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Transcript
```Solution Key: Homework 2
Chapter 3
Economics 101
1) The Congress wish to cut taxes. Suppose you are a policy analyst working for the Congressional Budget Office, and
it is your job to analyze the macroeconomic effects of a permanent tax cut. Suppose you have worked out the following
very simplified model to characterize basic features of the U.S. economy:
Y = 4K + 5L,
G = 3000
I = 2000 - 6000r
K=1000 and L= 800
T = 3000
C = 600 + .6(Y-T)
a) First find the equilibrium levels of the interest rate, investment and consumption for the economy described for
the equations above. (Assume a closed economy: Y = C + I + G).
b) Discuss the effects on the economy of lowering the level of T by 10%. You should compute the new
equilibrium values of the interest rate, consumption and investment. By how much would investment be
crowded out by the tax cut?
c) Discuss briefly the intuition for why the investment equation above includes the interest rate with a negative
sign. Discuss how it might be sensible for consumption to be negatively affected by the interest rate in a way
similar to investment. If consumption did behave this way, use your intuition and economic reasoning to
make an educated guess about how it would affect the degree to which the tax cut crowds out investment:
more, less or the same. Explain your reasoning.
d) Test your guess above by trying the following example: C = 600 + .6(Y-T) - 3000r, where you keep the other
equations in the model the same as in part (b) above. Compute the equilibrium value of investment before
and after the tax cut, and compare the amount by which investment is crowded out to what you found in part
(b).
a) equilibrium condition: Y = C + I + G
8000 = 600 + 0.6(8000-3000) + 2000 - 6000r + 3000
-600 = -6000r so r = 0.10
C = 600 + 0.6(8000-3000) = 3600 and I = 2000 - 6000(0.10) = 1400
b) Taxes fall by 0.1*3000 = 300, from 3000 to 2700
Y = C + I + G means 8000 = 600 + 0.6(8000-2700) + 2000 - 6000r + 2700
-780 = -6000r so r = 0.13
C = 600 + 0.6(8000-2700) = 3780 and I = 2000 - 6000(0.13) = 1220.
The tax cut raises disposable income, which leads people to consume 180 extra units.
Because there is a limited supply of goods, the interest rate rises and crowds out investment
by 180 units.
c) Investment is negatively affected by the interest rate because it implies a greater cost for
borrowing the funds to carry out an investment project. Consumption might be affected in
the same way, because some consumption purchases, such as cars, usually require people to
borrow funds. If consumption is negatively affected by a rise in the interest rate, the tax cut
will not raise consumption as much as the case above. As the rise in disposable income
raises consumption, the resulting rise in the interest rate will partly counteract the rise in
consumption. As a result, investment should be crowded out by less.
d) For the example with consumption function: C = 600 + 0.6(Y-T) - 3000r
Equilibrium before the tax cut: Y = C + I + G
8000 = 600 + .6(8000-3000) – 3000r + 2000 - 6000r + 3000
-600 = -9000r so r = 0.067 thus I = 2000 – 6000(0.067) = 1600
Equilibrium after the tax cut: Y = C + I + G
8000 = 600 + 0.6(8000-2700) –3000r + 2000 - 6000r + 3000
-780 = -9000r so r = 0.0867, thus I = 2000 - 6000(0.0867) = 1480
So the interest rate rises less and investment now is only crowded out by 120.
2) According to the neoclassical theory of distribution, if firms are competitive and subject to