Problem 4. Ricardian Equivalence in a Period of Low Interest Rates (20 points). You are a junior economist at the U.S. Treasury Department. In your first meeting with Treasury Secretary Janet Yellen, she informs you that lump sum taxation is pointless because it is institutionally difficult to collect lump sum taxes from a broad swath of people. After further discussion, you both agree that the "operational" or "working" definition of Ricardian Equivalence (or "quasi-Ricardian Equivalence") is: "Holding constant the flow of government spending across time periods, Ricardian Equivalence occurs if period-one private consumption ci does not change despite a change in the timing of proportional asset taxation between period I and period 2. " Secretary Yellen asks you to attempt to design a tax system that satisfies this modified version of the Ricardian Equivalence Theorem. Neither lump-sum taxes nor consumption sales taxes can be used in the tax system you attempt to design. However, asset taxes (aka, wealth taxes) imposed on the private sector can be used. More precisely, the new policy tools available for the design of the tax system are: 7: period-1 tax rate on end-of-period-1 (aka, beginning of period-2) private-sector assets a, . I w.2 : period-2 tax rate on end-of-period-1 (aka, beginning of period-2) private-sector assets a, . The period-1 and period-2 budget constraints of the representative consumer are: G+ (1+7,)a, = >+(1+r)a. C ta, = V2 + (1+72 )a, +ra, The period-1 and period-2 budget constraints of the government are: g, +h, = ta, + (1+r)b, g2 thy = Tw.za, + (1+r)b, Macroeconomic Theory and Policy - Midterm Exam | @ Sanjay K. Chugh 13 Problem 4 continued Because interest rates have been low the last several years, suppose that the real interest rate is r = 0. Both the representative agent and the government begin period I with zero net wealth (i.e., a. = 0 and b, = 0), and, as usual in a two-period analysis, both a, = 0 and b, = 0. Both the private sector and the public sector are free to borrow or lend as much as needed during the course of period 1. All of your tax-policy analysis is conducted at the very beginning of period 1. a. (6 points) At the very end of period 1 (aka, the very beginning of period 2), what is the sum a, + b, ? (NOTE: The solution for a, + b, is a precise numerical solution; if your solution for a, + b, is not a precise numerical solution, you may be awarded ZERO points.) (HINT: There is no international trade or international finance in this framework.)