a) Do a qualitative plot of U (h;T, 1}, A,l9, w) as a mction of the hours It for A = 2. If it helps, assume in = 20, T = HI], 9 = 1, and \"q = 1. Provide an interpretation for the parameter A. b) Do a qualitative plot of U (h; T, n, A, 9, m) as a function of the hours It for A = 1. If it helps, still assume in = 20, T = 100, 9 = 1, and n = 1. This is the utility flmction of Hank, a cab driver with a standard utility function (though with gain utility). c) In the next two points, we consider the mam'rnization problem of Hank, the standard cab driver, who wants to determine the optimal number of hours worked hf}. Maximize the utility function U (h; T, n, A, 9, m) , keeping in mind A = 1 for Hank. (Do not make any other assumption on the other parameters) Plot the resulting solution h}, = h}, (wk?) assuming a: = 20, T = 100, 9 = 1, and n = 1 and explain why this is Hank's labor supply function. Does the labor supply curve for Hank depend on '1}? Comment. d) Suppose that an econometrician observes repeated draws (hg, mm) from Hank's labor supply and estimates the labor supply mction with an OLS regression: hm = or + 51911: + E:- What estimates does the econometrician get for a and for ,8? Provide intuition on the sign and magnitude of the coefcients. Is the model well specied? e] Now we go back to the case of Colin1 with A = 2. Maximize the utility function U (h;T,n,A,9,m), keeping in mind A = 2 for Colin. This is harder than for Hank, keep in mind corner solutions (Hint: Distinguish three cases). f) Do a qualitative plot of the resulting solution hf: = hf; (w|T, 6', 1}, A) . Assume w = 20, T = 100, 9 = 1, n = 1, and A = 2. Compare Colin's labor supply flmction with Hank's and comment on the differences