Question #63611

Assume perfect capital mobility and fixed exchange rates. Furthermore, assume that no changes in the nominal exchange rate are expected and that there are no risk premia. The economy in characterized as follows: LM curve: i = 0.5Y - 0.1 M/P, IS curve i = -Y + R + 100, nominal exchange rate E = 7.5, price level P = 2, world interest rate i^W = 5.5, world price level P^W= 2. Calculate the change in Y if the price level changes from P_0=2 to P_1=1.

Expert's answer

LM curve: i = 0.5Y - 0.1 M/P, IS curve i = -Y + R + 100, nominal exchange rate E = 7.5, price level P = 2, world interest rate i^W = 5.5, world price level P^W= 2.

In equilibrum LM = IS, so:

0.5Y - 0.1 M/P = -Y + R + 100,

1.5Y = R + 0.1 M/P + 100

Y = (R + 0.1 M/P + 100)/1.5

The change in Y if the price level changes from P_0 = 2 to P_1 = 1 is:

Y1 - Y0 = (R + 0.1 M/1 + 100)/1.5 - (R + 0.1 M/2 + 100)/1.5 = 0.05M.

In equilibrum LM = IS, so:

0.5Y - 0.1 M/P = -Y + R + 100,

1.5Y = R + 0.1 M/P + 100

Y = (R + 0.1 M/P + 100)/1.5

The change in Y if the price level changes from P_0 = 2 to P_1 = 1 is:

Y1 - Y0 = (R + 0.1 M/1 + 100)/1.5 - (R + 0.1 M/2 + 100)/1.5 = 0.05M.

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