Question 1: Technology, Returns to Scale and Profit Maximization. (25 pts) A firm has a technology which allows it to produce as per the production function: y = f(k,l) = 2k1/211/2, where k is capital and I is labour (two factors of production). Prices of capital and labour are wk = 1 and w1 = 12 respectively, and the price of output is p = 6. (a) Does the production function exhibit constant, increasing, or decreasing returns to scale? (10 pts) (b) Find the marginal products (MP) of each factor and the technical rate of substitution (TRS). (5 pts) (c) Suppose the firm has a fixed amount of capital (fixed factor of production) such that, 7 = 4. Find the factor demand k*, the optimal supply y", and the firm's maximized profit " (Hint: when solving for *, you will need to find the optimal value of k* first by plugging in y*.). Illustrate graphically. (10 pts)