The theory of labor supply is based on the model of a consumer making a choice between consuming more goods and consuming more leisure. With it, we can elucidate the properties of labor supply and begin to understand the conditions of participation in the labor market. The model has been variously enhanced to make the theory of labor supply more precise and sometimes to modify it profoundly, principally by taking into account household production, the collective dimension of decisions about labor supply and the life cycle aspect of these decisions.
The basic model of a trade-off between consumption and leisure gives us the principal properties of the supply of labor. In particular, it shows that labor supply is not necessarily a monotonic function of wages. It suggests that labor supply grows when the wage is low, and subsequently diminishes with the wage when the latter is sufficiently high. Further, the study of the trade-off between consumption and leisure makes it possible to grasp the factors that determine participation in the labor market.
The trade-offs between consumption and leisure is shown with the help of a utility function proper to each individual, that is, U (C, L) where C and L designate respectively the consumption of goods and the consumption of leisure. Given that an individual disposes of a total amount of time, L0, the length of time worked, expressed, for example in hours, is then given h = L0 – L. It is generally supposed than an individual desires to consume the greatest possible quantity of goods and leisure; his or her utility function therefore increases with each argument. Moreover, the same individual is capable of attaining the same level of satisfaction with much leisure and few goods, or little leisure and many goods. The set of pairs (C, L) by which the consumer obtains the same level of utility U1, i.e., such that U(C, L) = U1, is called an indifference curve.
Each indifference curve corresponds to a higher level of utility, the farther out the curve is from the origin. Hence the consumer will prefer indifference curves situated farther out from the origin.
Indifference curve do not intersect. If they did, the point of intersection would correspond to a combination of leisure and consumption through which the individual would have two different levels of satisfaction. Incoherence in preferences of this kind are excluded.
The increase in the utility function in relation to each of its components implies that the indifference curves are negatively sloped. The slope of an indifference curve at a given point defines the marginal rate of substitution between consumption and leisure. It represents the quantity of goods which a consumer must renounce in exchange for an hour of supplementary leisure, for his or her level of satisfaction to remain unchanged.
It is assumed that the individual is ready to sacrifice less and less consumption for an extra hour of leisure when the amount of time dedicated to leisure rises. This property signifies that marginal rate of substitution between consumption and leisure diminishes with leisure time, or again that the indifference curves are convex, which is equivalent to the hypothesis of a quasi-concavity of the utility function.
An individual’s income derives from his or her activity as wage-earner and from his or her activity outside the labor market. If we designate the real hourly wage by w, the income from wages total wh. Investment income, transfer income, even gains deriving from undeclared or illegal activities are examples of what an individual may acquire outside the labor market.
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