1. In this question, you will derive the labor supply curve from individual consumer preferences for leisure and consumption. You will derive two different labor supply curves: one that has positive elasticity and one that is perfectly inelastic (like the labor supply curve in the Solow model). These two labor supply curves result from different assumptions about income and substitution effects on leisure.

(A-D are answered in another post I just need the rest)

(e) Is Ns 1 greater than, smaller than, or the same as Ns 2 ? What does that say about the change in the representative consumers labor supply in response to an increase in wages?

(f) The total effect on leisure of the wage increase is `2 `1 < 0. Next, we are going to separate this effect into the substitution and income effect of the wage increase on leisure.

i. In a third color, draw a line that is parallel to the new budget constraint but touches the original indifference curve (again, as we did in class: the theoretical exercise we are conducting with this approach is to assume that consumers face the new relative price of leisure but have only enough income to attain the original level of utility). This new line should be tangent to the original indifference curve. On the x- and y-axes, label the consumption bundle at the intersection between the new line and original indifference curve as (c 0 , `0 ).

ii. On the x-axis, identify the substitution effect on leisure. Describe the substitution effect in terms of `1 and ` 0 . Has the relative price of leisure increased or decreased? Is the substitution effect negative or positive?

iii. On the x-axis, identify the income effect on leisure. Describe the income effect in terms of `2 and ` 0 . Is the income effect positive or negative? Is the magnitude of the income effect larger, smaller, or the same as the magnitude of the substitution effect?

(g) Draw a new graph with the number of hours the representative consumer chooses to work, Ns , along the x-axis and the real wage, w, along the y-axis. Identify two points on this graph: (Ns 1 , w1) and (Ns 2 , w2). Connect the two points with a line. This line describes the representative consumers labor supply. Is it upward sloping, downward sloping, or have an infinite slope? What does this say about the impact of an increase in the real wage on the number of hours a worker is willing to work?

(h) Repeat steps 1 through 7 except, in step 4, draw the new indifference curve so that the new optimal bundle includes the same amount of leisure as the original bundle that is, `1 = `2.