Chapter 9 - Applications of Cost Theory, Solutions to Exercises

Exercise 1. a. An explanatory variable is statistically significant (at the .05 level) if the calculated t-value is greater than t.025,82. From Table 2 of Appendix B (t-distribution), t.025,82 is approximately equal to 2.000. Since each of the calculated t-values exceeds 2.000, we conclude that all three variables (i.e., Q, Q2, and X1) are statistically significant in explaining the average operating expense ratio.

b. A quadratic (Q2) cost output relationship is suggested by these results.

c. The cost-output relationship appears to be U-shaped, indicating the presence of economies of scale at lower output levels and diseconomies of scale at higher output levels.

Exercise 7. a. Sales = \$5,000,000 F = \$1,500,000 V/P = .60 Variable costs = .60(5,000,000) = \$3,000,000 EBIT = 5,000,000 − 3,000,000 − 1,500,000 = \$500,000

DOL at "X" = (Sales − Variable costs)/EBIT = (5,000,000 − 3,000,000)/500,000 = 4.0

b. %ΔEBIT = DOL × %ΔSales = 4.0 x 3% = 12%