Economics 442: Macroeconomic Policy - Problem Set 3
Q1. Consider the following data from US Treasury https://www.treasury.gov/resource-center/data-chart-center/interest-rates/Pages/TextView.aspx?data=yield
|
Date
|
1 Mo
|
3 Mo
|
6 Mo
|
1 Yr
|
2 Yr
|
3 Yr
|
5 Yr
|
7 Yr
|
10 Yr
|
20 Yr
|
30 Yr
|
|
03/01/16
|
0.29
|
0.33
|
0.50
|
0.68
|
0.85
|
0.98
|
1.31
|
1.62
|
1.83
|
2.28
|
2.70
|
|
03/02/16
|
0.28
|
0.36
|
0.48
|
0.67
|
0.85
|
1.00
|
1.34
|
1.65
|
1.84
|
2.27
|
2.69
|
|
03/03/16
|
0.25
|
0.28
|
0.46
|
0.65
|
0.85
|
0.99
|
1.33
|
1.63
|
1.83
|
2.23
|
2.65
|
|
03/04/16
|
0.25
|
0.29
|
0.47
|
0.67
|
0.88
|
1.04
|
1.38
|
1.69
|
1.88
|
2.29
|
2.70
|
|
03/07/16
|
0.27
|
0.32
|
0.49
|
0.67
|
0.91
|
1.08
|
1.42
|
1.72
|
1.91
|
2.30
|
2.71
|
Suppose the expectations hypothesis of the term structure holds.
1. Calculate the expected one year interest rate, one year from 3/7/2016.
2. Calculate the expected five year rate expected five years from 3/7/2016.
3. Given the interest rates given in the table, do you expect a recession in the next year? Why or why not?
Q2. Secular stagnation? Suppose the national saving (NS) and investment (I) functions (as a share of GDP) for an economy are given by the following equations.
NS = [S] + BuS = [α0 + α1r + α2d] + F0
α1 > 0, α2 < 0
I = β0 + β1r + β2z
Β1 < 0, β2 < 0
Where S is saving, BuS is the government budget balance (as a share of GDP), r is the real interest rate, d is a dependency rate (share of children in the economy), z is productivity of capital goods.
The equilibrium condition is: NS = 1
The r that solves this equilibrium condition is the equilibrium real interest rate (you can call it r*).
1. Draw a graph of these curves, with the vertical axis as r, and the horizontal axis as NS, and I. Indicate the slopes of these curves, and what shifts each of the curves.
2. Solve for the algebraic solution.
3. Now suppose all the parameters stay the same, as does z, but the youth dependency rate drops so much that the equilibrium real rate drops below that which is feasible (call that X%). Show the graph.
4. Suppose the real interest rate cannot drop below X%. What is the level of desired investment? What is the level of desired saving? Do these levels match?
5. Show what an increase in government spending (resulting in a reduction in national saving) does in this graph.
Q3. Multipliers. Suppose the short run and long run aggregate supply curves look like the following in the AD-AS diagram:
Aggregate demand is given by:
Y = γ^[Λ0 - b2μ0/h + (b2/h)(M0/P)] where γ^ = 1/1-c1(1-t1) + b2/h
1. Suppose output is currently at Yn, and interest rates are above 0%. What is the size of the multiplier for government spending, assuming the final level of income is below Yn and the central bank targets the money stock (and the interest rates end up above 0%)?
2. Suppose output is at Yn. What is the size of the government spending multiplier for an increase in government spending?
3. Using the same assumptions as in 3.2, state the size of the increase in income arising from a $1 billion increase in the money supply.
4. Suppose output is currently below Yn, but interest rates are already at zero. What is the size of the increase in income for a $1 billion real increase in money supply?