Problem
Suppose that we have obtained a sequence of observations of the production plans adopted by a firm for a sequence of prices. Specifically, we observe at one time that, at prices p1, the firm chooses production plan z1; at a later time, at prices p1 the firm chooses plan z2 and so on, with the last observation being that at prices p1 the firm chooses plan z1. The model we have is that the firm is competitive and chooses a profit-maximizing plan from its production possibility set at each point in time, but that the production possibility set may, because of technological advances, be growing through time. That is, at the time of the first choice, the firm has production possibility set Z1; at the second time, the firm has a production possibility set Z2 with Z1 ⊆ Z2, and so on. In the spirit of proposition 7.5, give necessary and sufficient conditions on the sequence of observations being consistent with this sort of model.
The response should include a reference list. Double-space, using Times New Roman 12 pnt font, one-inch margins, and APA style of writing and citations.