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Problem 3 Megan works in a mall, and can work as many hours per day (up to 24) as she wishes at a wage rate w. Let C be the amount of consumption per day (in dollars, i.e., the price of consumption is I) and let R denote the amount of leisure (in hours, per day). She has utility R"' over leisure and consumption. Suppose w = 10, and she additionally hms SCO in non-labor income she receives (daily) from song royalties. (a) What is Megan's full income (or "implicit inconW' (b) Write Megan's budget equation, and sketch the budget line (with C on the Y mxis). (c) In general, for Cobb-Douglas preferences of the form = with income m and prices and p2, demand for good I is equal to and demand for good 2 is equal to Use this fact to write Megan's choice of R as a function of the wage rate u and the full income, m(u). (d) Given Megan's preferences, how much C and R will Megan choose at the given w = 10? (e) Suppose the wage rate rises to $13_ Draw the new budget line, and solve for Megan's new value of R. Is Megan working more or ICN? (f) Decompose the change in R from into the substitution and the income effert. Note that you cannot use the calculus version of the Slutsky equation, since the change in w is not infinitesimal. (g) Explain the signs of the two effects that you found. You should answer this question even if you didn't solve (f) numerically.