1. (21 points) Suppose a small firm employs Capital (K) and labour (L) at its !" production of output. The production function of the firm is: = 5 + 10 K + 100#.%. Assume that K=25 in the short run. a. (3 points) What is its short-run production function? b. (6 points) What are the firm's marginal product of labour and average product of labour in the short run? c. (6 points) In the short run, when marginal output is maximized, what is the value of L? d. (6 points) Calculate the short-run elasticity of output with respect to labour when L=10 and K=25 (Hint: the firm's elasticity of output with respect to labour in the short run is a function of marginal product of labour and average product of labour) Question 2 (12 points). Will can produce a higher grade, Gw, on an upcoming economic exam by studying. His production function depends on the number of hours he studies marginal analysis problems, A, and the number of hours he studies supply and demand problems, R. Specifically, & = 2.5A#.!'R#.'(. His roommate David's grade production function is ) = 2.5A#."%R#.*%. a. (6 points) What is Will's marginal productivity from studying supply and demand problems? What is David's? b. (6 points) What is Will's marginal rate of technical substitution between studying the two types of problems? What is David's? Question 3. (16 points, 4 points for each function) Do the following functions exhibit increasing, constant, or decreasing returns to scale? Explain your answers. a. q = aL + bK, where a and b are positive constants. b. The production function Q = 2M 0.5K 0.5L 0.5, where M is materials, K is capital and L is labour. This production function has three inputs: M, K and L. c. q = 2+3L+2K d. = 0.5+/"!/" -Page 1- Questions 4. (12 points) Briefly answer the following questions and explain your answers. a. (4 points) Four years after graduating from college you must decide if you want to go on as an accountant (your college major) or if you want to make a career change and become a singer. Should the cost of your education matter for your decision after you have graduated from college? b. (4 points) You have two career options. You can work for someone else for $50,000 a year, or, you can run your own business, with annual revenue of $100,000, and explicit costs of $40,000 annually. Explain which career option a profit-maximizer would select and why. What are the opportunity cost and economic profit of running your own business? (Hint: economic profit takes into account the opportunity cost) c. (4 points) Simon is given a free ticket to see Coldplay Saturday night. He already has a ticket to see Sting in concert that night. The Sting ticket cost Simon $50 though he would have paid as much as $80 to go to the show. Simon knows that he can easily sell the Sting ticket on Craigslist for $60. What is his opportunity cost of seeing Coldplay? Question 5. (10 points) Suppose the cost of producing milkshakes is C = Q3/3- 3Q2 + 15Q + 50. What is the equation for marginal cost? At what point is marginal cost minimized? "" Question 6 (16 points). A company has a production function, = . It wants to minimize cost for a given production q. The wage rate and rental rate on capital are w and r, respectively. a. Write the Lagrangian expression for the cost minimization problem (3 points) b. Write the first-order conditions (5 points) c. Find the cost-minimizing L and K (5 points) d. Suppose the government provides a subsidy of $5 per unit of capital to the firm. Rewrite the cost-minimizing L and K. (3 points) Question 7. (13 points). Jason invests $5000 in a firm. The firm's production function is #.+ #.- = 10 . Workers cost $20 per unit and capital costs $100 per unit. a. (11 points) If Jason wishes to produce the most output with the finances ($5000) available, how much labor and capital should he employ? Use a Lagrangian method for output maximization to solve this problem. b. (2 points) Does this bundle of capital and labor also minimize the costs