1. Set up the Lagrangian for the household's optimisation problem and find first-orderconditions.2. Use the budget constraint to replace c in the first-order condition to obtain a singleequation that relates the household's choice of I to w and T.3. Suppose that the government uses all the tax revenue to hire emergency front-linehealth workers to help during the COVID-19 pandemic. The government pays theseworkers the prevailing wage rate. How much time (in units) can the government affordto purchase from the workers? Denote this number by m. 3 Supply side (weight 5%)An economy is populated by a representative household with the following preferences:u(c) + v(l),where consumption is c and lis leisure. The household has 1 unit of time so its budget isc=w(1-1)-T,where w is the wage rate and r is a tax that the government collects. Notice that 7 is alump-sum tax, not an income tax: the household must pay the same amount regardless ofhow much income it earns.1/₂T1"IViFigure 1: Consumption across two periods

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3 Supply side (weight 5%) An economy is populated by a representative household with the following preferences: u(c) +v(1), where consumption is c and I is leisure. The household has 1 unit of time so its budget is c=w(1-1)-T, where w is the wage rate and r is a tax that the government collects. Notice that is a lump-sum tax, not an income tax: the household must pay the same amount regardless of how much income it earns. S 9/2 I 9/1 Figure 1: Consumption across two periods

3 Supply side (weight 5%) An economy is populated by a representative household with the following preferences: u(c) +v(1), where consumption is c and I is leisure. The household has 1 unit of time so its budget is c=w(1-1)-T, where w is the wage rate and r is a tax that the government collects. Notice that is a lump-sum tax, not an income tax: the household must pay the same amount regardless of how much income it earns. S 9/2 I 9/1 Figure 1: Consumption across two periods

ECON MACRO

5th Edition

ISBN:9781337000529

Author:William A. McEachern

Publisher:William A. McEachern

Chapter11: Fiscal Policy

Section: Chapter Questions

Problem 1.7P

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