Nоte: Pleаse cleаrly lаbel yоur answers submissiоn sheet by section (Parts 1-4) and question number so it is straightforward to grade. Part 1: Modeling the effects of expanded unemployment benefits (33 points, 3 each) In class we showed how the spending of unemployed households responded strongly to the unemployment benefits that were sent out during the pandemic. Let’s use our consumption model to understand some forces that can help explain this and think about implications in our full macro model. As in our PIH modeling in class, assume that the interest rate is zero, households have log utility and do not discount the future. Suppose that someone is currently unemployed but they expect to return to work in the future. Specifically, suppose they have the following income over 3 periods where period 1 is the current period when they are unemployed: Y1=0, Y2=1.5, Y3=1.5. 1) Suppose they are PIH, non-liquidity constrained. What is their consumption today (C1)? 2) Suppose they face the same income as in (1) but are not allowed to borrow (i.e. S>=0), and so they are potentially liquidity constrained. What is their consumption today (C1)? Now let’s explore what happens when this household receives an increase in unemployment benefits today. In particular, suppose that they receive an unemployment check today that raises Y1, so now they have income Y1=3, Y2=1.5, Y3=1.5 instead of Y1=0, Y2=1.5, Y3=1.5. 3) What is C1 with this new income stream? [note: the answer is the same whether we allow them to borrow or not] 4) What is the MPC out of the unemployment benefit in period 1 if households are not borrowing constrained? [Hint: we are comparing question (3) to question (1)]. 5) What is the MPC out of the unemployment benefit in period 1 if households are borrowing constrained? [Hint: we are comparing question (3) to question (2).] 6) True or False (No explanation needed) The presence of liquidity constraints can help explain why unemployed households (who have temporarily low labor income) spend a large fraction of their temporary unemployment benefits. Now let’s imagine that unemployed households think this transfer will last for longer. In particular, instead of Y1=3,Y2=1.5,Y3=1.5, suppose that households think the transfer will continue for a long time and that they will thus have income Y1=3,Y2=3,Y3=3. 7) How much will they consume today, i.e. what is C1? 8) What is the MPC out of unemployment benefits in period 1 if the household is borrowing constrained? [Hint: we are comparing question (7) to question (2).] 9) True or False (No explanation needed): If the expiration of unemployment supplements in August 2020 was unexpected, this could help explain the large spending response to these supplements in the data in June and July of 2020. In the pandemic, the government sent out hundreds of billions of dollars in both expanded unemployment benefits and in stimulus checks. Given the above analysis I want you to think about the relative bang-for-the-buck of stimulus checks vs. expanding unemployment benefits in the way described above. Specifically, suppose that we can either expand unemployment benefits like described above or we can send stimulus checks to everyone in the population. Suppose that we spend $100 billion total on whichever policy we choose: 10) True or False (No explanation). The MPC out of unemployment benefits will be bigger than the MPC out of stimulus checks. 11) True or False (No explanation): Expanding unemployment benefits will shift the IS Curve further to the right and increase output by more in the short-run than if the government instead sent out the same total amount via stimulus checks.