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# 经济学生产问题代写 Economics 426代写 经济学作业代写

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## Economics 426: Problem Set 8 – Production

Due: Wednesday, April 29 (online 2:00pm).

Points Possible: 100.

### I.

Show that if A and B are closed subsets of Rn , then A+B is closed or provide a counter example. (20 pts)

### II.

Show that if A and B are strictly convex subsets of Rn , then A + B is strictly convex or provide a counter example. (20 pts)

function. Graph the technology set Y in L−y space (be sure to use negative values for L in the graph to denote an input). Show that the technology set violates the convexity assumption (P.1) (a graph is sufficient). (15 pts)

### IV. 经济学生产问题代写

Consider a firm j characterized by the production function y = f(x) = ex , where the e is the base of the natural log. The technology set

Yj = {(x, y) | 0 y ex , x 0}.

Show that the technology set does not fulfill P.5 (strict convexity). (15 pts)

### V. 经济学生产问题代写

The supply function Sj(p), may not be well-defined when assumption P.4 is not satisfied and firm j’s technology set, Yj , is unbounded. Consider the production technology in R2 :

Yj = {(x, y) R2 | x 0, y ≤ −2x + √−x}.

Recall that inputs are treated as negative co-ordinates and outputs are treated as positive, making this all a bit obscure (If we were writing a production function and x were measured positively instead of negatively, we would have y = 2x + x).

A. Demonstrate that Yj is unbounded, violating P.4. (15 points)

B. Show that for some prices, for example (px , py ) = (7, 7); that Sj(p) is not welldefined, i.e., there is no profit maximizing bundle. (15 pts)

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