1) (25 pts) Suppose the firm uses two inputs to produce its output: capital (K) and labor (L). The firm's production function is q 5051/217/2 The prices of capital and labor are r = 2 and w = 8. a) Does the production function display decreasing, constant, or increasing returns to scale? How do you know, and what does this mean? b) Draw the isoquants for the firm's production function, using the y-axis for K and the x-axis for L. How are the factors K and L? c) Derive the expansion path equation. Represent it graphically. How does the expansion path change when r = 1 and w = 8? d) Find the total cost function (Cost as a function of quantity). e) Represent in a diagram the firm's cost minimizing choice of factors to produce a given quantity q. If q =1000, how much K and L are used