8. cost versus expenditure Return to the two period inventory setting of Tables 11.1 and 11.2, where we framed a new product opportunity in terms of incremental revenue less incremental cost.

(a) Carefully explain the shadow prices on the initial inventory for the six cases in Table 11.1. Also verify these shadow prices using your favorite optimization software, e.g. Excel. Reconcile your approach with that in Chapter 2’s Appendix.

(b) Why is this shadow price the appropriate material cost in the incremental cost frame?

(c) Give a variation on the assumed prices and quantities such that the appropriate material cost in the incremental formulation is 8.1. Do not change any of the first period prices.

(d) What happens in the setting of Table 11.1 if we set P+ = 15 and P− = 14? What does this tell you about a formulation that uses these second period prices?

(e) Is the historical cost of the material a sunk cost? Can you provide a frame of the new product decision that makes this most obvious?

(f) Briefly discuss what happens in this setting if the firm faces a constant 40% marginal tax rate on accounting income.