Please show the calculations used to arrive at your answers. Draw graphs neatly and label axes and points clearly. In general, leave numbers in fractional form while solving problems. Round final answers to the first decimal place if necessary. A. Jacobson Inc. produces paper clips using the following production function: G = 50K+ 20L 0 = units of output, K: units of capital, and f. = units of labor Capital costs $80 a unit and labor costs $40 a unit. 0 sells for $2 a unit. (1) Does the production function exhibit increasing, constant, or decreasing returns to scale? Explain. (2) Graph two isoquants. (3) What is the marginal product of labor? (4) Write down the profit function for Jacobson. (5) How much labor should Jacobson buy? B. Tran Industries produces output 0 according to the production function 0: 6K 7/31. 7/2 , where K = units of capital and L = units of labor. Capital costs $2 a unit and labor costs $6 a unit. 0 sells for $30 a unit. (1) a. What is the marginal product of capital? b. What is the marginal product of labor? c. What is the technical rate of substitution for Tran? d. What is the optimal ratio of capital to labor for Tran? (2) a. Write down the profit function for Tran. How do we know that there is a unique profitmaximizing output? b. Write down the two conditions for Tran to maximize profits. (3) a. How much capital and labor will Tran use? b. How much output will Tran produce? What will its profit be? (4) If Tran were not allowed to purchase more than 79,507,000 units of capital, now what would your answers to (3) be? [Hint: Think carefully about whether or not your answer to (1) d. is still valid in this case]