5. Suppose a rm's production function exhibits (i) diminishing marginal product of labor, [ii] complementarity, (iii) positive marginal product of capital and labor. In addition we know that the rm uses positive amount of capital and labor to produce each quantity.r [i.e. we are not at a corner solution) for any rental price of capital and labor. This is all we know about the nn's production function. (a) Fix the rental prices of capital and labor. Argue that the amount of capital used optimally to produce quantity (.2 is increasing in Q using the following steps. i. Suppose that Q1 {2 Q2 but instead the amount of capital used is less at (.23. That is K1622} E K "' [Q1}. Under this assumption, how does the amount of labor used to produce each quantity compare, i.e. how does L"(Q2} compare to L\" (Q1 }? I H points ii. Use the bang for the buck equation and the properties above to establish that either (23 or (21 is not produced at minimal cost. 15 points (b) In the consumer problem we assume diminishing marginal utility which says that, along an indi'erence curve, increasing the amount of good a: and decreasing the amount of good 3; decreases the MRS between a: and y, i.e. g: , or in other words indifference cunres are convex. Let's compare the above result to the analogy in the consumer problem: when income increases, consumption of good :i: always increases. i. Evaluate the truth of the statement above. If false, what is diierent about our assumptions in the consumer problem and producer problem that leads to this different prediction. HI points