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.