Assignemnt 1_winter2023

-Page 1- Department of Economics Carlton University ECON2020G. Intermediate Microeconomics I: Producers and Market Structure Winter 2023 Assignment 1. Due at 8:00 pm on February 11, 2023 Total 2 pages with 7 questions Note: Students should show the step-by-step answers to the questions below. If only final answers were provided, NO marks will be counted for the question. Question 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 = 2 M 0.5 K 0.5 L 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࠵? +/" ࠵? !/"