# The Macroeconomic Theory of Fiscal Policy II

**3**

## The Permanent Level of Fiscal Variables

### Definition of the Permanent Level of an Economic Variable

In this chapter, we investigate the multiplier of government spending using a neoclassical macroeconomic model. In the neoclassical model, households behave rationally over time so that they may anticipate future economic conditions, including future fiscal policy, and current fiscal policy. Thus, when current government spending changes, the way in which it affects future fiscal variables has an important policy implication. In this situation, the notion of a permanent level of fiscal variables becomes useful. First, let us explain this notion.

For simplicity, imagine a two-period model with current (period 1) and future (period 2) periods. The permanent level of an economic variable Y is Y_{p} and is defined as the value that has the same value in both periods. At the same time, the present value is also equal to that of the original values, Y_{1} and Y_{2}. Namely, if Y_{1 }and Y_{2} are given, Y_{p} is defined as the following equation:

Here, r is the rate of interest.

Figure 3.1 shows the relationship between the permanent level of variables and the actual level of variables. Suppose Y_{1} and Y_{2} are given at point A. We can then draw the budget line that gives the same present value of Y_{1} and Y_{2}; namely, point A on Line PI, which corresponds to Eq. (3.1), is associated with the actual combination of Y, (Y_{1}, Y_{2}).

Following the definition of the permanent level, point E, which is the intersection of Line PI and the 45-degree line, is associated with the permanent level, Y_{p}. Any point on Line PI is associated with the same present value; thus, its permanent © Springer Science+Business Media Singapore 2017

T. Ihori, *Principles of Public Finance,* Springer Texts in Business and Economics, DOI 10.1007/978-981-10-2389-7_3

Fig. 3.1 **The permanent level of variables and actual level of variables**

value is the same. Simultaneously, at any point on the 45-degree line, the value is the same in both periods. Hence, the permanent value is given by point E.

For example, suppose r = 0 for simplicity. Y_{1} = 10, Y_{2} = 50. Then, Y_{p} is given

as

Thus, Y_{p} = 30. In other words, Y_{1} = Y_{2} = 30 gives the same present value of the actual pattern of Y_{1} = 10, Y_{2} = 50 if r = 0. If r = 0.25, then

Thus,