Slide 1 Copyright © 2004 McGraw-Hill Ryerson Limited

Appendix 10

Mathematical

Extensions of the

Theory of Costs

Slide 2 Copyright © 2004 McGraw-Hill Ryerson Limited

FIGURE A.10-1

The Short-Run and Long-Run Expansion Paths

The long-run expansion path isthe line OV. With K fixed at K ,the short-run expansion path is ahorizontal line through the point(0, K ). Because K is theoptimal amount of K forproducing 2 units of output, thelong-run and short-run expansionpaths intersect at T. The short-runtotal cost of producing a givenlevel of output is the costassociated with the isocost linethat passes through theintersection of the relevantisoquant and the short-runexpansion path. Thus, forexample, STC3 is the short-runtotal cost of producing 3 units ofoutput, at Z.

*2

*2

*2

Slide 3 Copyright © 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, STCQ approaches LTCQ. The two curves are tangent at Q = 2.

Slide 4 Copyright © 2004 McGraw-Hill Ryerson Limited

FIGURE A.10-3

SAC, SAVC, and SMC Curves Associated with Figure A.10-1

Slide 5 Copyright © 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.

Slide 6 Copyright © 2004 McGraw-Hill Ryerson Limited

EXERCISE A.10-1

Slide 7 Copyright © 2004 McGraw-Hill Ryerson Limited

ANSWER A.10-1