Assume that the investment function is a linear relation. The relation between investment and output is characterized by two parameters, a0 and a1:

The parameter a1 is called the propensity to invest. It gives the effect an additional dollar of output has on investment. A natural restriction on a1 is that it be positive: An increase in output is likely to lead to an increase in investment.

The parameter a0 has a literal interpretation. It is what the economy would invest if output in the current year were equal to zero.

Also assume that the consumption function is a linear relation. The relation between consumption and disposable income is characterized by two parameters, c0 and c1:

The parameter c1 is called the propensity to consume. It gives the effect an additional dollar of disposable income has on consumption. A natural restriction on c1 is that it is between 0 and 1.

The parameter c0 has a literal interpretation. It is what the people would consume if disposable income in the current year were equal to zero.

a). Government spending and taxes are constant. Solve for the equilibrium output.

b). What is the value of the multiplier? How is the value of the multiplier effected as compared to the case when investment was exogenous? For the multiplier to be positive what condition must (a1 + c1) satisfy? Explain.

c). Suppose that the parameter a0 increases. How will the equilibrium output be affected? Will investment change by more or less than the change in a0? Why? What will happen to national saving?

d). For given values of G and T, assume that consumer confidence (c0) falls. What will happen to output? What will happen to investment? What will happen to public saving? What will happen to private saving? What is the effect on consumption? Explain.

e). Suppose that the opposite had happened and consumers had decided to increase consumption expenditure, so that had increased. What would have been the effect on output, investment, and private saving in this case? What would have been the effect on consumption? Explain.

f). Comment on the following: "If the economy is in a recession what is needed is for the government to convince people to save more. Since saving equals investment then investment, and output, would increase."