PS 6 SOLUTIONS

 

1. True or False (3 points each 18 total)

 

  1. False. Under a fixed exchange rate regime, interest rates are fixed. Therefore, an increase in G will not crowd out investment, and the increase in Y will be larger than under a flexible regime.

 

  1. True. Under a fixed exchange rate, the central bank cannot conduct monetary policy. It must instead allow the money supply (and interest rates) to fluctuate in order to support the fixed E and keep the interest parity equation in balance.

 

  1. True. A large expected depreciation in the future will tend to increase today's exchange rate (a depreciation of the currency.) This will boost net exports and increase production (shift of IS to the right) until a new equilibrium is reached.

 

  1. False. As you can see in the interest parity equation (i = i* + (Ee - E)/E), a rise in Ee with E fixed will lead to an increase in the level of interest rates and will decrease output (shift of the LM to the left).

 

  1. False. If money supply increases and the interest rate goes down, this will weaken domestic currency. (E goes up a depreciation of the domestic currency.)

 

  1. False. The term refers to budget and trade deficits.

 

2. Open Economy IS-LM (40 points total)

 

  1. (3 pts) Yes. NX = (30 + 0.2Y*)E - 10 - 0.4Y. Therefore, NX is increasing in E.

 

  1. (2 pts) Goods market equilibrium, with i and E fixed:

Y = 24 + 0.4(Y - T) + 80 - 50i + G + (30 + 0.2Y*)E - (10 + 0.4Y)

Y = 100 - 50i + 50E

 

  1. (2 pts) The goods market multiplier is 1.

 

  1. (2 pts) LM:   80 = Y - 20i

 

  1. (2 pts) The interest parity relation is: i = 0.05 + (1.95 - E)/E.

 

  1. (4 pts) In equilibrium, Y = 100, i= 1, and NX= 0.

 

  1. (2 pts) This is derived from the interest rate parity condition. Your graph should have i on the vertical axis, E on the horizontal axis, and should have curve with i and E negatively related.

 

  1. (2 pts) The LM curve is drawn in i-Y space Y is on the horizontal axis, i on the vertical. The LM is an upward sloping curve, with Y and i positively related, determined from (d).

 

  1. (4 pts) The IS relates Y and i through a negatively sloped curve in the same plane as the LM curve above. When E is larger, the curve shifts more to the right.   

 

  1. (4 pts) G=20 implies Y=110 -50i +50E ; 80=Y - 20i ; i=0.05 +(1.95 - E)/E. Solving this system, one gets E=.95, Y=102.1, i=1.11.

 

  1. (4 pts) If M = 200, then E=2.02, Y=200.3, i=.15

 

  1. (4 pts) If Ee goes up to 2.5, then Y=102.8, E=1.20, and i=1.14.

 

  1. (5 pts) In part (i), your graph should look the same as under flexible exchange rates if E changes due to market fluctuations or due to changes in government policy, the effect on the IS via NX is similar. For part (j), the answer is more complicated. When you had flexible exchange rates in the first part of this question, your 3 endogenous variables were i, Y, and E. Now that exchange rates are fixed, your 3 endogenous variables are i, Y, and Ms . This means that you fix E = 1, Ee = 1.95, G = 20, and all the other variables as before, and solve the system of equations. This gives you, in equilibrium: MS = 90, Y = 110, E =1, NX = -4, and i = 1.

   

 

3. Exchange Rates and Expectations (4 points per question, 12 total)

 

  1. People expect a devaluation to a level where E is equal to 1.09.

 

  1. If the country devalues, E will rise. This will put pressure on the interest parity equation at the moment of devaluation (before i has had a chance to adjust), domestic bonds look more attractive than foreign bonds. This makes foreign investors want to buy domestic bonds they trade foreign currency for domestic at the central bank at the new exchange rate (1.09), driving up domestic money supply. This shifts out the LM, lowering i until i = i* = 0.6. This drop in interest rates will push investment up (moving along the IS curve) and therefore output will increase.

There is also be a second order effect on NX the new, higher E means that NX rises. This shifts out the IS curve, puts upward pressure on interest rates, and leads to further expansionary monetary accommodation. This has an additional boost on output.

 

  1. People will expect an even higher E for the future (Ee goes way up.) This shifts out the interest parity curve. The moment that these expectations change, the return on foreign bonds looks more attractive than domestic bonds see this in the arbitrage equation. This means that investors will want to move their currency out of the country, putting lots of pressure on the central bank to pay out its foreign reserves to support the exchange rate. In turn, this reduces the money supply, shifts in the LM curve, and pushes interests rates very high. Output will decrease from its levels in (b).

Note that as long as the country is defending its exchange rate, there is no effect on NX or the IS: NX moves when E moves, and E is still fixed here. It is possible to imagine a scenario where the central bank runs out of reserves if Ee keeps rising, and abandons its fixed E all together.

If you assumed that the conditions in (b) and (c) were happening at the same time (instead of sequentially, as above) then the 2 changes the devaluation and the rise in Ee would be pulling output in different directions. The ultimate effect on output would depend on the magnitude of the change in Ee.