1. Assume that women's marginal rate of substitution of leisure for consumption is given by the following function:

Where, C is consumption (with price=1) andis leisure. A(x) is a taste-shifting function of the following form:

Where theare k different observable factors that affect her preferences, andrepresent unobservable factors that affect the MRS.has the property that it can be described by a probability density function, such as the normal or uniform density.

a. Show that this functional form for the MRS represents preferences that exhibit a diminishing marginal rate of substitution. Give specific examples ofthat may affect the MRS.

b. Assume that an individual woman has non-labor income, y, (including her husband's income) and a time endowment of T. Derive an expression for this woman's reservation wage:. Show that if the market wage is w, this expression implies that a woman will participate if

Rerite this as an expression of the form, participate if, wheredepends on the market wage, nonlabour income, and preferences.

c. Assume thathas a standard normal distribution. Using your results from b), graphically show and explain how non-labor income, the market wage, and the various taste shifters affect the probability of a woman participating in the labor market.

1. Assume that women's marginal rate of substitution of leisure for consumption is given by the following function: C MRS = .400 T Where, C is consumption (with price=l) and l is leisure. A(x) is a taste-shifting function of the following form: .400 = expolxl + 32362 + + kak + 8) Where the x; are k different observable factors that affect her preferences, and 8 represent unobservable factors that affect the MRS. 8 has the property that it can be described by a probability density function, such as the normal or uniform density. a. Show that this functional form for the MRS represents preferences that exhibit a diminishing marginal rate of substitution. Give specic examples of xi that may affect the MRS. Assume that an individual woman has non-labor income, y, (including her husband's income) and a time endowment of T. Derive an expression for this woman's reservation wage: w*. Show that if the market wage is w, this expression implies that a woman will participate if lnw > lny lnT + 31x1 + 32x2 + + 5'ka + a Rewrite this as an expression of the form, participate if E