Homework 7 For this assignment the production function is the one used in Lectures 12 and 13, namely: = 2/5 2/5 1. For the first question, use the above production function and with the price of output, P, being $200 and the price per unit of labor and capital inputs being $4 (that is, w = v = 4). Solve for the profit maximizing output level and levels of input usages. Show all work (to solve this you have to find the conditional factor demand, then find the cost function, then find the marginal cost function, then set MC=P to solve for profit maximizing output, then plug this output into the conditional factor demands to find optimal input usages). Create a graph (with quantity of capital on the vertical axis and quantity of labor on the horizontal axis) of the equilibrium isocost line and isoquant. These will be tangent where input usages are optimal. 2. For this question, v and P are the same as in question 1, but w falls to $3. Solve for the profit maximizing output level and levels of input usages. Show all work (to solve this you have to find the conditional factor demand, then find the cost function, then find the marginal cost function, then set MC=P to solve for profit maximizing output, then plug this output into the conditional factor demands to find optimal input usages). Create a graph (with quantity of capital on the vertical axis and quantity of labor on the horizontal axis) of the equilibrium isocost line and isoquant. These will be tangent where input usages are optimal. 3. Create a graph combining the graphs you created for problems 1 and 2. The change in the equilibrium point from problem 1 to problem 2 is the total effect. Your job now is to break this total effect down into the substitution and scale effects. To find the substitution effect you need to use these two equations: first, the equation of the equilibrium indifference curve for problem 1; and, second, the equation of the tangency condition used in problem 2. The scale effect is the remainder of the total effect not explained by the substitution effect. On the graph you created for this problem, show the substitution and scale effects that you have calculated.