# Economic Effect of the Public Pension

## The Funded System

The issue of most concern about the economic effect of a public pension is the effect on savings in a macroeconomy. First, let us explain the impact of a funded system.

Consider a simple two-period model. In the first period, the agent is young and earns labor income. She or he saves with private assets and public pension contributions. In the second period, the agent is old and consumes all savings after retirement. The budget constraints are given as

where c_{1} and c_{2} denote first period consumption and second period consumption respectively; Y_{1} denotes the first period labor income; s means private saving; b means pension contributions; and r is the rate of interest. In the funded system, pension contributions are invested in the market and the rate of return is the same as with private savings.

In Eqs. (7.1) and (7.2), by eliminating s + b, the present value budget constraint is given as

The agent maximizes its utility subject to this budget constraint, (7.3). Hence, the optimal levels of first-period consumption and second-period consumption are independent of b. In other words, the agent is only concerned with the total amount of “savings,” b + s. If b increases, s declines by the same amount, so that s + b is fixed at the initial optimal level.

Since private saving and a funded public pension are perfect substitutes and thus indifferent for the agent, an increase in public pension contributions simply reduces private saving by the same amount. Note that the total amount of saving in a macroeconomy is given as s + b because b is also invested in the capital market as a public fund. As long as s + b remains constant, pension contributions do not affect aggregate saving; hence, capital accumulation does not change. Thus, in the funded system, a public pension does not reduce total savings in the economy.