6 Suppose that the economys LM curve is given by the equatio

6. Suppose that the economy\'s LM curve is given by the equation Y-100 + 10000 ×(r+ ?*) and that the expected inflation rate ?s constant at 3% per year. Suppose further that the economy\'s marginal propensity to spend (MPE) is 0.6, that the marginal propensity to import IMy is .25, that the initial level of baseline autonomous spending Ao is $500 billion, that a 1 percentage point increase in the real interest rate (i.e., an increase of 0.01 in r) reduces investment spending by $4 billion and reduces the value of the exchange rate by 10 points, and that a 1-unit increase in the exchange rate increases net exports by $0.6 billion. What is the effect on the domestic economy\'s equilibrium of a sudden 30-point increase in the exchange rate as foreign exchange speculators lose confidence in the economy?

Solution

Y = 100 + 10,000 x (r + 0.03)

(i)

A 10-point decrease (increase) in exchange rate is associated with 1-point increase (decrease) in interest rate. So,

A 30-point increase in exchange rate is associated with a (1 x 30/10) = 3 point decrease in interest rate.

(ii)

An 1-point increase (decrease) in interest rate decreases (increases) investment by $4 billion. So,

A 3-point decrease in interest rate increases investment by ($4 billion x 3) = $12 billion.

(iii)

A 1 unit increase in exchange rate increases net exports by $0.6 billion. So,

A 30 unit increase in exchange rate increases net exports by ($0.6 x 30) = $18 billion.

(iv)

Net increase in spending ($ billion) = Increase in net exports - Decrease in investment = 18 - 12 = 6

(v)

Spending multiplier = 1 / (1 - MPE + IMy) = 1 / (1 - 0.6 + 0.25) = 1 / 0.65 = 1.54

Increase in Y ($ billion) = Net increase in spending x Spending multiplier = 6 x 1.54 = 9.24

(vi)

Initial value of Y ($ billion) = 500.

From LM equation,

500 = 100 + 10,000 x (r + 0.03)

10,000 x (r + 0.03) = 400

r + 0.03 = 0.04

r = 0.01 (= 1%)

New value of Y ($ billion) = 500 + 9.24 = 509.24

From LM equation,

509.24 = 100 + 10,000 x (r + 0.03)

10,000 x (r + 0.03) = 409.24

r + 0.03 = 0.0409

r = 0.0109 (= 1.09%)

Net increase in interest rate = 1.09% - 1% = 0.09%