0 and b > 02Namely, his utility is increasing in consumption C but decreasing in labor L: His budget constraint (inreal terms) is the following:wC= L T(1)Pwhere T are taxes paid to the government. These taxes are levied both on consumption (think of it asa VAT tax) and on labor income. Namely:T=whereWandCWwL+PCC(2)are, respectively, the tax rates on labor income and on consumption.Answer to the followings.(a) Taking into account the budget constraint (1) and taxes (2), compute the derivative of U withrespect to L and set it equal to zero (this is the household? optimality condition)s(b) Using the expression found in a., derive an expression for the supply of labor as a function ofthe tax rate on labor income W and tax rate on consumption C:wP;(c) Plot the expression you have found in b. (this is the labor supply curve) in a graph with the realwage on the vertical axis and labor on the horizontal axis. Show what happens when:1.2.WCincreasesincreases7. Nominal and In?ation-Indexed Bonds (15 Points) Some of the bonds issued by the US Treasuryare in?ation-indexed. Answer to the followings.(a) Explain the di?erence between an in?ation-indexed bond and a regular (non-in?ation-indexed)bond.(b) From a household? point of view, which of the two is riskier? Explains(c) Explain why one way to measure expected in?ation is to look at the di?erence between the returnon an in?ation-indexed bond and the return on a regular bond.8. Consumption and Savings (15 Points)Consider the 2-period model. Assume that the household has the following utility:U (C1;C2) = ln C1 +ln C2(3)where is the discount rate: To simplify the notation, let Y1 be (real) labor income in period 1, and Y2be (real) labor income in period 2. The budget constrains in period 1 and period 2 are, respectively:C1 + S1C2= Y1= Y2 + (1 + i1) S1T2where T2 are taxes paid in period 2, and equal to:T2 =S(1 + i1) S1In other words, in period 2 the household has to pay a tax on his savings. Think ofassets.Derive the optimal consumption ratiowhat happens when S increases?C2C1Sas a tax onshowing how it depends on the tax rate on savings. Namely29. Seignorage (25 Points)Suppose that real money demand is given by the following expression:L (Y;i) =aY;for a > 0 and b > 0biwhere Y is output (or income) and i is the nominal interest rate. Let? de?ne seignorage - that is, thesreal revenue to the central bank from money printing - as follows:S=L (Y;i)where > 0 is the (net) rate of money growth (chosen by the central bank). Assume that the realinterest rate r is given and that in?ation is equal to:Answer to the followings.(a) Write the equation for the nominal interest rate i:(b) Derive an expression for S as a function of:(c) Compute the derivative of S with respect to:(d) Plot S in a graph, with S on the vertical axis andcurve for S? Brie? explain why or why not.
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