Relation Between Long Run Cost Short Short Run CostEconomies of ScaleEconomies of Scope, LearningCite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 1 1 Relation Between Long Run Cost Short Short Run Cost 14.01 Principles of Microeconomics, Fall 2007 Chia-Hui Chen October 17, 2007 Lecture 14 The Cost of Production and Profit Maximization Outline 1. Chap 7: Relation Between Long Run Cost and Short Run Cost 2. Chap 7: Economies of Scale 3. Chap 7: Economies of Scope, Learning 1 Relation Between Long Run Cost Short Short Run Cost Since firms can change capital in the long run, the long run cost is always no more than the s hort run cost: CLR(q) � CSR,K (q). Figure 1 shows three short-run total cost given different capital level. In the long run, firms will choose the capital level which minimizes the total cost. Thus, the long-run total cost is equal to the minimum of all possible short-run total cost, and so long run total cost is the envelope of all short run total costs. Likewise, long-run average cost is the envelope of all short run average cost. From Figure 1, we know for a given product q, long run marginal cost is eq ual to the corresponding short run marginal cost. Long run total cost and marginal cost also have the following relation: (see Figure 2) • If LM C < LAC, LAC is decreasing; • if LM C = LAC, LAC is minimized; • if LM C > LAC, LAC is increasing.Cite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 2 1 Relation Between Long Run Cost Short Short Run Cost TCTCSR2 TCLR SR1 2 1 TCSR3 0 0 1 2 3 4 5 6 7 8 9 10 q Figure 1: Deriving Long Run Total Cos t from Short Run Total Cost. C 10 9 8 7 6 5 4 3 5 10 15 C LAC LMC SAC1 SMC1 SAC3 SMC3 SAC2 SMC2 0 0 5 10 15 q Figure 2: Deriving Long Run Average Cost and Marginal C ost from Short Run Average Cost and Marginal Cost.Cite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 3 2 Economies of Scale 2 Economies of Scale • Constant economies of scale: C(aq) = aC(q), a > 1, and in this case, AC is cons tant; • Economies of s c ale: C(aq) < aC(q), a > 1, and in this case, AC is decre asing; • Diseconomies of scale: C(aq) > aC(q), a > 1, and in this case, AC is increasing. 0 1 2 3 4 5 6 7 8 9 10 q Figure 3: Production Dependence of Average Cost, Different Economies of Scale. 3 Economies of Scope, Learning Economies of Scope. When producing more than one type of product that are closely linked, the cost is lower than when producing them separately. Product Transformation Curve. Shows various combinations of outputs that can be produced with a given set of inputs. 0 1 2 3 4 5 6 7 8 9 10 C AC economies of scale diseconomies of scaleCite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 4 3 Economies of Scope, Learning Example (Product Transfor mation Curve with Economies of Scope). To produce 1 car and 1 truck, if we produce them separately, we need 2 units of K and 2 units of L; but if we produce them together, we only need 1.5 units of K and 1.5 units of L (se e Fig ure 4). In this case, it is cheaper to produce them together; thus the firm has economies of scope. K=1.5 L=1.5 (1,1) K=1 L=1 (0.7,0,7) 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Cars Figure 4: Product Transformation Curve with Economies of Scope. In the case of economies of scope, the pr oduct transformatio n c urve is neg-atively sloped and concave. The degree of economies of scope is defined as follows: C(q1) + C(q2) − C(q1, q2)SC = . C(q1, q2) • If SC > 0, it is e conomies of scope; • if SC < 0, it is dis e c onomies of scope. The learning curve for a firm is shown in Figure 5, with the firm’s cumulative output as the vertical coordinate, and amount of inputs needed to produce a unit of output as the horizontal coordinate. Learning causes a difference in cost between the new firm and the old firm (see Figure 6). 2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 TrucksCite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 5 3 Economies of Scope, Learning 10 9 8 7 6 5 4Hours of Labor Per Unit of Output3 2 1 0 0 1 2 3 4 5 6 7 8 9 10 Cumulative Number of Outputs Produced Figure 5: L e arning Curve of a Firm. 3 4 5 6 7 8 9 10 C AC* AC 2 1 0 0 1 2 3 4 5 q 6 7 8 9 10 Figure 6: Shift of Cost Curve from Learning.Cite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 6 3 Economies of Scope, Learning Figure 7: Structur e of Pr oduction