# Economic Growth and Fiscal Policy

**5**

## A Simple Growth Model

### Long-Run Growth Rate in the Harrod-Domar Model

In the short-run macroeconomic model, investment is an important component of aggregate demand. Certainly, investment is a part of current effective demand. At the same time, it may increase production capacity by accumulating capital stock in the long run. This is an important function of public investment. It is also useful to investigate the impact of taxes on economic growth, since public investment is normally financed by taxes and an increase in taxes in the private sector depresses private investment. Thus, in this chapter, we investigate the supply-side effect of public investment and the impact of fiscal policy on long-run economic growth.

First, we explain how economic growth is determined by using a simple dynamic model. From the supply side, GDP is determined by three factors: capital stock, labor input, and technology level. We may formulate this relationship as the macroeconomic production function.

Equation (5.1) is one of the fundamental equations for an economic growth model, where Y represents income, K capital, and A productivity. The equation specifies the productive effect of investment or the supply effect of capital stock. Namely, production capacity Y can be increased by the amount of A per capital stock, K. Full employment of K may produce AK amounts of output. A denotes the technology level of a country. For simplicity, we do not consider in this section the constraint of labor supply in production.

Next, we formulate the capital accumulation equation, © 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_5

where s is the propensity to save (or the saving rate) and ДК denotes an increase in capital stock or investment I. The right-hand side of Eq. (5.2) means a simple saving function as in the Keynesian model of Chap. 2. In a closed economy, saving is used for investment. From Eqs. (5.1) and (5.2), we have

Alternatively, the growth rate ю is determined as

The long-run growth rate ю is given by the saving rate s multiplied by productivity A. The higher the saving rate and productivity, the higher the growth rate. Since Y and A are linearly related by Eq. (5.1), the growth rate of Y is the same as the growth rate of K, ю.

This model of economic growth was originally formulated by Harrod (1939) and Domar (1946). Thus, it is called the Harrod-Domar model. In Harrod and Domar’s formulation, the inverse of productivity 1/A is called the capital/output ratio or the capital coefficient, K/Y.