A firm uses capital K and labour L to produce output q according to the following production function: q = J? + L Let w denote the price of each unit of labour and r denote the price of each unit of capital. a.) Does this production function exhibit constant, increasing or decreasing returns to scale? Explain your answer. (1 Point) b.) Derive a formula for this firm's expansion path in terms of w and r. You can assume that q 2 fr. Provide a brief description of this expansion path and illustrate it with an appropriate diagram. (4 Points) c.) In the case of q 2 :7 determine the cost function C(q) of the firm as a function of output q, the wage w, and the cost of capital r. (2 Points) d.) Suppose that w = 8 and r = 1. How much of each input should the firm use to produce an output of q = 2? Illustrate your answer with an appropriate diagram. (3 Points)