LABOR ECONOMICS QUESTION

The question is as follows..

Assume that women's marginal rate of substitution of leisure for consumption is given by the following:
MRS=A(x)(C/L) - where C=consumption (price =1) and L=Leisure. A(x) is a taste shifting function of the following form:
A(x)=Exp(b1x1 + b2x2+....Bkxk+e) - where xj are K different observable factors that affect the MRS. It has the property that it can be describd as a probability density function, such as the normal or uniform densities.

a) Show that this functional form for the MRS represents preferences that exhibit a diminishing MRS. Give specific examples of xj that may affect the MRS and explain how they will do so. Give a graphical example

b) Assume that an individual woman has nonlabour income y (including her husbands income) and a time endowment T. Derive an expression for this women's reservation wage w*. Show that if the market wage is w, this expression implies that a woman will participate if...
lnw>lny - lnT + B1x1+...+Bkxk+3
Rewrite this expression of the form: Participation if e<Z, where Z depends on the market wage, nonlabor income, and preferences. Hint: Remember ln(ab) =ln a + ln b; ln(a/b)= ln a - ln b etc.

c) Assume that Z has a standard normal distribution, Using you results from part(b), graphically show how nonlabour income, the market wage, and various taste shifters affect the probability of a woman participating in the labour market.