Pleae help to solve the sub question (c), where there is an extra condition for the sophiscated Robinson's two period consumption decision ( No borrowing and Y1>=Y2)

(e) Compute the equilibrium wage and labor from the labor demand and supply curves you have derived (in Questions 3(a) and 3(d))t (f) What will happen to the equilibrium wage and labor if the government raises the income tax rate 7'. Explain using a graph with labor demand and supply curves. (g) As we've discussed in class, people work longer in Hong Kong than in other countries Can this model explain this observation? Explain (Max. 10 sentences). 3 Chapter 4: Goods Market 1. Consider sophisticated Robinson's two-period consumption decision problem. The notations of variables are the same as the slides for Chapter 4' His life time utility is given by U(C1, c2) :lnC1 + 17.02 Here we are assuming discount rate = 1' Budget constraints are given by 01 + B = 16,02 = Y2 + (1 + r) B, in period 1 and 2 respectively (a) Derive the intertemporal budget constraint for Robinson (Hint: Combine two budget constraints to eliminate 3.). Provide the interpretation of the intertemporal budget constraint. (b) Solve the utility maximization problem and derive the optimal level of consumption in each period, 01 and Cg (i.e. Express Cl and C2 in terms of Y1 and Y2 .). (c) Now suppose Robinson cannot borrow. Namely, B 2 0. What is the optimal level of consumption in each period if Y1 2 Y2? Provide intuition for your answert (Hint: With the optimal level of consumption you nd in question (b), what is the implied borrowing B? Does it satisfy the borrowing constraint B 2 0? If not, what is the best for Robinson to do? Is it optimal to set B = 0, namely consuming everything you have in period 1'!)