14.02 Principles of Macroeconomics
Problem Set 2: Spring 1998

This problem set is due on Friday, February 20, 1998, in your recitation. Please make sure to put your TA name and section time on your work.

1. Suppose that an economy is characterized by the following behavioral equations:

C = 100 +0.6Y_d
I = 50
G = 250
T = 100
a.- Solve for equilibrium levels for GDP (Y), disposable income (Y_d), consumption spending, private saving, public saving and the value of the multiplier.
b.-What would the effect of a decrease in government spending of 100 be on the values you have computed in a)?
c.- If the consumption function changes to C = 100 + 0.8Y_d, would you expect the equilibrium level of income to be lower or higher?
d.- Verify that in equilibrium "production equals demand" and "total savings equals investment"
e.- If the government wanted to increase GDP by 200 what change in G would be required? If G could not be changed, how should T change?

2. What would be the implications for the model in 1) if taxes were proportional to income (T=tY)?

3. The budget surplus (BS) for the government is defined as government revenues minus government expenditures. (Taxes are proportional to income like in 2.))
Analyze the effect on the BS of:
a.- An increase in business confidence
b.- An increase in government expenditures
c.- A decrease in consumer confidence
d.- Derive the multiplier if the government runs a balanced budget (BS=0)

4. Although the marginal propensity to consume states the relation between aggregate income and aggregate consumption, it can also apply to the relation between income and consumption for an individual.
a.- Determine your own marginal propensity to consume out of current income (hint: how much would your spending increase if your hourly wages goes up from $8 to $10. how much would your spending increase if you start working this summer for $3000/month?)
b.- Is your marginal propensity to consume consistent with the two "natural restrictions" stated in the text. If not, explain.

5. "True" or "false" (explain briefly)
a.- In a dynamic model of the goods market, there is no multiplier
b.- In a dynamic model of the goods market, firms maintain constant levels of inventories from period to period
c.- In a dynamic model of the goods market, the only way to calculate equilibrium GDP is to run a simulation and add up the changes to GDP in each period.

6. Consider the following dynamic model of the goods market

C_t = 0.5 + 0.75(Y_t - T)
I = 25
G = 150
T = 100
Z_t = C_t + I + G
Y_t+1 = Z_t
a.- Solve for equilibrium GDP, under the assumption that GDP is constant
b.- Suppose that the economy is in equilibrium, and then government spending decreases by 100 in period t. Construct a table showing what happens to consumption (C), demand (Z), and output (Y) in periods t, t+1 and t+2.
c.- Plot income and demand over time, from t to t+2
d.- When output eventually returns to a new constant value, what are the values of: income, demand, and consumption?
e.- How many periods must pass before 75% of the ultimate decrease in output has occurred?