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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