cost CurvesFigure 6 Big Bob’s Cost CurvesCopyright © 2004 South-Western(a) Total-Cost Curve$18.0016.0014.0012.0010.008.006.004.00Quantity of Output (bagels per hour)TC42681412102.00TotalCost0null(a) Total-Cost CurveFigure 6 Bib Bob’s Cost CurvesFigure 6 Big Bob’s Cost CurvesFigure 6 Big Bob’s Cost Curves(b) Marginal- and Average-Cost CurvesQuantity of Output (bagels per hour)Costs$3.002.502.001.501.000.5004268141210MCATCAVCAFCnull(b) Marginal- and Average-Cost CurvesFigure 6 Bib Bob’s Cost CurvesnullFigure 6. Big Bob’s Cost Curve. Many firms, like Big Bob’s Bin, experience increasing marginal product before diminishing marginal product and, therefore, have cost curves shaped like those in this figure. Panel (a) shows how total cost (TC) depends on the quantity produced. Panel (b) shows how average total cost (ATC), average fixed cost (AFC), average variable curve (AVC), and marginal cost (MC) depends on the quantity produced. These curves are derived by graphing the data from the table. Notice that marginal cost and average variable cost fall for a while before starting to rise. null13.3.4 Typical Cost CurvesThree Important Properties of Cost Curves Marginal cost eventually rises with the quantity of output. The average-total-cost curve is U-shaped. The marginal-cost curve crosses the average-total-cost curve at the minimum of average total cost null13.4 Costs in the Short run and in the Long RunFor 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. 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. Figure 7 Average Total Cost in the Short and Long RunFigure 7 Average Total Cost in the Short and Long RunCopyright © 2004 South-WesternQuantity ofCars per Day0AverageTotalCost1,200$12,000nullSources of Increasing Returns to Scale The sources of increasing output per unit of input when a firm grows include technical, managerial, purchasing, marketing and financial economies. nullEconomies and Diseconomies of Scale Economies of scale (increasing returns to scale ) refer to the property whereby long-run average total cost falls as the quantity of output increases. Diseconomies of scale (decreasing returns to scale ) refer to the property whereby long-run average total cost rises as the quantity of output increases. Constant returns to scale refers to the property whereby long-run average total cost stays the same as the quantity of output increases. Figure 7 Average Total Cost in the Short and Long RunFigure 7 Average Total Cost in the Short and Long RunCopyright © 2004 South-WesternQuantity ofCars per Day0AverageTotalCostnullBecause fixed costs are variable in the long run, the average-total-cost in the short run differs from the average-total-cost curve in the long run. Figure 7 Average Total Cost in the Short and Long RunsnullnullThe terms “economic costs,” that include “normal profits,” and “economic profits” that are not included in “economics costs” are often confusing. Using the term “excess or economic profits” helps. Economists classify normal profits as costs, since in the long run the owner of a firm would close it down if a normal profit were not being earned. Since a normal profit is required to keep the entrepreneur operating the firm, a normal profit is a cost. Economic profits are not costs of production since the entrepreneur does not require the gaining of an economic profit to keep the firm operating. In economics, costs are whatever is required to keep a firm operating. (McConnell,Economics,15edition,ch22 production cost.)nullSummaryThe goal of firms is to maximize profit, which equals total revenue minus total cost. When analyzing a firm’s behavior, it is important to include all the opportunity costs of production. Some opportunity costs are explicit while other opportunity costs are implicit. nullSummaryA firm’s costs reflect its production process. A typical firm’s production gets flatter as the quantity of input increases, displaying the property of diminishing marginal product. A firm’s total costs are divided between fixed and variable costs. Fixed costs do no change when the firm alters the quantity of output product, variable costs do change as the firm alters quantity of output produced. nullSummaryAverage total cost is total cost divided by the quantity of output. Marginal cost is the amount by which total cost would rise if output were increased by one unit. The marginal cost always rises with the quantity of output. Average cost first falls as output increases and then rises.nullSummaryThe average-total-cost curve is U-shaped. The marginal-cost curve always crosses the average-total-cost curve at the minimum of ATC. A firm’s costs often depend on the time horizon being considered. In particular, many costs are fixed in the short run but variable in the long run.Mankiw-chapter13. Problem and AnswerMankiw-chapter13. Problem and Answer5.假定某厂商的边际成本　　　　　　　　 ，且生产10单位产量时的总成本为1000。 求: (1) 固定成本的值。 (2) 总成本函数、总可变成本函数，以及平均成本函数、平均可变成本函数。(高鸿业《西方经济学》第三版，第五章成本论)Mankiw-chapter13. Problem and AnswerMankiw-chapter13. Problem and AnswerProblem and AnswerProblem and Answer6. 某公司用两个工厂生产一种产品，其总成本函数为 ，其中Q1示第一个工厂生产的产量，Q2表示第二个工厂生产的产量。 求：当公司生产的产量为40时能够使得公司生产成本最小的两工厂的产量组合.(高鸿业《西方经济学》第三版，第五章成本论)Problem and AnswerProblem and Answer7. 已知生产函数　　　　　　　　；各要素价格分别为PA＝1，PL＝1，PK＝2；假定厂商处于短期生产，且 　　　　。 推导：该厂商短期生产的总成本函数和平均成本函数；总可变成本函数和平均可变成本函数；边际成本函数。nullnull8. 已知生产函数　　　　　　　 ;当资本投入量K＝50时资本的总价格为500；劳动的价格PL＝5。 求: (1)劳动的投入函数L=L(Q) (2)总成本函数、平均成本函数和边际成本函数。 (3)当产品价格P＝100时，厂商获得最大利润的产量和利润各是多少？(高鸿业《西方经济学》第三版，第五章成本论)nullnull5、已知生产函数Q=min(L,4K)。求： （1）当产量Q=32时，L与K值分别是多少？ （2）如果生产要素的价格分别为PL=2，PK=5，则生产100单位产量时的最小成本是多少？ 解答：（1）生产函数Q=min(L,4K)表示该函数是一个固定投入比例的生产函数，所以，厂商进行生产时，总有Q=L=4K。 因为已知产量Q=32，所以，相应地有L=32，K=8。 （2） 由Q=L=4K，且Q=100，可得： L=100，K=25 又因PL=2，PK=5，所以有： C= PL·L+PK·K =2×100+5×25=325 既生产100单位产量的最小成本为325。nullnullnullnullnullnullnullProblem and AnswerProblem and Answer10.试用图从短期总成本曲线推导出长期总成本曲线，并说明长期总成本曲线的经济含义。 11. 试用图从短期平均成本曲线推导长期平均成本曲线，并说明长期平均成本曲线的经济含义。 12.试用图从短期边际成本曲线推导长期边际成本曲线，并说明长期边际成本曲线的经济含义。 (高鸿业《西方经济学》第三版，第五章成本论) nullExercise and Answer3、为了实现既定成本条件下的最大产量或即定产量条件下的最小成本 , 如果企业处于 MRTSLK> 或者MRTSLK＜ 时 , 企业应该分别如何调整劳动和资本的投入量 , 以达到最优的要素组合 ? 为什么 ? 解答 ：要点如下 ： (1) 研究给定条件下的产量最大化或成本最小化的分析工具是等产量曲线和等成本线。等产量曲线的斜率的绝对值可以用两要素的边际技术替代率 MRTSLK 来表示 , 等成本线的斜率为- ， 即两要素的相对价格。在几何图形的分析中，生产者追求既定约束条件下的产量最大化或成本最小化的均衡点都发生在等产量曲线和等成本线的相切点上 ,于是有生产者最优生产要素组合的均衡条件为：nullMRTSLK= 。其经济含义为：在厂商的生产要素最优组合的均衡点上，厂商在生产中的两要素的边际技术替代比率(即MRTSLK)，即用一单位的劳动所替代的资本的数量，应该恰好等于该厂商能够在市场用一单位的劳动去交换资本的数量(即 ) 。 (2)在MRTSLK> 时，厂商对生产要素投入组合的调整 , 可以用图1-19来说明。先看表示给定成本条件下的产量最大化的(a)图。在(a)图中的α点上有等产量曲线的斜率的绝对值大于等成本线斜率的绝对值，即MRTSLK> ，且α点的要素投入组合为(L1,K1),相应的产量由等产量曲线Q1表示。但在成本给定(即等成本线AB给定)的条件下,a点的要素投入组合生产的产量并不是最大的。厂商应该从α点出发,沿着给定的表示约束条件的等成本线AB向均衡点E靠拢，比如说，由α点运动到α'点，则厂商就可以在不改变成本的条件下，将要素 调整到null (L2，K2)，从而达到更大的产量水平，此产量 水平用过 α'点的等产量曲线 Q2( 虚线 ) 来表示。很清楚，只要厂商由α点出发，沿着既定的等成本线AB，按箭头所示方向往下向均衡点E靠拢，最后就可以在等产量曲线Q3和等成本线AB的相切点E处实现最大的产量。此时，在均衡点 E上，有MRTSLK= 。 相类似地，再看表示定产量条件下成本最小化的(b) 图。在（b）图中的α点上同样也有MRTSLK ＞ ，在α点处的要素投入组合为(L1，K1)，响应的成本由等成本线AB表示。但在产量给定（既等产量曲线Q给定）的条件下，α点要素投入组合所导致的成本并不是最小的。厂商同样应该从α点出发，沿着给定的表示产量约束条件的等产量曲线Q向均衡E靠拢，比如说，由α点运动到α'点，则厂商就可以在生产产量Q的条件下， 将要素投入组合调整到(L2，K2)，从而达到更小的成本， 此成本便是过α'点的等成本A'B'点所表示的。nullnull 很清楚，只要厂商由α点出发，沿着既定的等产量曲线 Q 按箭头方向往下 向均衡点E靠拢，最后就可以在等产量曲线Q和等成本线A”B”相切点实现给定产量条件下的最小成本。此时，在均衡点上,有 MRTSLK= 。  (3) 至于MRTSLK < 的情况，在图中分别是图(a)中的b点和图(b)中的b点。与以上(2)中的分析道理相类似 , 在图(a)的b点时 , 厂商由b点出发 , 沿着既定的等成本线AB往上向均衡点E靠拢，比如运动到b’点，就可以在成本不变的前提下，通过对要素投入量的调整而不断地提高产量 , 如达到等产量曲线Q2的产量，最后在均衡点E实现最大的产量。同样，在图(b)的b点时，厂商从b点出发 , 沿既定的等产量曲线 Q 往上向均衡点E靠拢 , 比如运动到b‘点 , 就可以在产量不变的前提下，通过对要素投入量的调整而不断地降低成本, 如达到等成本线A'B'的成本 , 最后在均衡点 E 处实现最小的成本。nullnullnullnullnullnullnullnullnull （1） （2） （3）nullnull9、利用图说明厂商在既定成本条件下是如何实现最大产量的最优要素组合的。 解答：以图1-20为例，要点如下： （1）由于本的约束条件是既定的成本，所以，在图1-20中，只有一条等成本线AB；此外，有三条等产量线Q1、Q2和Q3以供分析，并从中找出相应的最大产量水平。 （2）在约束条件即等成本线AB给定的条件下，先看等产量曲线Q3，该曲线处于AB线以外，与AB线即无交点又无切点，所以，等产量曲线Q3表示的产量过大，即定的等成本线AB不可能实现Q3的产量。再看等产量曲线Q1，它与既定的AB线交于a、b两点。在这种情况下，厂商只要从a点出发，沿着AB线往下向E点靠拢，或者从b点出发，沿着AB线往上向E点靠拢，就都可以在成本不变的条件下，通过对生产要素投入量的调整，不断地增加nullnullnull