University of California Los Angeles Real Business Cycle Model Report

1. 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?

2. 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)?

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3. Suppose that due to increased drug addiction in the United States, consumers’ preferences

shift toward more leisure and less consumption goods. Using the RBC Model, what are the

impacts on the following outcomes (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)?