An economy has full-employment output of 6000 . Government purchases, \(G\), are 1200. Desired consumption and desired investment are

\[ \begin{aligned} C^{d} & =3600-2000 r+0.10 Y, \text { and } \\ I^{d} & =1200-4000 r \end{aligned} \]

where \(Y\) is output and \(r\) is the real interest rate.

a. Find an equation relating desired national saving, \(S^{d}\), to \(r\) and \(Y\).

b. Using both versions of the goods market equilibrium condition, Eqs. (4.7) and (4.8), find the real interest rate that clears the goods market. Assume that output equals full-employment output.

c. Government purchases rise to 1440 . How does this increase change the equation describing desired national saving? Show the change graphically. What happens to the market-clearing real interest rate?

\[
\begin{equation*}
Y=C^{d}+I^{d}+G \tag{4.7}
\end{equation*}
\]

\[
\begin{equation*}
S^{d}=I^{d} \tag{4.8}
\end{equation*}
\]