Public Affairs 974-001 Fall 2010 - Problem Set 1
1. IS-LM. Suppose the economy is described by the following two equations:
(a) i = A0/b - ((1-c(1-t))/b)Y
Where A0 ≡ a0 - c(TA0) + IN0 + GO0 + NX0
(2) i = μ0/h - (1/h)(M0/P0) + (k/h)Y
1.1 Show equilibrium, graphically. Assume k/h > 0, -(1-c(1-t))/b < 0.
1.2 Show the impact of an increase in government spending.
1.3 Show the impact of an increase in money supply.
1.4 Show what the central bank has to do in order to keep interest rates constant. What is the size of the increase in output?
2. Modified IS-LM. Suppose the IS curve is as in equation (1), but the LM curve is given by:
(3) i = μ0/h - (1/h)(M0/P0) + (j/h)(M0/P0 + B0/P0) + (k/h)Y
2.1 Show the impact of an increase in government spending, starting from initial budget balance. Assume k/h > 0.
2.2 Show what happens if the central bank simultaneously increases the money supply.
2.3 How does your answer to problem 2.1 change if h = ∞?
Q3. AD-AS. Suppose aggregate demand and the Phillips Curve are given by:
(4) Y = α^[A0 + (b/n)(M0/P) - (b/h) μ0]
3.1 Draw the AD-AS diagram, assuming initial long run and short run equilibrium.
3.2 Show what happens if autonomous spending decreases, both initially, and over time.
3.3 Show what happens if autonomous spending decreases, but so too does Y*.
3.4 Redo 3.3, assuming the government and the central bank seek to restore income to its initial level.
Q4. What is the yield to maturity of a $1000 face value discount bond maturing in one year that sells for $900? Show your algebraic work, "boxing-in" your answers.
Q5. Calculation of real interest rates.
Take the 3 month interest rates for the U.S., the Euro area, and Japan reported in the tables below (drawn from the Oct. 2nd issue of the Economist). Calculate the real interest rate, assuming that the expected (annualized) inflation rate for the next 3 months equals the most recently recorded inflation rate. [For future reference: These data are updated weekly, and are available at: https://www.economist.com, and are also reported in the hard copy version of the magazine.]
Trade, exchange rates, budget balances and interest rates
|
Trade balance* latest 12 months, $bn
|
Current-account balance
|
Currency units, per $
|
Budget
balance % of GDP
2010†
|
Interest rates, %
|
|
latest 12
months, $bn
|
% of GDP 2010†
|
3-month
latest
|
10-year gov't
bonds, latest
|
|
Sep 29th
|
year ago
|
|
United States
|
=604.7 Jul
|
=430.9 02
|
=3.2
|
=
|
=
|
=9.0
|
0.23
|
2.50
|
|
Japan
|
+87.5 Jul
|
+180.3 Jul
|
+3.4
|
83.6
|
89.5
|
-7.6
|
0.19
|
0.90
|
|
China
|
+179.0 Aug
|
+286.8 02
|
+4.9
|
6.69
|
6.83
|
-2.2
|
2.61
|
3.01
|
|
Britain
|
-138.1 Jul
|
-33.7 01
|
-1.6
|
0.63
|
0.63
|
-10.1
|
0.80
|
3.01
|
|
Canada
|
-5.6 Jul
|
-41.102
|
-2.2
|
1.03
|
1.07
|
-4.6
|
0.90
|
2.75
|
|
Euro area
|
+12.9 Jul
|
-68.2 Jul
|
-0.3
|
0.74
|
0.68
|
-6.5
|
0.89
|
224
|
Output, prices and jobs % change on year ago
|
Gross domestic product
|
Industrial
production
latest
|
Consumer prices
|
Unemployment
rate‡, %
|
|
Latest
|
qtr*
|
2010†
|
2011†
|
latest
|
year ago
|
2010†
|
|
United States
|
+3.0 02
|
+1.6
|
+2.7
|
+2.4
|
+6.2 Aug
|
+1.1 Aug
|
-1.5
|
+1.6
|
9.6 Aug
|
|
Japan
|
+2.4 02
|
+1.5
|
+2.8
|
+1.4
|
+15.4 Aug
|
-0.9 Jul
|
-2.2
|
-0.8
|
5.2 Jul
|
|
China
|
+10.3 02
|
na
|
+9.9
|
+8.4
|
+13.9 Aug
|
+3.5 Aug
|
-1.2
|
+3.0
|
9.6 2009
|
|
Britain
|
+1.7 02
|
+4.7
|
+1.5
|
+1.9
|
+1.9 Jul
|
+3.1 Aug
|
+1.6
|
+3.0
|
7.8 Jul††
|
|
Canada
|
+3.4 02
|
+2.0
|
+3.2
|
+2.7
|
+8.1 Jun
|
+1.7Aug
|
-0.8
|
+1.8
|
8.1 Aug
|
|
Euro area
|
+1.9 02
|
+3.9
|
+1.5
|
+1.3
|
+7.1 Jul
|
+1.6 Aug
|
-0.2
|
+1.5
|
10.0 Jul
|