Economics 607
Fall 2011
Homework 1
Due Thursday, October 6
1. Answer the questions below based upon the following model:
| y = C(y - t) + I(i- πe) + G |
IS Curve |
| M/P = L(i, y) |
LM Curve |
a) Find the slope of the IS and LM curves.
b) Show graphically and mathematically how the LM curve shifts when M increases.
c) Show graphically and mathematically how the IS curve shifts when πe increases.
d) Show graphically, mathematically, and explain intuitively how i and y change when (i) there is an increase in g, and (ii) there is an increase in M.
e) Find the slope of the aggregate demand curve (in this case, relating P and y)
f) Does an increase in the absolute values of Li make monetary policy more or less effective? Explain graphically, mathematically, and intuitively.
2. Romer: pgs. 306-308, problems 6.1, 6.2, 6.3, 6.4 and 6.6.
3. Sargent pg. 75, problem 5 (a),(b).
4. Given the following model:
| y = E(y,r,g,t) |
goods market |
| r = r(y, P) |
policy reaction function |
| y=F(n,k0) |
production function |
| W=W0 |
labor supply |
where y = real output, g = real government spending, t = real taxes, r = the real interest rate, W0 = the fixed nominal wage, n = labor, and k0 = the fixed capital stock, and where all partials have their usual signs:
(a) Find dy/dW0, dP/dW0, dr/dW0, and d(W/P)/dW0.
5. Given the following model:
| y = E(y,r,g,t) |
goods market |
| r = r(y, P) |
policy reaction function |
| y=F(n,k0) |
production function |
| W=Peg(n) |
labor supply |
where Pe = the (exogenous) expected price level, y = real output, g = real government spending, t = real taxes, r = the real interest rate, W0 = the fixed nominal wage, n = labor, and k0 = the fixed capital stock, and where all partials have their usual signs:
(a) Find dy/dt, dP/dt, dr/dt, dW/dt, dn/dt, and d(W/P)/dt.