Question

Assume the VMP is the marginal revenue brought by one of its workers to a company throughout her lifetime. Also, assume that the payment made to that worker is equal to her marginal product. Assume further that the line w* shows the reservation wage 0 (the minimum wage she needs to get in order to work) throughout her lifetime. When will this particular worker retire, if she is free to choose her retirement age?

Answer 1

VMP stands for Value of Marginal Product. For a particular resource, the value of Marginal product (VMP) is the resource's marginal product multiplied by the product price. The marginal revenue product of a resource is defined as the increase in a firm's total revenue distributable to employing one more unit of that resource. The trend toward earlier retirement has been one of the most important labour markets developments in the past fifty years. During this period, participation rates of older workers have fallen in virtually all OECD countries. The decrease in labour market participation implies considerable economic costs, particularly through social security benefit payments and a lower tax base.

A large body of economic literature has analyzed early -retirement behaviour from a labour-supply perspective. According to this literature, worker's retirement decision is based on an assessment of future stream of wages and pension payments from public and private sources. The optimal retirement date is chosen in order to maximize a worker's future expected utility. Examples of such lifecycle retirement models are the contributions by Burkhauser (1979), Gordon and Blinder (1980), Mitchell and Fields (1982), Burltess (1986) and the Gustman and Steinmeter (1986). An important theoretical prediction of this theory is that earlier and more generous availability of public old-age benefits will increase the incidence of early exits from the labour force because early retirement becomes a more attractive choice for the individuals.

The effects of labour demand on early retirement have received far less attention. Classical theory predicts that firms should pay their workers their marginal product and should have no incentive to induce early retirement. Although Lazear (1979) does not explicitly address the issue of early retirement, his analysis provides both supply- and demand-side explanation of the institution of mandatory retirement. In his moral hazard model, employers and employees agree to a contract that pays younger workers wages below their VMP (value of the marginal product), and older workers more than their VMP. Due to moral hazard, such contracts assure that worker's lifetime VMP is larger than in the absence of such contracts. However, a necessary condition for such payments scheme is mandatory retirement. i.e a date at which a worker is no longer entitled to receive a wage greater than his VMP. If a worker's position affects utility and /or productivity, then a firm can induce its workers to retire before their marginal product equals their reservation wage.

In the question, it is given that payment made to the worker is equal to her marginal product and w ^* shows the reservation wage 0 (the minimum wage she needs to get in order to work ) throughout her lifetime, this worker can choose to retire anytime before her marginal product equals her reservation wage.

However, older works have better jobs which are more productive and provide the most position utility. The retirement of an older worker implies that a younger worker can be promoted, thus becoming more productive, enjoying greater position utility and, as a result, requiring lower wages in order to remain at the firm. Hutchens (1999) develops an implicit contract model in which early retirement also arises out of the firm's profit maximization behaviour. Firms actively use wage and pension structures to influence or even determine worker's retirement decisions. Particularly, as a response to adverse demand shocks, firms choose to direct workers toward early retirement.