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Microeconomics Practice Questions

Question 1. (18 points)

Note: Students should show the step-by-step answers to the questions above. If only final answers were provided, NO marks will be counted for the question.   

Question 1. (18 points) A firm has the following production function:q=5LK^0.5+2L^2 K-L^3 K
    (4 points) What is its short-run production function if capital is fixed at K=9?
    (7 points) What are the firm’s marginal product of labour and average product of labour in the short run?
   (7 points) Show that 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. Calculate the short-run elasticity of output with respect to labour. 

Question 2 (16 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, G_w=2.5A^0.36 R^0.64. His roommate David's grade production function is G_D=2.5A^0.25 R^0.75.
a. (8 points) What is Will's marginal productivity from studying supply and demand problems? What is David's.
b. (8 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.  q = 2L + 6K

Question 4. (16 points) Answer the following questions and explain your answers.
    (8 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?

    (8 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 the college?

Question 5. (17 points) Consider a firm with the production functionf(L,K)=L^0.5 K^0.5. The wage rate and rental rate on capital are w and r, respectively. 
    (12 points) Use the Lagrangian for cost minimization to derive the long-run cost function for this firm. 
    (5 points) Suppose the government provides a subsidy of $10 per unit of capital to the firm. Rewrite the long-run cost function.

Question 6. (17 points). Jeremy is running a business and his production function is: q=20L^0.5 K. Jeremy is able to accumulate $10,000 to finance the business. Workers cost $10 per unit and capital costs $50 per unit.
a. (12 points) If Jeremy wishes to produce the most output with the finances available, how much labor and capital should he employ? Use a Lagrangian for output maximization to solve this problem. 
b. (5 points) Does this bundle of capital and labor also minimize the costs? 

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