[Joseph_E._Stiglitz,_Carl_E._Walsh]_Economics(Bookos.org) (1)

Y goes from 7,000 to 8,000, disposable income goes from 5,300 (7,000 − 1,700) to
6,050 (8,000 − 1,950). Consumption rises from 4,600 to 5,200, an increase of 600.
The MPC is the increase in C per dollar increase in disposable income, or 600/750 =
.8. Using these values, we can calculate the multiplier to be 1/(1 − (1 − .25) × .8) =
1/(1 − .75 × 8) = 1/(1 − .6) = 1/.4 = 2.5, the same value we found directly by finding the
new equilibrium after an increase in G.
How would things change if we were dealing with an open economy? In an open
economy, aggregate expenditures consist of C + I + G + X − M, where X denotes
exports and M denotes imports. Suppose we have the information in Table 30.2.
Exports do not depend on the level of GDP; in our example, they are equal to 500.
Imports rise with income, and the example assumes a marginal propensity to import
of .1. Just as in the closed economy, equilibrium occurs when Y = AE. In this example,
as in the previous one, the equilibrium level of GDP is 7,000. For this economy,
net exports are positive at the equilibrium level of GDP. A comparison between the
AE column in the two tables reveals that as income rises, aggregate expenditures
increase faster in the closed economy than in the open economy. In the latter, a positive
marginal propensity to import means that imports rise as income rises, reducing
net exports.
Given a marginal propensity to import of .1, a marginal propensity to consume
of .8, and a marginal tax rate of .25, the formula for the multiplier tells us that a
$1 increase in G will increase equilibrium income by 1/[1 − .75(.8 − .1)] = 2.1. If
G increases by 400, then equilibrium income will increase by 840, from 7,000 to
7,840. Recall that in the closed economy described in Table 30.1, the multiplier
was 2.5. Again, the marginal propensity to import explains why it is smaller in the
open economy.
Table 30.2
EQUILIBRIUM OUTPUT IN AN OPEN ECONOMY
Y T C I G X M AE
1,000 200 1,000 1,200 1,100 900 200 4,000
2,000 450 1,600 1,200 1,100 900 300 4,500
3,000 700 2,200 1,200 1,100 900 400 5,000
4,000 950 2,800 1,200 1,100 900 500 5,500
5,000 1,200 3,400 1,200 1,100 900 600 6,000
6,000 1,450 4,000 1,200 1,100 900 700 6,500
7,000 1,700 4,600 1,200 1,100 900 800 7,000
8,000 1,950 5,200 1,200 1,100 900 900 7,500
9,000 2,200 5,800 1,200 1,100 900 1,000 8,000
10,000 2,450 6,400 1,200 1,100 900 1,100 8,500
11,000 2,700 7,000 1,200 1,100 900 1,200 9,000
12,000 2,950 7,600 1,200 1,100 900 1,300 9,500
13,000 3,200 8,200 1,200 1,100 900 1,400 10,000
682 ∂ CHAPTER 30 AGGREGATE EXPENDITURES AND INCOME