Megan works in a mall, and can work as many hours per day (up to 24) as

she wishes at a wage rate w. Let C be the amount of consumption per day

(in dollars, i.e., the price of consumption is 1) and let R denote the amount of

leisure (in hours, per day). She has utility R

1

2 C over leisure and consumption.

Suppose w = 10, and she additionally has $60 in non-labor income she receives

(daily) from song royalties.

(a) What is Megan's full income (or "implicit income")?

(b) Write Megan's budget equation, and sketch the budget line (with C on

the Y axis).

(c) In general, for Cobb-Douglas preferences of the form u(x1, x2) = x

1 x

1

2

,

with income m and prices p1 and p2, demand for good 1 is equal to m

p1

and demand for good 2 is equal to (1)m

p2

. Use this fact to write Megan's

choice of R as a function of the wage rate w and the full income, m(w).

(d) Given Megan's preferences, how much C and R will Megan choose at the

given w = 10?

(e) Suppose the wage rate rises to $15. Draw the new budget line, and solve

for Megan's new value of R. Is Megan working more or less?

(f) Decompose the change in R from into the substitution effect and the

income effect. Note that you cannot use the calculus version of the Slutsky

equation, since the change in w is not infinitesimal.

(g) Explain the signs of the two effects that you found. You should answer

this question even if you didn't solve (f) numerically.