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Unformatted text preview: increases disposable
income changes by dollar. Consumption then increases byon consumption tis smaller.G. Expenditure and income
less than total income, so the effect an amount (1 – )MPC × Δ
When taxes are fixed, we know that ∆Y/∆G = 1/(1 – MPC). We found this by increase even more. The process
increase by this amount, which in turn causes consumption to considering an increase in government purchases of ∆G; the initial effect of this
continues, and the total change in output is
change is to increase income by ∆G. This in turn increases consumption by an
amount equal to the marginal propensity to consume times the change in 3
income,
ΔY = ΔG {1 + (1 – t)MPC + [(1 – t)MPC]2 + [(1 – t)MPC] + ....}
MPC × ∆G. This increase in consumption raises expenditure and income even further. The process continues indefinitely, and we derive the multiplier above.
= ΔG [1/(1 – (1 – t)MPC)].
When taxes depend on income, we know that the increase of ∆G increases
total income by ∆G; disposable income, however, increases by only (1 – t)∆G—less
Thus, Consumption then increases by an amount (1 t )
than dollar for dollar.the governmentpurchases multiplier becomes 1/(1 – (1 ––t)MPC) rather than 1/(1 – MPC).
This means a much smaller by this amount, which in turn causMPC × ∆G. Expenditure and income increasemultiplier. For example, if the marginal propensity to consume MPC
i 3/4 and the tax more. 1/3, process continues, and the total
es consumption tos increase even rate t is The then the multiplier falls from 1/(1 – 3/4), or 4, to 1/(1 – (1 –
change in output is1/3)(3/4)), or 2.
∆Y = ∆G {1 + (1 – t)MPC + [(1 – t)MPC]2 + [(1 – t)MPC]3 + ....} c. In this chapter, we derived the IS curve algebraically and used it to gain insight into the = ∆G [1/(1 – (1 – t)MPC)]. interest rate and output. To determine how this tax system alters the
relationship between the
slope of the IS curve, we can derive the IS – (1 – t MPC) in which taxes depend on income.
Thus, the governmentpurchases multiplier becomes 1/(1curve for )the caserather
Begin with a national income accounts For example, if the marthan 1/(1 – MPC). This meansthemuch smaller multiplier. identity:
ginal propensity to consume MPC is 3/4 and the tax rate t is 1/3, then the multiplier falls from 1/(1 – Y = C +4, + G. – (1 – 1/3)(3/4)), or 2.
3/4), or I to 1/(1
In this chapter, we derived the IS curve algebraically and used it to gain insight
into the relationshiphe consumption function is and output. To determine how this
T between the interest rate
tax system alters the slope of the IS curve, we can derive the IS curve for the case
in which taxes depend a + income. Begin with the national income accounts identiC = on b(Y – T – tY).
ty: Note that in this Y = C + I + Gfunction taxes are a function of income. The investment function is
consumption .
the sameis in the chapter:
as
The consumption function
C = a + b(Y – T – tY).
Note that in this consumption function taxes are a function of income. The investment function is theubstitute the the chapter: and investment functions into the national income accounts identity to
S same as in consumption I = c – dr.
obtain: I = c – d r.
Substitute the consumption and investment functions into the national income
Y = [a +
accounts identity to obtain: b(Y – T – tY)] + c – dr + G.
Yolving for r: T – tY)] + c – dr + G.
S = [a + b(Y –
Solving for r:
r= È b (1  t )  1 ˘
a  bT + c + G
+Y Í
˙.
d
d
Î
˚ Chapter 10 Aggregate Demand I 93 The slope of the IS curve is therefore: pe of the IS curve is therefore: Dr b (1  t )  1
=
.
Dy
d
that t is a number that is less than 1. As t becomes a bigger number, the
Recall in absolute value than 1. As increases, becomes
f the IS curve increases that t and b are less terms andt the curve the slope of the IS curve increases in absolute
value terms is 0.80, t is 0.1, and d steeper. Suppose, for example, that b is 0.80, t is 0.1, and d is
. Suppose, for example, that b and the curve becomes is 0.5. The slope of the
0.5. The increases to 0.2, then the slope becomes –0.72.
e is –0.56. If the tax rate slope of the IS curve is –0.56. If the tax rate increases to 0.2, then the slope becomes –
ely, if the tax rate 0.72. Intuitively, any givenrate is higher, then interest rate
is higher, then if the tax reduction in the any given reduction in the intere...
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This note was uploaded on 10/01/2013 for the course ECON 302 taught by Professor Alvero during the Winter '09 term at The University of British Columbia.
 Winter '09
 ALVERO
 Economics

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