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

Calculating Equilibrium Output
At this point, it may be helpful to work through two simple examples, one illustrating
the calculation of equilibrium GDP in a closed economy and the other showing
the same calculation for an open economy. Suppose we have the following information
on a closed economy. Each row in Table 30.1 gives the level of income (Y ) in the
first column and the levels of taxes (T), consumption (C), investment (I), and government
purchases (G) at that level of income. I and G are assumed to be constant,
regardless of the level of income, but both taxes and consumption rise with income.
The final column calculates aggregate expenditures; it is simply equal to C + I + G
for our closed economy.
Equilibrium output occurs at the point where Y is equal to C + I + G. Using the
information in Table 30.1, we can add up C, I, and G. If we do this, we find that equilibrium
output is 7,000. At this output level, consumption is 4,600, investment is
1,200, and government purchases are 1,200; therefore, AE = C + I + G = 4,600 + 1,200
+ 1,200 = 7,000 = Y.
Suppose G increases to 1,600. Recalculating aggregate expenditures (C +
I + G ) at each income level, we can find that the new equilibrium level of output
will be 8,000. The increase of G by 400 increases Y by 1,000, so the multiplier
is 2.5.
We also know that when taxes depend on income, the multiplier is equal to
1/[1 − (1 − t)MPC]), where t is the marginal tax rate. Using the information in the
table, we can see that as income rises by 1,000, say from 7,000 to 8,000, taxes increase
by 250, one-fourth as much. So t = .25. As total income increases by 1,000, disposable
income increases by 750. Consumption then rises by 600. In the same example, as
Table 30.1
EQUILIBRIUM OUTPUT IN A CLOSED ECONOMY
Y T C I G AE
1,000 200 1,000 1,200 1,200 3,400
2,000 450 1,600 1,200 1,200 4,000
3,000 700 2,200 1,200 1,200 4,600
4,000 950 2,800 1,200 1,200 5,200
5,000 1,200 3,400 1,200 1,200 5,800
6,000 1,450 4,000 1,200 1,200 6,400
7,000 1,700 4,600 1,200 1,200 7,000
8,000 1,950 5,200 1,200 1,200 7,600
9,000 2,200 5,800 1,200 1,200 8,200
10,000 2,450 6,400 1,200 1,200 8,800
11,000 2,700 7,000 1,200 1,200 9,400
12,000 2,950 7,600 1,200 1,200 10,000
13,000 3,200 8,200 1,200 1,200 10,600
CALCULATING EQUILIBRIUM OUTPUT ∂ 681