1. Slide 1Copyright © 2004 McGraw-Hill Ryerson Limited Appendix 10 Mathematical Extensions of the Theory of Costs

2. Slide 2Copyright © 2004 McGraw-Hill Ryerson Limited FIGURE A.10-1 The Short-Run and Long-Run Expansion Paths The long-run expansion path is the line OV. With K fixed at K, the short-run expansion path is a horizontal line through the point (0, K ). Because K is the optimal amount of K for producing 2 units of output, the long-run and short-run expansion paths intersect at T. The short-run total cost of producing a given level of output is the cost associated with the isocost line that passes through the intersection of the relevant isoquant and the short-run expansion path. Thus, for example, STC 3 is the short-run total cost of producing 3 units of output, at Z. *2*2 *2*2 *2*2

3. Slide 3Copyright © 2004 McGraw-Hill Ryerson Limited FIGURE A.10-2 The LTC and STC Curves Associated with the Isoquant Map in Figure A.10-1 As Q approaches 2, the level of output for which the fixed factor is at its optimal level, STC Q approaches LTC Q. The two curves are tangent at Q = 2.

4. Slide 4Copyright © 2004 McGraw-Hill Ryerson Limited FIGURE A.10-3 SAC, SAVC, and SMC Curves Associated with Figure A.10-1

5. Slide 5Copyright © 2004 McGraw-Hill Ryerson Limited FIGURE A.10-4 The Family of Cost Curves Associated with a U-Shaped LAC The LAC curve is the “outer envelope” of the SAC curves. LMC = SMC at the Q value for which the SAC is tangent to the LAC. At the minimum point on the LAC, LMC = SMC = SAC = LAC.

6. Slide 6Copyright © 2004 McGraw-Hill Ryerson Limited EXERCISE A.10-1

7. Slide 7Copyright © 2004 McGraw-Hill Ryerson Limited ANSWER A.10-1