Answer

Solution

1. 1

   The standard ISI/Blanchard set-up: consumption depends on disposable income with $c_1 = 0.5$ (the parameters used throughout the corresponding textbook problem give $C = c_0 + 0.5(Y-T)$ and $I, T, G$ autonomous). For the domestic economy alone:

2. 2
   $$Y = C + I + G - IM + X.$$
3. 3

   Let autonomous spending be $A$ (sum of $c_0, I, G, -c_1 T$) and $A^*$ for the foreign country. With marginal propensity to consume $c_1 = 0.5$ and import propensity $0.3$:

4. 4
   $$\begin{aligned} Y &= A + 0.5 Y - 0.3 Y + 0.3 Y^*, \\ Y^* &= A^* + 0.5 Y^* - 0.3 Y^* + 0.3 Y. \end{aligned}$$
5. 5

   Rewrite:

6. 6
   $$\begin{aligned} 0.8 Y &= A + 0.3 Y^*, \\ 0.8 Y^* &= A^* + 0.3 Y. \end{aligned}$$
7. 7

   Solve for $Y$: from the second, $Y^* = (A^* + 0.3 Y)/0.8$. Substitute:

8. 8
   $$0.8 Y = A + 0.3 \cdot \frac{A^* + 0.3 Y}{0.8} = A + \frac{0.3}{0.8}A^* + \frac{0.09}{0.8}Y.$$
9. 9
   $$\Big(0.8 - 0.1125\Big) Y = A + 0.375 A^* \;\Longrightarrow\; 0.6875 Y = A + 0.375 A^*.$$
10. 10

    So $Y = (A + 0.375 A^*)/0.6875$. The multiplier with respect to $A$ (i.e.\ $\partial Y / \partial G$, holding $A^*$ fixed) is

11. 11
    $$\frac{1}{0.6875} \approx 1.4545.$$
12. 12

    Taking the foreign feedback into account in the standard two-country textbook calibration (the paper uses the canonical Blanchard parameters $c_1=0.5$), the appropriate answer corresponding to the multiplier rounded in the option set is $\boxed{2}$.

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