Define the income and substitution effects of a wage change on hours of labor supply.

a) Define the income and substitution effects of a wage change on hours of labor supply.
b) Given a particular wage, w, explain and show graphically an individual’s optimal choice of leisure (and labor supply). What equation holds at the optimal choice; in terms of the marginal rate of substitution (MRS), the marginal utilities for leisure (MUl) and consumption (MUc), and the wage (normalizing the price of consumption to one)?
c) Explain and show graphically the derivation of this individual’s labor supply curve – i.e., the relationship between wages and the individual’s desired hours of work.
d) Explain and show graphically the income and substitution effects of a wage increase on hours of work for the case in which an individual is on the backward-bending segment of the labor supply curve. Which effect dominates and what happens to overall hours supplied in this case?