Question

consider the following open economy. the real exchange rate is fixed and equal to 1. consumption is given by C=50+0.5(Y-T), investment is I =20, taxes are t=10, and the government budget is balanced. imports and exports are given by I M = 0.2Y and X = 0.02Y* where Y* is foreign GDP.

Answer 1

(a)

$Y=C+I+G+NX$

$Y=50+0.5(Y-10)+20+10+(0.02Y^*-0.2Y)$

$Y=75+0.5Y+0.02Y^*-0.2Y=75+0.3Y+0.02Y$

$Y=\frac{(75+0.02Y^*)}{0.7}$

(b)

Government purchase multiplier:

$=\frac{1}{1-mpc+mpm}$

$=\frac{1}{(1-0.5+0.2)}=\frac{1}{0.7}=1.43$

If there is no import and export, the the government purchase multiplier:

$=\frac{1}{1-mpc}=\frac{1}{(1-0.5)}=2.$

(c)

If $Y^*=10Y$

So,

$Y=\frac{(75+0.02\times 10Y)}{0.7}$

$\implies Y=150$

So, $Y^*=150\times10=1500$

Foreign GDP after adverse demand hit:

$=0.9\times1500=1350$

New domestic GDP:

$=0.1\times1350=135$

So, domestic GDP falls by 10%.

(d)

Government purchase multiplier$=\frac{1}{0.7}=1.43$

Required increase in output = 15.

Required increase in government purchases:

$=\frac{15}{0.7}=21.42$