Economics 607 - Core Macro

Homework 6

Homework 6 is here. It is due Friday 12/2 by 5:00 p.m.

Homework 5

Homework 5 is here.

Homework 4

Homework 4 is here.

Homework 3

Homework 3 is here.

Homework 2

Economics 607
Fall 2011
Homework #2
Due Oct. 13

1. Consider the model

y = c(y-t) + I(i-π^e)+g                 IS Curve

M(i)/P = L(y,i)                              LM Curve

dy/dt = k₁*EDG

di/dt = k₂*EDM

For what values of M_i is the model unstable? Draw the phase diagrams for an unstable case.

2. Given the model

y = c(y-t) + I(i-π^e)+g(y)            IS Curve

r = r(y, π)                                        MP Curve

dy/dt = k₁*EDG

dr/dt = k₂*(r(y, π)-r)

where government spending depends upon the level of output, characterize the conditions for stability mathematically (in terms of the admissible values of g_y) and illustrate the conditions using phase diagrams. Is countercyclical fiscal policy stable?

3. Given the model

y = c(y-t,r) + I(i-π^e)+g               IS Curve

r = r(y, π)                                         MP Curve

dy/dt = k₁*EDG

dr/dt = k₂*(r(y, π)-r)

where c_r < 0 and all other partial derivatives have their usual signs, (a) show that the model is stable. (b) Show graphically and explain intuitively how the effectiveness of fiscal policy changes when consumption becomes more responsive to changes in the interest rate.

4. Given the classical model

y* = c(y*-t,π) + I(i-π^e)+g               IS Curve

r = r(y*, π)                                            MP Curve

dπ/dt = k₁*EDG

dr/dt = k₂*(r(y*, π)-r)

where c_π < 0 and all other partial derivatives have their usual signs (the natural rate of output, y*, is assumed to be fixed), (a) show that the model is stable. (b) Show graphically (in i-π space with i on the vertical axis and π on the horizontal) how i and π change when t increases. Explain intuitively.

5. Problem 6.5 in Romer.

Homework 1

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 π^e 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 L_i 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 P^e = 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.

Homework 6

Homework 6 is here. It is due Thursday (12/2).

Homework 5

Homework 5 is here.

Homework 4

Homework 4 is here.

Homework 3

Homework 3 is here.