304CHAPTER 9. THE NEW INTERNATIONAL MACROECONOMICS

Problems

1. Solve for e ect on the money component of foreign welfare following a permanent home money shock in the Redux model.

(a) Begin by showing that

∆Ut 3 = −γ µ P0

¶

−

·Pˆt

+

1 −β β Pˆ ¸

M

1

²

Next, show that Pˆt = −nSˆt and

Pˆ =

rn(θ2 − 1)

Sˆt.

²[r(1 + θ) + 2θ]

Finally, show that

− # µ P0 ¶

t

"

²[r(1 + θ) + 2θ]

t

∆U

3 =

−(θ2

− 1)

1

M

1−² nγSˆ

This component of foreign welfare evidently declines following the permanent Mt shock. Is it reasonable to think that it will o set the increase in foreign utility from the consumption and leisure components?

2.Consider the Redux model. Fix Mt = Mt = M0 for all t. Begin in the ‘0’ equilibrium.

(a)Consider a permanent increase in home government spending, Gt = G > G0 = 0. at time t. Show that the shock leads to a home depreciation of

ˆ	(1 + θ)(1 + r)

St = r(θ2 − 1) + ²[r(1 + θ) + 2θ]g,ˆ

and an e ect on the current account of,

	ˆb =	(1 − n)[²(1 − θ) + θ2 − 1]	gˆ.
		²[r(1 + θ) + 2θ + r(θ2 − 1)]

ˆ

What is the likely e ect on b?

9.2. PRICING TO MARKET

305

(b)Consider a temporary home government spending shock in which Gs = G0 = 0 for s ≥ t + 1, and Gt > 0. Show that the e ect on the depreciation and current account are,

	ˆ		(1 + θ)r
	St =		²[r(1 + θ) + 2θ + r(θ2 − 1)]	gˆt,
	ˆb =		−²(1 − n)2θ(1 + r)	gˆt.
		r²[r(1 + θ) + 2θ + r(θ2 − 1)]

3. Consider the pricing-to-market model. Show that a permanent increase in home government spending leads to a short-run depreciation of the home currency and a balance of trade deÞcit for the home country.

306CHAPTER 9. THE NEW INTERNATIONAL MACROECONOMICS