sunk cost and interactions Ralph purehased 200 units of a speeial eatalyst. The market for this eatalyst has sinee collapsed, and it eannot be sold; it ean be disposed of for zero ineremental cost.

Ralph paid 1,000 per unit for the eatalyst.

a] The catalyst can be used to produce any feasible combination of two products.

Denote their respective quantities x ~ 0 and y ~ O. A unit of either product requires a unit of the catalyst, so the overall constraint is x + Y s 200. The net gain, exclusive of any catalyst cost, from a feasible x and y combination is 240x - x2 + 200y _ y2.

Detennine Ralph's optirnal use of the 200 units. Is the 1,000 per unit acquisition eost a sunk eost?
bJ Now frarne the analysis to focus explieitly on units of x. Let the ineremental profit be measured by 240x - x2 - ex, where e should be interpreted as the eost of a unit of the eatalyst. Find a value of

e, a eost per unit of eatalyst, such that maximizing this ineremental profit measure wilI lead Ralph to the optimal ehoice.
e] Carefully explain how a material whose eost is sunk turns out to have a strietly positive eost in part [b J.AppendixLO1