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Unformatted text preview: oblem of the consumer's income-leisure choice as follows: [1] The consumer has a utility function defined on income, M, and leisure, (where leisure, = 24 L in a day). U = U ( , M) The indifference curve corresponding to a given utility level connects all combinations of income and leisure (M , ) that satisfy the equation U ( , M) = Within this income-leisure choice framework, the marginal rate of substitution refers to the change in income as a result of a marginal change in leisure MRS = M M Indifference Curve U ( , M) = 55 [2] Suppose the consumer has a time endowment of Tbar = 24 hours per day to spend either on work to produce income or on play to produce pleasure. Given the market wage, w, if she allocates a time amount for play then the value of her leisure would be w (which is the income lost by playing around) or the opportunity cost of choosing not to work. The income earned from work would be M = w (Tbar ) The budget constraint for the income-leisure choice can be written as: w + M = w Tbar M wTbar Budget Line w + M = wTbar Tbar The budget line is thus a straight line with slope w as described by the equation M = w Tbar w [3] The consumer choice problem can now be formulated as the standard constrained utility maximization problem: Maximize U ( , M) Subject to w + M = w Tbar 56 M Indifference Curve wTbar M* Consumer's Equilibrium Income-Leisure Choice Budget Line * Tbar Remember, at the consumer equilibrium point, the indifference curve must be tangent to the budget line. [4] Solving for the optimal quantities for leisure, *, and income, M*, we can derive the optimal amount of labour, L*, supplied by the consumer at a given market wage. L* = Tbar * In general, if we can write the amount of labour supply as a function of the market wage, w, then we have the following individual supply of labour by the consumer: L = L(w) How do we go about this? Let's use an example to illustrate... Recall that consumers are endowed with time. Essentially, there are two uses of time in this model....
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This note was uploaded on 05/25/2010 for the course ECON 301 taught by Professor Sning during the Spring '10 term at University of Warsaw.

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