Suggested Solutions to Problem Set 9

Transcription

1 roblem 1: a: Suggested Solutions to roblem Set 9 Figure 1: Effects of Reduced Government Spending in (,)-space Effects of Reduced Government Spending LRAS SRAS AD AD* A B 1 B 2 C Starting from a long-run equilibrium in A (the SRAS, LRAS and AD intersect), the above figure summarizes both the short- and long-run effects of a reduction in government spending, G. The Short-Run: from A to B 1 The reduction in G causes an inward or downward shift of the aggregate demand curve (AD to AD ). This results in a short-run equilibrium, B 1, with lower output ( ) and a lower price level (). Since output and the unemployment rate are inversely related, = (1 u)n, unemployment is higher in B 1. The decrease in the price level has an immediate effect in the money market: it increases real(!) money supply, M s. This outward shift in real money supply is depicted in the money market diagram on the next page (recall: nominal money supply is fixed by the central bank and, therefore, real money supply is a vertical line; nominal money demand, M d, is a downward sloping line, because the interest rate is the opportunity cost for holding money). Again, it is a shift from A to B 1. Notice that the money demand curve does not shift after the change in from A to B 1, because we assumed a simplified money demand function M d = M zi, where M is a constant. The increase in real money supply leads, in turn, to a decrease of the interest rate: agents find themselves holding more money than they want, and they will try to buy bonds with this extra money. That will drive up bond prices and, thus, drive down the interest rate on bonds (recall: inverse relation between the price of an asset and its rate of return). Remark: This and the following diagram is one way to analyze the interest rate effect in the money market. It was carried out in real terms for money demand and money supply. Alternatively, you could have done the analysis in nominal terms. In this case, (nominal) money supply would have stayed unaffected by a change in, but (nominal) money demand would have decreased (the curve shifted down) with a decrease in the price level. 1

2 Figure 2: Money Market Spillover Effects on the Money Market M s /(A) M s /(B 1 ) M s /(C) M d / A i B 1 B 2 C M d /,M s / A decrease in the interest rate will lead to an increase of investment in B 1. Notice that the decrease in government spending is partially offset through the money market mechanism by an increased spending on investment - even in the short-run. We can call this a partial crowdingin. Notice that all these effects would be exacerbated, if the money demand function depended on income,. In that case, decreasing income from A to B 1 would shift money demand downwards, lowering the interest rate and increasing investment even further. Finally, the effect on consumption. Algebra: Recall that C = C + b( T ). In our analysis, T has not changed, by assumption. has decreased, so C decreases as well. Diagram: Figure 3: Multiplier Diagram Consumption Aggregate Expenditure Spillover Effects in the Keynesian Cross A B 2 C, d C a + b(-t)+i+g B 1 C=C a + b(-t) Recall the multiplier diagram: income/output is on the x-axis and consumption - the lower bold line with diamonds - and aggregate expenditure - the upper bold line: d = C +b( T )+ 2

3 I + G - on the y-axis. Equilibrium occurs, where the aggregate expenditure(!) line intersects the 45 degree line (A). A decrease in G in the multiplier diagram means a downward shift of the aggregate expenditure line, d. The new short-run equilibrium occurs in B 1, with a lower level of consumption. Notice that the consumption line never changed ( C and T never changed). Remark 1: C a in the diagram is the same as C (the program did not allow an upper bar). Remark 2: oints B 1 in the (, )-diagram and the multiplier diagram already take into account not only the drop in G, but also the countervailing effects of an increase in aggregate investment. That means: behind the aggregate expenditure line in the multiplier diagram that leads to the short-run equilibrium B 1 there really is a decreased G and an increased I. The following table summarizes the effects of a drop in government spending on all the variables in question (in the short-run: from A to B 1 ): u i I C decline decline increase decline increase decline Changing rice Expectations: from B 1 to B 2 The equilibrium in B 1 is an equilibrium with the same price expectations, e, as the original long-run equilibrium in A. Now we adapt these expectations downward, causing an outward or downward shift of the SRAS curve. This will lead to a new equilibrium in point B 2, for instance. In this new equilibrium the negative effect on the price level will be enforced (we see a further decline), the negative effect on output will be countervailed (we see an increase in output). The other variables can be grouped in two classes: the first group depends on the price level effect, i.e. here the original effect will be enforced: this is the case for the interest rate (declines further) and investment (increases further). ou can see this in the money market diagram for the interest rate, and for investment in the multiplier diagram. The second group depends on the output effect: unemployment will decrease and consumption increase. The latter can again be seen in the multiplier diagram. Notice that the increase in output is matched by the increase of the aggregate demand components, C and I. The long-run: C As the economy moves from point B 2 to point C, its new long-run equilibrium, the same effects as from B 1 to B 2 take place. How does the new long-run equilibrium compare to the old long-run equilibrium? Again, for the price level, the interest rate and investment the effects that took place from A to B 1 and from B 1 and B 2 are re-enforced. For output, the unemployment rate and consumption we have that the initial effects from A to B 1 are fully offset in the long-run: there is no change in these variables. 3

4 Also, we know that G = I, i.e. the decrease in government spending is fully compensated by an increase in private investment spending (crowding-in). Output in both long-run equilibria is the same, taxes and consumption have not changed, so it must be that G = I. Recall: = C + I +G in a closed economy. The following table summarizes how equilibrium C differs from equilibrium A. u i I C no change lower no change lower higher no change b: This question was a difficult one! The difficulty arises because it requires you to put two somewhat different economic models together: the AS-AD model and the theory of Ricardian equivalence/consumption smoothing. This putting together invariably has to be somewhat loose, given the scope of this introductory course. However, it is a good lesson about applying your economic toolbox to the real world. To answer this question, we recall the two-period model with Ricardian equivalence in lecture 10. In the context of this model, it is best to assume that the AS-AD model and its short-run implications are a good model about the first period of this two-period model. To keep the analysis as close as possible to the analysis in lecture slides 10, suppose that does not change (the reality is more complicated, but also more difficult to analyze). Recall the two equations necessary for the Ricardian equivalence argument, the definition of average disposable income and the balanced budget: Ȳ di sp = ( 1 T 1 ) + ( 2 T 2 ), (G 1 T 1 ) + (G 2 T 2 ) = 0. 2 In the text you were given that: T 1 = 0 and G 2 = 0, so that a balanced budget requires: G 1 = T 2. Also, assuming that 2 = 0, average disposable income increases by T 2 2 = G 1 2. Ricardian equivalence implies that in the short-run consumption, C 1, would go up with an increase in average disposable income, by G 1. But this would lead to a mitigated inward or 2 downward shift of the AD curve in the short-run, compared to 1a. oint B 1 would have higher output and price level, compared to 1a. Since all other effects are derived from either the change in or, they would be mitigated as well. To sum up: the short-run effects in 1a would qualitatively still be present, but quantitatively muted. 4

5 roblem 2: a: Housing wealth is a large part of the total wealth of a typical U.S. household. Since decreasing housing prices (and thus decreasing housing wealth) lead to lower consumption - because households cannot borrow as much against their wealth -, an ensuing decrease in aggregate consumption could lead to a recession: lower output and lower price level. The strength of this recession depends on the strength of the link between wealth and consumption as well as countervailing parallel developments, like falling oil prices. b: The analysis of a drop in C is almost(!) identical to the analysis in 1.a. The (, ) diagram and the money market diagram display the same movement of curves. Only the multiplier diagram is different in that now not only the aggregate expenditure line shifts downward, but also the consumption line (the one with diamonds). Notice that the consumption line shifts downward by more than the aggregate expenditure line, because we recall that in point B 1 aggregate investment has increased (money market mechanism). Aggregate investment shifts the aggregate expenditure line ( d ) partially back, but not the consumption line. Figure 4: Multiplier Diagram Consumption Aggregate Expenditure New Consumption New Aggregate Expenditure Spillover Effects in the Keynesian Cross A C, d B 1 In the long-run we have: and u are unchanged. and i have decreased. I has increased. Aggregate consumption has decreased by the same amount that I has increased: C = I. Remark 1: Whereas in question 1 the decrease in government spending lead to a compositional shift in aggregate spending from G to I, now we have a compositional shift in aggregate spending from C to I. Remark 2: Since is unchanged (and so is T by assumption) we also know that the change in consumption was completely caused by the drop in autonomous consumption. The nonautonomous part of consumption that depends on current disposable income has not changed between the two long-run equilibria; it increases back from B 1 to C. 5

6 Question 3. A B C D E F 1 Total roduction by Country () 2 US (financial services) China (manuf. goods) Saudi Arabia (oil) Who consumes what? World 7 US China SA roduction 8 Financial services Manuf. goods Oil Consumption (C) Exports (X) Imports (M) Net exports (NX = X-M) roduction ( = C + NX) There are three countries and three goods produced in this economy. We know that each country produces only one good, so its total production () corresponds to the production of the corresponding good it produces. Cells C2, C3, and C4 give the total production (in US$) of US, China, and Saudi Arabia, respectively, as given in the problem. Next, we observe the amounts consumed of each good by each country (cells C8:E10). Column F, rows 8-10 shows the total world production of each good, which is just the sum of the amounts consumed by all three countries. All of the information up to here is provided in the problem. With this information we can calculate consumption (C) in each country, which is not required by the problem but it is easy to calculate and can help us calculate GD (production) later to make sure our calculations are correct. Consumption for each country is just the sum of the amount of financial services, manufacturing goods, and oil that it consumes, regardless of where these goods are produced. So, C = 1200 for the US, 250 for China, and 250 for Saudi Arabia, as shown in cells C11-C13. Then in rows 13 and 14 we calculate exports (X) and imports (M) for each country. Exports corresponds simply to the total amount produced by each country that is not consumed domestically and is sold abroad. For example, the US produces $1000 worth of financial services but pays $700 for domestic consumption of these financial services, and the remainder $300 are consumed abroad--so X = 300 for the US. On the other hand, imports (M) correspond to the dollar value of goods and services that are produced abroad but consumed domestically. Again, in the case of the US, the country consumes $300 worth of manufacturing goods produced in China and $200 in oil produced in Saudi Arabia. The sum of these two items are total imports (M = 500). Finally, we can calculate nex exports (NX) as the difference between exports and imports (X-M). The results are shown in row 16. Note that the sum of NX for all countries is equal to zero because the world is a closed system. As a quick check of our calculations, we can verify that GD = C + NX (because I = G = 0 in this problem) is equal to the original production number we had for each individual country. Note that the numbers in cells E18:G18 are equal to the original numbers given in C2:C4.

7 roblem 4. (a) Just read. (b) 1 USD = 10 RMB (yuan) and 1 USD = 0.7 EUR Then, 1 EUR = 1 EUR * 1 USD/0.7 EUR * 10 RMB / 1 USD = 10/0.7 RMB = RMB. So, exchange rate (XR) is RMB/EUR. Equivalently, if we would like to write the exchange rate in terms of yuan: 1 RMB = 1/14.29 EUR. So the XR = 0.07 EUR/RMB. Note: these are nominal exchange rates. (c) Big mac prices: 1.5 USD in US; 18 RMB in China; 1.2 EUR in Europe. RER = e/*, where e is the nominal exchange rate in terms of the home currency, are local prices and * are foreign prices. For each pair, the second country denotes the home country. CHN - USA: RER = e/* = 10 RMB/USD * 1.5 USD / 18 RMB = EUR - USA: RER = 0.7 EUR/USD * 1.5 USD / 1.2 EUR = CHN - EUR: RER = RMB/EUR * 1.2 EUR / 18 RMB = Thus, for neither pair does hold exactly because the RER is always different from 1. (d) Assume holds, then RER = 1 for each pair. Again, second country in pair is home country. CHN - USA: 1 = e * 1.5 USD / 18 RMB ==> e = 12 RMB/USD

8 EUR - USA: 1 = e * 1.5 USD / 1.2 EUR ==> e = 0.8 EUR/USD CHN - EUR: 1 = e * 1.2 EUR / 18 RMB ==> e = 15 RMB/EUR (e) Comparing the actual exchange rates computed in part (b) and the exchange rates predicted by as calculated in part (d), we can tell which currency will appreciate in the long-run according to theory. If the actual rate is lower than the predicted exchange rate, then the home currency is the one that must appreciate according to (remember that the exchange rate is given in terms of the home currency and that the second country in the pair is assumed to be the home country). So, air Actual XR redicted XR () Currency that appreciates CHN USA 10 RMB/USD 12 RMB/USD USD EUR USA 0.7 EUR/USD 0.8 EUR/USD USD CHN EUR RMB/EUR 15 RMB/EUR EUR