Economics Problems: Intertemporal Budget Constraints, Interest Rates, and Capital Markets, Assignments of Economics

Download Economics Problems: Intertemporal Budget Constraints, Interest Rates, and Capital Markets and more Assignments Economics in PDF only on Docsity! Jason DeBacker ECON 4020 Problem Set #5 Solutions 1. Chapter 16, Problems and Applications (6 points): #2, #4 • #2 (a) We can use Jill’s intertemporal budget constraint to solve for the interest rate: C1 + C2 1 + r = Y1 + Y2 1 + r 100 + 100 1 + r = 0 + 210 1 + r The interest rate that makes this budget constraint hold is r = 10%. Jill borrowed $100 for consumption in the first period and used her second period income to pay $110 on the loan ($100 in principle and $10 in interest) and $100 for consumption. (b) The rise in interest rates leads Jack to consume less today and more tomor- row. This is because of the substitution effect: it costs him more to consume today than tomorrow, because of the higher opportunity cost of forgone in- terest. By the principle of revealed preference, we know that Jack is better off: at the new interest rate he could still consume his $100 in each period, so the only reason he would change his consumption pattern is if the change makes him better off. (c) Jill will consume less in the first period. She faces both an income effect and a substitution effect. Because consumption today is more expensive, she substitutes out of it. Also, since all her income comes in the second period, the higher interest rate raises her cost of borrowing, and thus lowers her income. Assuming consumption in period one is a normal good, this provides an additional incentive to lower consumption in period one and two. We know that Jill is worse off with the higher interest rates because her new budget constraint is entirely below her old budget constraint. • #4 (a) Temporary fiscal policy is more potent when borrowing constraints are present. This is because borrowing constraints make it more likely that peo- ple would like to consume more today, but can’t because they can’t borrow against future earnings. Recall that without borrowing constraints, Ricar- dian Equivalence suggests that a temporary tax cut will have no effect on consumption/aggregate demand. (b) Future fiscal policy is less potent when borrowing constraints are present. This is because borrowing constraints make it more difficult to move that future increase in disposable income to today because people may already be borrowing all that they can. 1 2. Chapter 16, “Made up problem”- Fisher 2-period life cycle model (5 points): (a) The intertemporal budget constraint is given by: C1 + C2 1 + r = Y1 + Y2 1 + r C1 + C2 1.05 = 10 + 15 1.05 (b) Given that U(C1, C2) = C 1 2 1 C 1 2 2 , we can solve for the optimal choices of C1 and C2 by using the condition that the slope of the budget line and the slope of the indifference curve be equal at the optimal choice of C1 and C2 and the budget constraint. • Step 1: Find the MRS and set it equal to the slope of the budget line to solve for C2 in terms of C1 and r: MRS = MUC1 MUC2 = 1 2 C −1 2 1 C 1 2 2 1 2 C 1 2 1 C −1 2 2 = C2 C1 The slope of the budget line equals the “price of C1” divided by the “price of C2. Looking at the budget constraint reveals that this is given by 1 1 1+r = 1+r. Therefore, setting the slope of the budget line equal to the MRS we get: C2 C1 = 1 + r, which means that C2 = C1(1 + r). • Step 2: Plug the result of Step 1 ( C2 = C1(1+ r)) into the budget constraint: C1 + C2 1 + r = Y1 + Y2 1 + r C1 + C1(1 + r) 1 + r = Y1 + Y2 1 + r C1 + C1 = Y1 + Y2 1 + r =⇒ C1 = Y1 + Y2 1+r 2 =⇒ C1 ≈ 12.14 • Step 3: Plug the result of Step 2 into the result from Step 1: C2 = C1(1 + r) = 12.14 ∗ 1.05 = 12.75 Since C1 > 10, the agent is a borrower. (c) If borrowing is not allowed (i.e. S ≥ 0), then the optimal choices become C1 = 10 and C2 = 15. (d) With the borrowing constraint, raising income in period 2 has no effect on con- sumption in period 1, but raises C2 to 20. (e) In this case, follow Steps 2 and 3 from part (b) above to find that C1 becomes approximately 14.52 and C2 becomes 15.25. 3. Chapter 17, “Made up problem”- Neoclassical Model of Investment (4 points): 2 (c) When the interest rate, i, increases, velocity also increases. As people hold less money to make the same about of expenditures, it must change hands faster. (d) When the price level increases, nothing happens to the velocity of money (P is not in the equations for velocity in parts (a) or (b)). This is because a change in the price affects both nominal money holdings and nominal expenditures equally. (e) As the economy grows, Y increases. But as the economy grows, wages also increase. In the Solow growth model (from Chap 7) we see that wages go up at the same rate as GDP. Thus, F , the cost of going to the bank will also increase (because wages are higher, it is more costly to waste time in line at the bank- the opportunity cost being measured in foregone wages). So F and Y may increase at the same rate, meaning no change in the velocity of money. (f) If the number of trips to the bank is fixed, then (a) says that the velocity of money will not change. 5. Chapter 19, Problems and Applications (6 points): #1, #2, #3 • #1 – In response to temporary good weather, Crusoe will work more. Because he is more productive with the nice weather, he substitues towards more labor today and less labor in the future (intertemporal substituion of labor). – In response to permanantly better weather, it is unclear what Crusoe will do. There is no intertemporal substituion because he will be just as produc- tive today as tomorrow. The income effect says he will work less, since he is not richer (permantly more productive), but the substituion effect says he’ll work less (because he’s more productive the opportunity costs of lesuire is higher). It’s unclear which of these effects will dominate. • #2 (a) If output increases, then prices fall (you can see this by thinking about the new eq’m in the AS/AD model after the veritcal supply curve shifts to the right). If output falls, then prices increase. That is, there is a negative rela- tionship between P and Y . (b) As output increases, so does the money supply. As output falls, the money supply contracts. That is, there is a positive relationship between the money supply and output. (c) The correlation between the money supply and output is not evidence against RBC theory. If the Fed follows the rule of part (b) where they try to maintain constant prices, then we will see such a positive relationship between the money supply and output in an economy where fluctuations are caused by shifts in productivity. • #3 (a) Draw the normal form game by making a box with four quadrants. In the top left will be the outcome “work hard, work hard” with payoffs of $80 for players one and two. In the bottom right, will be the outcome “be lazy, 5 be lazy” with the payoffs of $60 for both players. In the other two corners, will be the outcomes where one player works hard, but the other is lazy. In these boxes, the payoff for being lazy when the other is working is $70. The payoff for working when the other is lazy is $50. (b) Andy and Ben would prefer that both work hard so they each get the max- imum payoff, $80. (c) If Andy expects Ben to work hard, then Andy’s best strategy is to also work hard. If Ben expects any to work hard, then Ben’s best strategy is to also work hard. Thus working hard is an equilibrium; if each player expects the other to work hard, then both players will work hard and satisfy each other’s expectations. (d) If Andy expects Ben to be lazy, then Andy’s best strategy is to also be lazy. If Ben expects any to be lazy, then Ben’s best strategy is to also be lazy. Thus being lazy is an equilibrium; if each player expects the other to be lazy, then both players will be lazy and satisfy each other’s expectations. (e) Yes because businesses are likely to need coordination among the employ- ees. No because it wouldn’t be too difficult to coordinate with just one other person, so coordination failures would be rare. Also, most business partnerships involve repeated interactions, making coordination easier to obtain. 6