Solution Key: Homework 2 Economics 101
Chapter 3
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, K=1000 and L= 800
G = 3000 T = 3000
I = 2000 - 6000r 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).
Answer)
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 constant return to scale, how would total income be distributed?
Answer)
In competitive markets with constant return to scale technology out put is distributed according to the amount of each factor and its marginal productivity, i.e. Y = MPL x L + MPK x K
3) True-False:
Say if the following statements are True or False. If they are false write the correct statement
a) Disposable income is that part of consumption used for consumption
b) In a closed economy exports have to equate imports.
Answer)
a) False. Disposable income is the total income net of taxes. It may be consumed or saved.
b) False. In a closed economy not only Export=Import but both have to be equal 0.