uestion Consider a firm with a production function as: y = Ka-a Where K is capital, L is labor, y is output and 0 < a < 1. Assume, that = 0.4. Suppose that each unit of capital costs pk while each unit of labor costs PL. The firm wants to find the cheapest way to produce y units of output. a) Write down the optimization problem for the firm and the corresponding Lagrangian function. Sketch a graphical representation of the problem. Describe, using the graph, the properties of the solution of this optimization problem. [5 marks] b) Write down the first order conditions for this problem and find K*, L* and identify the sign of 1*(no need to compute the exact value). What is the interpretation of ^^*? [10 marks] c) Is there any assumption you need to make about Pk, PL and to make the optimal values of K and L economically meaningful?