Multipliers, openness and fiscal policy
Consider an open economy characterised by the equations below:
$$
\begin{aligned}
C & =c_0+c_1(Y-T) \\
I & =d_0+d_1 Y \\
I M & =m_1 Y \\
X & =x_1 Y
\end{aligned}
$$
The parameters $\mathrm{m}_1$ and $\mathrm{x}_1$ are the propensities to import and export. Assume that the real exchange rate is fixed at a value of 1 and treat foreign income, $Y^*$, as fixed. Also assume that taxes are fixed and that government purchases are exogenous (that is, decided by the govermment). We explore the effectiveness of changes in $\mathrm{G}$ under alternative assumptions about the propensity to import.
a. Write the equilibrium condition in the market for domestic goods and solve for $Y$.
b. Suppose that government purchases increase by one unit. What is the effect on output) (Assume that $0<m_1<c_1+d_1<1$. Explain why.)
c. How do net exports change when government purchases increase by one unit?
Now consider two economies, one with $\mathrm{m}_1=0.5$ and the other with $\mathrm{m}_1=0.1$. Each economy is characterised by $\left(\mathrm{c}_1+\mathrm{d}_1\right)=0.6$.
d. Suppose that one of the economies is much larger than the other. Which economy do you expect to have the larger value of $m$ ? Explain.
c. Calculate your answers to parts (b) and (c) for each economy by substituting the appropriate parameter values.
f. In which economy will fiscal policy have a larger effect on output? In which economy will fiscal policy have a larger effect on net exports?