- Suppose you are given the utility function U(C, l) = lnC + 5L, where C = consumption and L = leisure, and the budget constraint the individual faces is simply C = (1 – t)wN, where t is the labor tax rate, w is the real hourly wage, and N is the number of hours the individual works. Assume that hours of leisure/work are normalized as representing fractions of a day (or equivalently, a value of 1 represents 24 hours).
Suppose w = $20 per hour, and t = 20%.
a) What are the optimal hours of work?
b) What are the optimal hours of leisure?
c) What is the optimal level of consumption?
Now suppose w = $20 per hour, and t = 30%.
d) What are the optimal hours of work?
e) What are the optimal hours of leisure?
f) What is the optimal level of consumption?
- Using the RBC Model, suppose that the value of equities (stock in companies) is included as a form of individual wealth that impacts the individual’s consumption / leisure decision. Suppose that equity prices are increasing. What are the implications on the following (make no assumptions regarding the magnitudes of particular shifts of curves):
a) Output supply (increase / decrease / indeterminate / no change)?
b) Output demand (increase / decrease / indeterminate / no change)?
c) Output (increase / decrease / indeterminate / no change)?
d) Interest rate (increase / decrease / indeterminate / no change)?
e) Labor supply (increase / decrease / indeterminate / no change)?
f) Labor demand (increase / decrease / indeterminate / no change)?
g) Employment (increase / decrease / indeterminate / no change)?
h) Wages (increase / decrease / indeterminate / no change)?
i) Money supply (increase / decrease / indeterminate / no change)?
j) Money demand (with price level on vertical axis)
(increase / decrease / indeterminate / no change)?
k) Price level (increase / decrease / indeterminate / no change)?