The paradox of saving revisited You should be able to complete this question without doing any algebra, although you may find making a diagram helpful for part

a. For this problem, you do not need to calculate the magnitudes of changes in economic variables - only the direction of change.

a. Consider the economy described in Problem 8.

Suppose that consumers decide to consume less (and therefore to save more) for any given amount of disposable income.

Specifically, assume that consumer confidence \(\left(c_{0}ight)\) falls. What will happen to output?

b. As a result of the effect on output you determined in part

a, what will happen to investment? What will happen to public saving? What will happen to private saving? Explain. (Hint: Consider the saving-equals-investment characterization of equilibrium.) What is the effect on consumption?

c. Suppose that consumers had decided to increase consumption expenditure, so that \(c_{0}\) had increased. What would have been the effect on output, investment, and private saving in this case? Explain. What would have been the effect on consumption?

d. Comment on the following logic: "When output is too low, what is needed is an increase in demand for goods and services. Investment is one component of demand, and saving equals investment. Therefore, if the government could just convince households to attempt to save more, then investment, and output, would increase."

Output is not the only variable that affects investment. As we develop our model of the economy, we will revisit the paradox of saving in future chapter problems.

Data from problem 8

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.