经济学生产问题代写 Economics 426代写 经济学作业代写

Economics 426: Problem Set 8 – Production

经济学生产问题代写 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

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) = e^x , where the e is the base of the natural log. The technology set

Y^j = {(x, y) | 0 ≤ y ≤ e^−x , 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 S^j(p), may not be well-defined when assumption P.4 is not satisfied and firm j’s technology set, Y^j , is unbounded. Consider the production technology in R² :

Y^j = {(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 Y^j is unbounded, violating P.4. (15 points)

B. Show that for some prices, for example (p^x , p^y ) = (7, 7); that S^j(p) is not welldefined, i.e., there is no profit maximizing bundle. (15 pts)

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