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In: Economics

Consider McCallum’s small open-economy macro model under fixed exchange rates. Write down the 5 equations of...

Consider McCallum’s small open-economy macro model under fixed exchange rates. Write down the 5 equations of the model and explain their meaning. Make sure you explain all notation. Classify the model’s variables into endogenous and exogenous. Show graphically and explain verbally the short-run and long-run effects of expansionary monetary policy

Solutions

Expert Solution

Y=+NX = + cY - bi + - mY + R or Y= ( - bi + + R)/ (1 - c + m)


A = is the autonomous expenditure
i = is the interest rate
Y = is the output/income

= autonomous export
m = is the marginal propensity to import
= is the responsiveness of the trade balance to the real exchange rate
b = is the responsiveness of interest on investment
c = is the marginal propensity to consume
R = is the real exchange rate

The greater , and , and R the greater the income Y, ceteris paribus.
The greater b, m, the lesser the change in income Y, given a change in for example.
The greater c, he greater the change in income Y, given a change in for example.

LM equation:/= kY - h

Here,

/ = is the real stock of money
k = is the responsiveness of money demand on income
= is the nominal foreign interest rate
h = is the responsivenss of change in foreign interest rate on income

The greater the value of k, the larger the change in interest rate is required to keep the money supply constant.
The greater the value of h, the larger the change in income necessary to keep the money supply constant.

Fisher equation: = r+ or r = -

Here, is the nominal foreign interest rate
r = is the real interest rate
= is the expected inflation.

This equation says that the real interest rate equals to the nominal world interest rate minus the expected inflation rate. Therefore, real interest rates fall as inflation increases, unless the world nominal rates increase at the same rate as inflation.  

Uncovered interest parity:

1 + i(d) = E(t + k) / S(t)(1 + i(c))

Here,
k =is the number of time periods into the future from time t
= the foreign interest rate
= the domestic interest rate.
E(t + k) / S(t) = the expected rate of change in the exchange rate, which in other words is simply the projected exchange rate at time (t + k) divided by the spot rate at time t.


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