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EXERCISE Question 1 (IS Curve and Short-run Fluctuation) The IS Curve shows the relationship between short-run output (Y,) and real interest rate (R,) on horizontal and vertical axes, respectively, expressed in percentage. The relationship is given by Y, = a - b(R; - 7), where a, b and 7 (marginal product of capital) are parameters. (a) If the output is at the potential (), = 0) when the real interest rate equals to F, what is the value of a? (b) How sensitive are the economy to the real interest rate? (Hint: Elasticity) (c) Plot the IS curve. Be careful on the values on the axes. (d) Suppose there is a technological advancement shock so that the potential output increases from It = 0 to It = a at the same real interest rate F. What does this represent on the IS curve? Draw the curve. Question 2 (The Multiplier) Recall from the class that if the consumption also depends proportionately on short-run output, namely, C:/Y. = a, + TY. We have the multiplier effect towards the IS curve such that ) = 1Ly [a - b (R. - 7)]. The multiplier is (a) If you want to draw the IS curve with multiplier, compare the slopes of the IS curves with and without the multiplier, what would be your conclusion? What if now, we also have that investment also depends proportionately on short-run output as well, namely, I/Y. = 0 -b(Re - F) + ZY (b) What would happen to the size of multiplier? (c) Is there any restriction on 7 and ?? (d) Facing recession, the government sees that the output drops by $100. The government wishes to restore the output level, what should be the size of tax cut to achieve this? Question 3 (Consumption Smoothing) Why should you take something from the future and consume today? The marginal utility from consuming T-bone steak is 100, 80, 60, 40, and 20 for the Ist, 2nd, 3rd, 4th, and 5th piece, respectively. Suppose you live for 2 periods. In Period 1, you have sufficient income for just 1 piece of steak. In Period 2, you have sufficient income for 5 pieces of steak. Assuming that you can shift the consumption across time without any cost, what should you do? Explain. Question 4 (The Monetary Policy - MP Curve) The MP curve is represented by the real interest rate equation, R = 4 - at, where i, and a, are nominal interest rate and inflation rate, respectively. One key assumption is that, inflation does not adjust quickly, namely, constant. The IS-MP diagram combines IS and MP curves with short-run output (Y,) and real interest rate (R,) on horizontal and vertical axes, respectively. (a) Suppose n = 2% and it = 4%, draw an MP curve. "b) Central banker uses the nominal interest rate as the policy instrument. Seeing the economic boom as the IS curve is shifted rightward, central bank must curb down the economic expansion by increasing the nominal interest rate. Draw two IS curves and two MP curves that exhibit this story.Part I. True/False/Uncertain Justify your answer with a short argument. 1. Paradox of saving occurs when the attempts by people to save more lead to a decline in output and an increase in saving. 2. When mpc increases and investment decreases, goods market equilibrium output increases. 3. If investment is really sensitive to changes in the interest rate (b, large), then IS is flatter and fiscal policy is more effective. (assume: 1= bo - bji ) 4. The price of bonds increases when the interest rate rises. 5. Monetary contraction and fiscal expansion together lead to an increase equilibrium output and interest rate. 6. The money multiplier is always less than 1. Part II. THE MONEY MARKET (all units are trillions of US $) Money Demand: M" = $Y (0.2-1) Nominal Income: $Y = 2000 Money Supply: M' = 300 1. Find M for i = 10% and i = 5%. 2. What is the relationship between i and M". 3. Graph M' and M" and calculate the equilibrium i. 4. Alan Greenspan decreases M' by 50. What happens to money market equilibrium? (solve & graph ) 5. Describe how the Fed changes i in the US. Part III. Money Multiplier Checkable deposits: D" = $900 billion Total money supply: M' = $1800 billion Reserve ratio: 0 = 0.2 Ratio of (CU* / My) : c =0.5 1. Find CUS , R" and D. in equilibrium. 2. Find the money multiplier. 3. Describe 2 different ways the Fed can decrease money supply. 4. If the Fed wants to decrease the money supply by $500 million (in order to raise i), what amount of bonds would it have to sell/buy?Part IV. IS - LM (All units are millions of US dollars) C = 200 +(0.25) YD I = 150 + 0.25Y - 1000 i T = 200 G = 250 (M/P) = 1600 (M/P)" = 2Y - 8000 i 1. Find the equation for aggregate demand (Z). 2. Derive the IS equation. 3. Derive the LM equation. 4. Solve for equilibrium real output, interest rate, C and I. 5. Graph the IS-LM diagram of the above with correct labels. 6. Monetary expansion: Let M' (nominal money supply) increase to 1840. Find equilibrium Y, i, C and I. What happens to Y, i, C and I when the Fed increases money supply through open market operations? 7. Graph part 6 (a new graph starting from part 5). 8. Fiscal expansion: (Continue from part 5) Let G increase to 400. Find equilibrium Y, i, C and I. What happens to equilibrium Y, i, C and I when government spending increases? 9. Graph part 8 (a new graph starting from part 5). 10. There is a sudden drop in consumer confidence and co drops from 200 to 100. How can the government counterbalance the drop in GDP using government spending as a policy instrument?Part I. True/False/Uncertain Justify your answer with a short argument. 1. Suppose interest rates for a one-period deposit are 5% in the US (the home country) and 2% in Canada. Assume that the risk premium in Canada is the same as in the US. This implies that the investor should invest in the US. 2. Dan (a US citizen) pays $160,000 in cash to a US Mercedes Benz dealer for a 2005 SL500 Roadster. The dealer then pays $150,000 to Mercedes Benz of Germany. Mercedes deposits $150,000 in its US bank account. This transaction has increased the US capital account surplus. (Assume there is no statistical discrepancy.) 3. Following a real depreciation, the trade balance necessarily improves. 4. Consider the Mundell-Flemming model of a small open economy. If the government increases taxes, the exchange rate will depreciate. (Assume taxes are lump-sum, not proportional.) In order to bring the exchange rate down to its original level, the Fed should expand the money supply. 5. Compared to the closed economy, a given increase in government spending will cause a larger increase in output in the open economy with flexible exchange rates. (Assume that the two economies start in equilibrium.) 6. In an open economy, fiscal policy is more effective than (or at least as effective as) monetaryPart II. The Goods Market in a Two-Country Model Consider two open economies, Blanchardostan and the Republic of Caballeria. Assume that these countries only trade with each other. Variables with subscript B and variables with subscript C correspond to Blanchardostan and the Republic of Caballeria, respectively. The two economies are characterized by the following set of equations: Ci = coi + chi(Y; -T.) where i = B or C (B for Blanchardostan and C for Caballeria) 1= I T= LY, IM, = imoi + imnYi 8 = 1 1. Derive the expression for equilibrium output Y's as a function of GB and Yc (Note that Yc is exogenous from the perspective of Blanchardostan.) Similarly, derive the expression for Yc. 2. Let: COB = Coc = 200 CIB = CIC = 0.5 I = 250 GB= 114 Gc=120 te= to = 0.4 imos = imoc = 40 imIB = 0.05 imic = 0.3 E = 1 All figures are in millions of US dollars. Calculate the equilibrium levels of output in the two countries. 3. Calculate the trade balance (i.e. the current account) for each country. Is there a trade/current account deficit or surplus in Blanchardostan? In the Republic of Caballeria? 4. Draw a diagram to show equilibrium output and net exports for Blanchardostan. Label the equilibrium output Yo" and the output at which there is trade balance, YTB " 5. Suppose the government of Blanchardostan wants to increase government spending by 147 million. What will be the new equilibrium output levels in the two economies? What is the multiplier in Blanchardostan? 6. Assume that exports are exogenously given from now on. What is the open economy multiplier in Blanchardostan? Suppose the two economies decide to close. What is the multiplier in Blanchardostan now, assuming all the other figures remained the same? Compare the different multipliers that you found in parts 5 and 6. Part III. Fixed Exchange Rates Consider a small open economy (call it Mundellia) which obeys our Mundell-Flemming model and is the domestic country. Assume that it has a credible fixed exchange rate regime and starts out in equilibrium. Assume that for Mundellia, US represents "the rest of the world." 1. Use intuition and diagrams to explain what happens in Mundellia as a result of the following changes. a. There is an increase in consumer confidence in Mundellia. b. The US Fed decreases money supply. 2. Discuss the pros (if any) and cons (if any) of the Mundellian fixed exchange rate regime. (Use intuition and your analysis in part 1 to answer this question.)
