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Consider two economies, Home and Foreign.  The DC/FC exchange is determined by the asset approach to the exchange rate.

 

Both countries are identical in the following ways:

  • Production function is given a typical Cobb-Douglas function: Y = AKαL(1-α).
  • The (real) money demand is given by hY – kR,

where     h = fraction of income held in the form of money, 1> h > 0

k = sensitivity of money demand (MD) to a change in (nominal) interest rate. 

 

Home and Foreign differ in the following ways:

 

Home

Foreign

Level of total factor productivity

4

1

Supply of capital

50625

40000

Supply of labour

10000

62500

Capital’s share of income

0.25

0.5

Nominal money supply

67200

28080

Fraction of income held in the form of money

20%

30%

Sensitivity of MD to a change in (nominal) interest rate

8000

8000

Long-run nominal interest rate

10%

12%

 

Note: 

  • Quote the exchange rate as EDC/FC.
  • Interest rates are expressed in decimal points (i.e., if R = 0.1, then it is interpreted as 10%).
  • Keep your answer to at least 4 decimal points.

 

  1. Initially, both countries are in their respective long-run equilibrium.  Find the long-run levels of prices in both countries and the DC/FC exchange rate if the (initial) expected DC/FC exchange rate is given by the ratio of domestic price level to foreign price level.  (6 points)

 

Suppose there are permanent changes in the domestic money market such that the central bank of Home shrinks its balance sheet.  As such, the level of money supply changes by 10%.  At the same time, the sensitivity of (domestic) money demand (MD) to a change in (nominal) interest rate changes to 6000.  In addition, any permanent change will cause the market the to revise their expected exchange rate by 0.3474 DC per FC. 

  1. Find the short-run equilibrium DC/FC exchange rate. (5 points)
  2. Find the new long-run equilibrium levels of prices in both countries and the DC/FC exchange rate. (4 points).
  3. Now, suppose the central bank of Foreign finds the change in the short-run exchange rate in part (b) undesirable and wants to keep it EDC/FC at 1.75 via a temporary change in monetary policy. Is it possible for the foreign central bank to achieve this goal?  Yes/No, explain.  (5 points)
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