ECON 310 Problem Set 3 - Python Assignment Instructions: • You have to use Python in order to do this Problem Set. • Please submit the answers to this problem set as a word document attachment via Blackboard i.e., you upload the .docx file. • Copy/paste the graphs/figures you made with Python into this word document and then upload the .docx file on Blackboard. 1 Log Utility Suppose you have the following utility function of a consumer U(C, l) = ln (C XXXXXXXXXXa × ln(l), where C is consumption, l is leisure and a is some preference parameter that tells you how much you like leisure compared to consumption. The maximum time available for work and leisure is XXXXXXXXXXSet l = 0.5, a = 0.3, and plot the utility of consumption over the range C ? [0, 5] 2. Set C = 4, a = 0.3, and plot the utility of leisure over the range l ? [0, 1] 3. Derive this function w.r.t. C. Set l = 0.5, a = 0.3, and plot the marginal utility of consumption for C ? [0, 5] 4. Derive this function w.r.t. l. Set C = 4, a = 0.3, and plot the marginal utility of leisure for l ? [0, 1] 2 Utility Suppose you have the following utility function of a consumer U(C, l) = C a + l (1-a) , where C is consumption, l is leisure and a is some preference parameter that tells you how much you like leisure compared to consumption. The maximum time available for work and leisure is XXXXXXXXXXSet l = 0.5, a = 0.3, and plot the utility of consumption over the range C ? [0, 5] 2. Set C = 4, a = 0.3, and plot the utility of leisure over the range l ? [0, 1] 3. Derive this function w.r.t. C. Set l = 0.5, a = 0.3, and plot the marginal utility of consumption for C ? [0, 5] 4. Derive this function w.r.t. l. Set C = 4, a = 0.3, and plot the marginal utility of leisure for l ? [0, 1] 1 3 Linear Production Function Suppose a firm uses the following production function Y = z × Nd, where Y is output, z is TFP (i.e., technology) and Nd is labor. 1. Set z = 2 and plot the production function over the range Nd ? [0, 5] 2. Derive this function w.r.t. Nd. Set z = 0.5 and plot the marginal product of labor (MPN) over the range Nd ? [0, 5] 4 Cobb-Douglas Production Function Suppose a firm uses the following production function Y = z × K0.3 × N 0.7 d , where Y is output, z is TFP, K is capital, and Nd is labor. 1. Set z = 10, K = 5 and plot the production function over the range Nd ? [0, 5] 2. Derive this function w.r.t. Nd.Set z = 10, K = 5, and plot the marginal product of labor (MPN) over the range Nd ? [0, 5] 3. What does the MPN measure. Explain in words. 2