¡Descarga Impact of Interest Rates on Aggregate Demand and Investment: IS-LM Analysis - Prof. 855 y más Apuntes en PDF de Administración de Empresas solo en Docsity!
Universitat Pompeu Fabra Introduction to Macroeconomics Academic year 2013- 2014 Professors: Fernando Broner, Teresa García-Milá, Danilo Guaitoli, María Gundín-Castro Problem set 3 SECTION 1: CHOOSE THE CORRECT ANSWER (JUST ONE)
- If the exogenous variables in the IS relation, such as taxes and government spending, are constant, then and increase in the interest rate will: a) increase investment b) increase output c) not affect output d) decrease output d) is the correct answer: aggregate demand ZZ = c0 + c1(Y-T) + I(i,Y) + G where investment I is decreasing in the interest rate i and increasing in income Y. An increase in i shifts aggregate demand downwards. Since aggregate supply adjusts to aggregate demand, in order to have an equilibrium in the goods market (demand = supply) aggregate supply must reduce to Y’. This is why the IS curve is downward sloping.
- If government spending and taxes increase by equal amount, then the a) IS curve will shift to the left b) IS will not shift c) IS will shift to the right d) LM curve will shift to the right c) aggregate demand is ZZ = c0 + c1(Y-T) + I(i,Y) + G where c1, propensity to consume, is 0 < c1 < 1. An increase in G increases aggregate demand by an amount ΔG. But an increase in T reduces aggregate demand by an amount c1 x ΔT. Therefore the total effect on aggregate demand is ΔZZ = ΔG - c1 x ΔT. If ΔG = ΔT = Δ, then ΔZZ = (1 – c1) Δ. Since 0 < c1 < 1, 1 – c1 is still positive and ΔZZ > 0, meaning that aggregate demand finally increases and the IS curve shifts to the right.
- Suppose the relationship between investment, sales and interest rate is described by : I = aY +bi, where 1> a > 0 and - 1 < b < 0 are two parameters capturing the magnitude of the effect of a change in Y and i on the level of investment. What happens to investment when i decreases? a) decreases by Y times a b) increases by i times b c) it falls to zero d) it does not change b) I = aY +bi, a unitary change in i affects I by an amount b (the derivative of I with respect i is b). If the change in i is Δi < 0, ΔI = b x Δi which is positive as both b and Δi are negative.
- IS is a downward sloping function because: a) When interest falls so does investment, such that production must increase for equilibrium. b) When interest falls so does money demand, such that production must increase for equilibrium. c) When interest falls investment increases, such that production must increase for reaching equilibrium. d) When output falls, interest rate must increase for stimulating Investment. c) investment I is decreasing in the interest rate i and increasing in income Y. See answer to question 1.
- LM has a positive slope because: a) facing an increase in income, Md^ increases and interest rate must decline. b) facing an increase in income, Md^ increases and interest rate must grow. c) as interest rate increases, also does income, so Md^ must increase. d) as interest rate increases, also does income, so Md^ must decrease. b) money demand Md^ = Y L(i) where L is a decreasing function in i because the interest rate represents the opportunity cost of holding money. A higher interest rate makes buying bonds more appealing while holding money is less convenient. However money demand is increasing in income Y, as it is positively related to the level of transactions of the economy. So, an increase in income increases money demand which is now higher than money supply. Given that money supply is fixed, in order to reach again the equilibrium in the financial markets, the increase in money demand must be offset by an increase in the
- Government policy can increase output without changing the interest rate only when a) both monetary and fiscal policies are used b) a contractionary fiscal policy is used c) an expansionary monetary policy is used d) an expansionary fiscal policy is used a) except for very extreme cases, when one or both the IS and LM curves are horizontal or vertical, both monetary and fiscal policies, if implemented alone, affect also the interest rate. The only way to increase output without changing the interest rate is to combine a monetary policy with a fiscal policy.
- Consider the fiscal multiplier. The effect of an increase in autonomous spending on the equilibrium outcome will be lower when the sensitivity of investment to interest rate is a) low b) equal to the propensity to consume c) high d) equal to one c) let’s assume I = I0 + d1Y – d2i where d1,d2 > 0. d2 is the sensitivity of investment. The equilibrium condition in the goods market is Y = c0 + c1(Y-T) + G + I0 + d1Y – d2i. In order to have an expression for the IS, we solve the previous equation for i: i = [c0 – c1T + I0 + G]/ d2 – Y(1 – c1 – d1)/d2. The bigger is d2, the flatter is the IS curve. Therefore an increase in autonomous spending shifts the IS to the right. The final effect on the equilibrium level of income Y* will be smaller the flatter is the IS, so the larger is d2.
- Consider the IS-LM model. Suppose that in this economy the government decides to adopt an expansionary fiscal policy. What happens to the LM curve? a) it becomes vertical b) it goes down c) it goes up d) it is not affected d) a reduction of taxes T or an increase in government spending G (or both) do not affect money demand, and so the LM curve is not affected. An expansionary fiscal policy affects only the IS curve.
SECTION
- Watch this video and answer the following questions: http://economia.elpais.com/economia/2014/01/08/agencias/1389191321_583855.html 1.1 When, on January 9th 2014, Mario Draghi, president of ECB, refers to keeping ECB interest rates unchanged. Is he referring to nominal interest rates or to real ones? Explain He is referring to nominal interest rates, which are those under control of the monetary authority, the European Central Bank. 1.2 He says underlying price pressures in the Eurozone are Ok. Explain Mario Draghi explains that according to ECB analysts inflation over the medium term is under control and in line with the ECB target. Future prospects of inflation revised with the most updated information seem to validate previous evidence and to confirm the expectations of ECB analysts. As a consequence, ECB will keep the current interest rates levels unchanged. 1.3 He also mentions the midterm worry for inflation and the aim of his institution for ensuring price stability in both directions. 1.3.1 What is he referring to when saying “both directions”? He is referring to the risks of inflation on the one hand, and of deflation on the other. The objective of ECB is price stability, e.g. to keep inflation stable at a rate below, but close to, 2% over the medium term. 1.3.2 Which kind of monetary policies should the ECB apply in each of both directions? In case of deflation, the ECB should run an expansionary monetary policy in order to stimulate demand and avoid a deflationary spiral. Therefore the ECB should cut interest rates through open market operations (buying bonds) and so injecting liquidity in the financial system. In case of an inflation rate higher than the medium term target, the ECB has to slow down the overheating economy, by running a contractionary monetary policy. When a booming economic growth cannot be sustained by the productive capacity of the economy and this generates an excessive aggregate demand, the monetary authority must counteract the price pressures by tightening the monetary policy. So, interest rates are increased and the central bank withdraws liquidity.
- Imagine that the Central Bank of the euro area publishes in its annual report the following information: the currency ratio c (the fraction of the total quantity of money that agents hold as currency) is 20%, the monetary base H is 40.000 €, and the total money supply M is 100.000 €. It also says that nominal GDP (€Y, or PY) in the area is 1.000.000 € and, according to the central bank estimates, the aggregate money demand function is Md^ = €Y (0,2 – i), where i is the short-term nominal interest rate. 1.1 What is the short-term nominal interest rate i? If nominal GDP decreases to 800.000 €, what happens to the interest rate? From Md^ = M we have that €Y (0,2 – i) = M so that i = 0.2 – M / €Y. So iold^ = 10% while inew^ = 7.5%. Therefore i decreases. 1.2 Derive the value of the reserve ratio θ (assuming that banks reserves as a fraction of deposits are never higher than the minimum requirements set by the central bank). What is the amount of deposits held by agents in this economy? What is the amount
3.2 Using the financial market equilibrium derive the LM relation ( i as a function of Y) M/P = (M/P) d 5085 / 3 = 1,8Y - 7683 i Solving for i: i = (1,8Y – 1695) / 7683 = 1,8Y / 7683 – 1695 / 7683 = 0,000234Y – 0. 3.3 Now, using IS and LM, solve for the equilibrium real output. Let’s find the intersection point of the two lines, the IS and the LM, we have derived before. Substitute the expression for i obtained in 3.2 into the IS relation. We get Y* = 1354, 3.4 Find the equilibrium interest rate Plug Y* into the equation for i (the LM). The equilibrium interest rate i* = 9,67% 3.5 Find the equilibrium values of aggregate consumption and investment C = 889,1 and I =217. 3.6 Consider that the price level increases from P = 3 to P = 4 (taking price level as given). Calculate the new equilibrium values for Y, i, C, and I. Compare these new values with the ones under the initial lower price level and comment the results. Represent graphically the two equilibria. Y* = 1295, i* = 13,79% C = 874, I = 172, An increase in the level of prices pushes the LM to the left, but it doesn’t affect the IS. Therefore the equilibrium level of Y decreases while the one for i increases. 3.7 Let us check now the effects of fiscal policy on this economy. Go back to P= and see what happens to Y, I, and C when Government expenditure decreases to G=200, that is there is a contractionary fiscal policy. Y* = 1298, i* = 8,35% C = 875 I = 223,
A contractionary fiscal policy shifts the IS to the left, resulting in a new equilibrium with lower Income and lower interest rate than before. 3.8 Let us check now the effects of monetary policy on this economy. Go back to P=3 and see what happens to Y, I, and C when an expansionary monetary policy takes place, that is Money supply = 7000 Continue to assume that G = 200 as in 3.7. Y* = 1387, i* = 2,13% C = 897, I = 290 An expansionary monetary policy shifts the LM to the right, resulting in a new equilibrium with higher income and lower interest rate.
So my take away is that fiscal policy should focus on avoiding precipitous drops in spending via automatic stabilisers in the labour market and by unrestricted block grants at state and local levels.
http://www.economist.com/economics/by-invitation/guest-contributions/automatic-
stabilisers-make-good-fiscal-stimulus
Answer the following questions: 4.1 Why unemployment insurance is considered to be an "automatic stabiliser"? When a recession hits an economy, we usually observe an increase in unemployment and a consequent drop in aggregate demand. The reduction in demand implies that many firms have to cut costs and so lay off part of their employees. Welfare programs to protect the workers, like unemployment insurance, give unemployed workers some purchasing power that they would not have otherwise. That increases the aggregate demand and helps the economy to recover. Those programs, by the way they are designed, are higher when the economy is in recession, introducing in an automatic way a stimulus to the economy when it is more needed, and therefore acting as stabilizers. Such measures are aimed to counteract the decrease in aggregate demand due to the increase in unemployment and are automatically activated during recessions. So, even though people lose their jobs or see the number of hours worked reduced, their consumption is sustained by this special type of insurance. 4.2 How do fiscal policies at the local & state level act as de-stabilisers? Which are the expected effects on a local economy derived from budget cutbacks? Local and state government budget cutbacks can act as de-stabilisers: during recessions as aggregate demand declines and production slows down, tax revenues decrease. Therefore local and state authorities tend to cut spending to avoid deficit. However, by doing so, aggregate demand would decrease even more and the already impaired economic conditions would worsen. Moreover, a weaker aggregate demand could produce further reductions in tax revenues. 4.3 Why do you think the author recommends local grants, proposed by Obama, not to be automatic? Because if these grants were automatic, local governments would have no incentives to balance the budget as they would expect the Federal government to rescue them. And they may be tempted to spend excessively on projects that would not be well targeted to fight unemployment. “ States would certainly learn to game the system” using these resources for other purposes instead of giving stimulus to aggregate demand.
