Investment and income This problem examines the implications of allowing investment to depend on output. Chapter 5 carries this analysis much further and introduces an essential relation — the effect of the interest rate on investment-not examined in this problem.

a. Suppose the economy is characterized by the following behavioral equations:

\[
\begin{aligned}
C & =c_{0}+c_{1} Y_{D} \\
Y_{D} & =Y-T \\
I & =b_{0}+b_{1} Y
\end{aligned}
\]

Government spending and taxes are constant. Note that investment now increases with output. (Chapter 5 discusses the reasons for this relation.) Solve for equilibrium output.

b. What is the value of the multiplier? How does the relation between investment and output affect the value of the multiplier? For the multiplier to be positive, what condition must \(\left(c_{1}+b_{1}\right)\) satisfy? Explain your answers.

c. What would happen if \(\left(c_{1}+b_{1}\right)>1\) ? (Trick question. Think about what happens in each round of spending).

d. Suppose that the parameter \(b_{0}\), sometimes called business confidence, increases. How will equilibrium output be affected? Will investment change by more or less than the change in \(b_{0}\) ? Why? What will happen to national saving?