Question 2. In this question, we include the scal policy to IS curve. Suppose C, I, NX are the same with the lecture notes, but tax and government spending is dierent. Assume that government collects proportional income tax. Let t be the income tax, hence tax revenue is:

T = t Y .

a.) Suppose that government spending is given exogenously as G (G with an line above it). Find the function of Y in terms of interest rate i .

B.) By denition, government spending is part of GDP. One might naively expect that, if G went up by one dollar, then output would go up by one dollar. However, when people debate the pros and cons of scal stimulus, they want to know whether a dollar of government spending can increase output by more than a dollar.

Suppose that the government increases G by one without adjusting taxes. Holding i constant, how much does output increase? How does the response of output depend on the marginal tax rate t ?

C.) Now suppose that government has a balanced budget: T = G. Find the function of Y in terms of interest rate i . What is the impact of a $1 increase in government spending?

D.) Now, suppose government does not have a balanced budget and tax is still T = t Y . Instead, the government decides that it systematically wants to increase expenditures when the economy is in recession, and cut expenditures when the economy is in expansion. In reality, spending on programs like food stamps and welfare tend to go up during recessions. Assume that the government now chooses expenditures to satisfy: G = G a (Y Y ^p)

where G is autonomous expenditure, Y ^p is potential output, and a is a parameter that captures the sensitivity of government spending to changes in output. Notica that if output is at potential (Y = Y ^p ), then government spending is imply equal to G .

D.i) Find the function of Y in terms of interest rate i .

D.ii) If interst rate increases by one, then how much does Y change? How does the sensitivity of Y changes in i depend on a?

D.iii) Government programs that increase spending during recessions are often called automatic stabilizers`. In light of your answer to part ii, where do you think this name comes from?