14.02 Quiz 2 CONFLICT Solutions

# Question 1: TRUE OR FALSE

a.       FALSE

This question is actually trickier than many realized.  A recession in a foreign country is a fall in Y*.  This results in a drop in exports for the domestic economy, which lowers domestic income, Y.  But lower domestic income means lower purchases of imports.  The total effect on net exports is not ambiguous, however.  If the import effect outweighed the export effect, then NX would rise, but this would imply that Y also rises (the only change in the model is the fall in Y*), contradicting the assumption that Y fell causing Q to fall.  Thus the fall in Y* causes a decrease in both Y and NX.

b.      TRUE

An appreciation will cause an immediate increase in net exports.  The Marshall-Lerner condition says that an appreciation will cause net exports to fall, but this is only after both prices (the exchange rate) and quantities (X and Q) have adjusted.  In the very short run, quantities are fixed so the fall in the exchange rate causes net exports to rise before they fall since NX = X(E) - EQ(E).

c.       TRUE

The domestic demand for goods is C + I + G, the demand for domestic goods is C + I + G + NX.  If NX = 0, or the trade deficit is zero, these are equal.

d.      FALSE

A depreciation of the currency is consistent with a fall in the interest rate (the arbitrage equation is downward sloping).  A monetary expansion would cause a decrease in i, but it would also have the effect of increasing Y (as we move along the IS curve).  A fiscal contraction would cause a decrease in i, but with a decrease in Y.  A combination of these two policies, however, can lower the interest rate, depreciating the currency, without changing Y.  You cannot keep Y constant with just one of the policy tools.

e.       TRUE

Under perfect capital mobility, the interest parity condition must hold: i = i* + (E(e)-E)/E.  Each of the variables on the right hand side is fixed or exogenous under fixed exchange rates, so the domestic interest rate is determined and the government is not free to choose it.  Full credit may be given for arguing that, under a credible fixed exchange rate regime, the expected exchange rate is equal to the exchange rate so that the interest parity condition implies that the domestic interest rate is equal to the foreign interest rate.  (You should have made the assumption of credible fixed exchange rates explicit if you made this argument.)  Finally, it is not correct to assume that the country is the ‘lead country’ and hence it can set its interest rate and everyone else has to follow.  This is because, first, one should not make unwarranted assumptions outside the model, and second, there does not have to be a ‘lead country’ (this might make sense if you’re considering the US in an exchange rate system with several Caribbean islands, but not if it’s a group of similarly sized economies).

f.        TRUE

If the US dollar is expected to depreciate, then Ee>E.  So the interest parity condition, i = i* + (Ee-E)/E, then implies that i>i*.  One could also argue that foreign investors in US bonds must be compensated for the loss they will make on the currency side of their transactions with a higher nominal interest rate.

g.       TRUE

This question is about overshooting, which is covered in the appendix to chapter 21.  The increase in the interest rate generated by a contractionary monetary policy will attract investment to the domestic economy.  This causes an appreciation of the currency, i.e. a decrease in the exchange rate.  But this only tells you the direction of the effect on the exchange rate, not the magnitude of the effect. Arguing that if the exchange rate is higher for longer, more investment will be attracted, so the effect is bigger is not acceptable.  Rather, the magnitude of the effect is determined by the arbitrage equation: the expected depreciation of the currency in each year of the contraction must be equal to the difference in domestic and foreign interest rates.  So the current appreciation is equal to the number of years the monetary expansion is expected to last times the difference in interest rates.  (To see this from the arbitrage equation, consider that if  the exchange rate is expected to return to its long-run level at time t+2, and the currency is going to depreciate by, say, 2% from t+1 to t+2, then you expect the exchange rate to be 2% lower at time t+1 than the long-run level, i.e. Ee(t+1) changes.  But then for the currency to depreciate 2% from t to t+1, the exchange rate must now be (approximately) 4% lower at time t than its long-run level.)  A longer contraction will thus result in a greater current appreciation.  See the text for the graphs and additional explanation.

Additionally, please note that a contraction is a sudden event: the money supply is moved from one level to another quickly.  The duration is the amount of time before the money supply is returned to its pre-contraction level, not the amount of time it takes to get to the lower level.

# QUESTION 2

1. (3 points)  LM: 295=Y-50*i; this is an upward-sloping line in the Y-i space.  The interpretation of this equation is that it represents equilibrium in the money market.  There are no differences r/e the closed economy; equilibrium is driven by liquidity need for transactions.  Since you only need domestic currency for liquidity, openness should not (significantly) affect the money market.

1. (4 points)  Goods market equilibrium is Y=C+I+G+NX, where demand is equal to supply of goods. The difference between the closed and open economy is that you have to add net exports, which introduces the real exchange rate and foreign output as other variables that influence demand. Net exports are increasing in output, which decreases the feedback (multiplier) effect.

Note: “solving” this model for the closed economy (with the same numbers) gives a “negative” multiplier; doing this alone is not a complete answer to the question of the difference between the closed and open systems.

1. (5 points)  A complete answer to this question must begin with stating the returns on domestic bond investment, (1 + i), and foreign bond investment, (1/Et )(1 + i*)(Et+1 ).  Answers should equate the two, get the precise formula; then state the convenient (approximate) form: i = i* + (Eet+1  - Et )/Et.  The graph is a downward-sloping curve in the i-E space.

1. (5 points)  The IS curve combines the goods market and interest parity relations:  Y=0.8*Y+92-20*i-30/E=0.8*Y+92-20*i-30-30*i=30*i* =0.8*Y+65-50*i, so Y=325-250*i.  The graph is downward sloping in the Y-i space.  The interpretation is that the equation shows output for a given interest rate, consistent with both interest parity and goods market equilibrium.  Higher interest rates depress investment, and appreciate the currency and thus depress net exports.  Both effects generate a decrease in demand, which then gets multiplied and translates into smaller output. The distinctions between open and closed are the different multiplier (smaller in the open economy) and a second interest rate channel (through the exchange rate and net exports.)

Note: if you answered with an IS curve that did not include E substituted in (i.e. holding E constant), and used this expression, you may also receive full credit.  You must in this case, however, explicitly worry about “second order shifts” of the IS curve in the next exercises (G changing so IS moves, but then E changes which moves IS again, so that net effect is either larger because the IS moves in the same direction, or may be smaller, etc.)

1. (12 points)  With a fiscal contraction, lower G means decreased demand for any level of the interest rate, so the IS shifts in. This means lower output, lower interest rates (because the money supply is fixed, so interest rates must decrease to make people happy with their existing cash holdings but less income), thus a depreciation (lower interest rates here, so the country must have an appreciation by tomorrow – this implies a depreciation today).  The effect on investment is ambiguous, since lower output decreases I but lower interest rates increase I.  For net exports, lower Y increases NX, lower i (via higher E) also has a positive effect, so NX goes up.

For a monetary contraction, lower M implies higher interest rates for any level of output.  The LM curve shifts in.  Higher interest rates depress I and NX (moving along the IS curve), so we have lower Y, higher i and thus lower E (appreciation) eventually. Investment is lower, NX is unclear (Y effect vs. E effect).

1. (7 points)  The government can accomplish this goal with a policy mix of fiscal expansion and monetary contraction.  In this case, the LM shifts in and the IS shifts out, keeping Y fixed.  This decreases E, so the only effect on NX is due to lower E: NX decreases.

1. (6 points)  In our model, the government has M, G and T as policy tools. However, G and T have the same effect on everything (but C), so it is as if in fact we have only two instruments. To achieve three targets, this is not, in general,  enough.  In reality (and this can be incorporated into the model), you can influence net exports through export subsidies, import tariffs, etc. – any third policy tool that has a direct effect on NX would do.

QUESTION 3

1. (10 points)  With a fiscal contraction: G goes down, so the IS must shift in (there is lower demand for any fixed i). To maintain i=i*, the country must have a decrease in M as well (by the Central Bank (CB), or by investors buying foreign currency from the CB and giving up domestic currency in return).  This results in the LM shifting in, keeping i fixed. So output goes down, i is unchanged, but NX must have gone up.

1. (10 points)  With a revaluation, for any level of i, NX is lower, so demand and hence output are lower.  This means that the IS shifts in.  Again, this shift in the IS comes with a shift in LM.  This movement in the LM might come from an open market operation (changing B) or automatically (by changing R, foreign currency reserves).  Y is lower, i is the same, and NX should also be lower: the E effect dominates the Y effect. (Precise argument for bonus points: using the ZZ and DD lines, one can show that NX must go down because DD is flatter than the 45o line.)

1. (10 points)  If there is a speculative attack, i<i* follows from the interest parity condition.  This means that the CB must cut interest rates – i.e., expand M.  Again, this may be achieved either by an expansionary open market operation (changing B, not R) or automatically (increasing R). Here the CB has little motivation to use the open market operations since it usually content to let reserves rise.  This increase in M would imply a movement along the IS curve, lower interest rates, and higher output (via increased investment).  If, for this (or any other) reason, the CB is not ready to decrease i fully (not buying enough bonds), then investors would sell the CB foreign currency, and require domestic currency in return. This gradual process would continue until either expectations are cooled down (the crisis is over, with higher reserves but i back to i*), or the country has a revaluation, either because reserves are “too high” or the government abandons its fixed E.