# PROBLEM SET 4: Solutions

1.  TRUE OR FALSE:

a.       FALSE.  A country has a trade deficit if net exports (X – Q) are strictly negative.  If there are only 2 countries in the world, and both have trade deficits, then X-Q <0 and X* - Q* <0.  But X = Q* and X* = Q with 2 countries – this would imply that X-Q< 0 and Q-X<0.  This cannot happen, so both countries cannot have trade deficits.

b.      FALSE.  E is defined as the amount in dollars it would cost to purchase one unit of French currency (1 franc.)  So if E falls, then it is cheaper for US citizens to buy one franc, or, conversely, more expensive for the French to buy US dollars.  This means it is less attractive for French tourists to visit the US.

c.       FALSE.  The real exchange rate is defined as e = EP*/P.  Therefore, e may remain unchanged when E changes if (P*/P) offsets any movement in E.

d.      FALSE.  The US finances its trade deficit by having foreigners increase their holdings of US assets.

e.       FALSE.  You need more information than this – you have to know the expected nominal exchange rate in the next period (t+1) as well.  Without this information, you cannot be sure that it is advantageous to purchase Canadian bonds.

2.  DYNAMICS OF THE IS-LM:

a.       Find the equilibrium condition in the goods market:  Y = Z, which implies that Yt = 50 + 0.75[0.5(Yt –Tt) + 0.5(Yt-1 –Tt-1)] + 50- 120it + 50.  Plugging in the values given here, leads to the equilibrium condition: Yt  = (3669/10) – 192it .  The equilibrium in the money market: Mdt = Mst  , so Yt = 225 + 300it.  Use these 2 equations to solve for the interest rate i* = (1419/4920) = 28.8%, and for Yt * = 311 ½ .  Graph this equilibrium in a standard IS-LM  framework, with the IS curve downward- and the LM curve upward-sloping.

b.      Yt  does not change!  Her plan fails because she does not understand the dynamics of the IS-LM (short run) model.  While she changes Gt , it is Gt-1 that affects current output.  This parallels the results we see in real economies:  it takes some time for changes in fiscal policy to filter through the goods market and affect output.

c.       In period (t+1), the old president’s policy of increasing Gt has finally begun to take effect in the economy.  This means the IS curve has shifted to the right, and increased output and interest rates in the economy.  The Fed chair’s goal is to shift these interest rates back down – she can increase money supply to do this.  This immediately changes interest rates – monetary policy does not have the lag that fiscal policy does.  In the model here, the LM curve shifts out, raising Yt+1 and lowering it+1 .

3.  EXCHANGE RATES:

a.       \$600 = K150 implies that E = 4 (i.e. it costs \$4 to buy 1 K.)

When the dollar appreciates, it costs fewer US dollars to buy K150.  This means E falls.  When the kontanto depreciates, it means that \$600 will buy more than K150, so E falls here, too.

b.      The real exchange rate e = EP*/P.  P is the GDP deflator in the US (nominal GDP/real GDP), so P = 5/4.  P* is the foreign GDP deflator, and P* = 5/6.  Since E = 4 from (a), e = 8/3.  When nominal Esperanza GDP is K80, P* = 4/3, so e = 64/15.  When E changes (to 10/3), e = 20/9.

c.       Use the uncovered interest rate parity condition to find the interest rates: (1 + i) = (1 + i*)(E e t+1 / Et ).  This means the interest rate in Esperanza is 40% (2/5).  If the US interest rate falls to 4%, the Esperanza rate = (29/75), or 38 2/3%. This makes sense – if the US return goes down, with all else held constant, the return in Esperanza should fall, too.   If the expected nominal E in (t+1) falls to 2, the interest rate in Esperanza rises to 110% (11/10).  This also makes sense – if expected E is lower, then when US investors want to convert their investment back into dollars at the end of the period, they will get fewer dollars per kontanto.  This means US investors will require a higher return to be willing to hold Esperanza bonds.

The reason you can always calculate i* is due to arbitrage – that is what underlies the uncovered interest rate parity equation.  If the equation did not hold, and the return on foreign bonds (right hand side of equation, or RHS) was higher, everyone would put their money into foreign bonds.  This means they would all buy kontantos in the currency markets, and would drive the price of kontantos up.  This is equivalent to a depreciation of the dollar – Et  rises, and the RHS falls.  Also, the increased purchases of foreign bonds drives up the price of these bonds and pushes i* down, which also makes the RHS fall.  Through these two factors, the dollar return on foreign bonds is driven back down; this is the mechanism behind interest rate parity.

d.      EM = 5, EM = 5, P =1, PK =4/3, and PM = 5/4.  The multilateral real exchange rate is the weighted average of the real exchange rates between the US/Esperanza and US/Monolando, with ¾ of the weight on the US/Esperanza rate.  That means the multilateral US e = 105/16. When EK changes to 4, the US e = 89/16.  When EM falls to 4, US e = 25/4 (or 100/16).  The reason that the multilateral exchange rate is different in the 2 cases is that in the first case, when the dollar appreciates against the kontanto, Esperanza is a larger trading partner than Monolando.  This means there is a larger effect on the exchange rate than when EM moves in the second case.

4.  GOODS MARKET IN OPEN ECONOMY:

a.       Z = Y = C + I + G, so Y = 5 (54) = 270.  The multiplier is 5, and autonomous spending is 54.  The graph of DD should have Demand on the Y-axis, output on the X-axis, and be an upward sloping line flatter than the 45-degree line.  It looks just like the basic goods market model of Ch. 3.

b.      Z = Y = C + I + G + X – eQ, so Y = (5/2)(108) = 270.  Output is the same in the closed and open economy.  However, the slope of the ZZ curve is flatter than the DD curve in part (a), and has a higher intercept.  The multiplier is 5/2, and autonomous spending is 108.  Net exports = X – Q, so here NX = 0.  There is neither a trade deficit nor surplus.

c.       When G changes, output in the closed economy rises by 50 (the change in G times the multiplier), and Y is 320.  In the open economy, the multiplier is smaller, so Y rises by 25 and the new equilibrium Y is 295.  The multiplier effect exists because, when Y rises, people consume a fraction of their income and boost output even further.  In the open economy, however, they spend a portion of their increased income on foreign goods (imports) so output rises less than in a closed economy.  In this way, some of the rise in G leaks out of the economy, and boosts foreign production, so fiscal policy is less effective.  NX becomes negative here – NX = -5 – so the country now has a trade deficit.  This is because the rise in G has increased imports but has not affected exports.

d.      When G* changes, nothing happens in the closed economy.  In the open economy, output rises to 295, the same as in part (c ).  There is a big difference in the trade balance, however.  When Y* rises, imports are unaffected, but exports rise.  This gives the country a trade surplus: NX = 5.  Thus when foreign output rises, the domestic country gets a boost in output without increasing the trade deficit.