Economics 219

Answers to Problem Set #7

1) a)-c)

 

Old Tax Code

Flat Tax Code

I = $20,000

Marginal Rate = 10%

Marginal Rate = 25%

Tax Bill = (.10)($15,000) = $1,500

Tax Bill = (.25)($10,000) = $2,500

Average Rate = $1,500/$20,000 = 7.5%

Average Rate = $2,500/$20,000 = 12.5%

 

I = $60,000

Marginal Rate = 40%

Marginal Rate = 25%

Tax Bill = (.10)($20,000) + (.20)($30,000) + (.40)($5,000) = $10,000

Tax Bill =  (.25)($50,000) = $12,500

Average Rate = $10,000/$60,000 = 17%

Average Rate = $12,500/$60,000 = 21%

 

I = $110,000

Marginal Rate = 40%

Marginal Rate = 25%

Tax Bill = (.10)($20,000) + (.20)($30,000) + (.40)($55,000) = $30,000

Tax Bill = (.25)($100,000) = $25,000

Average Rate = $30,000/$110,000 = 27%

Average Rate = $25,000/$110,000 = 23%

d) For the $20,000 a year earner, the effect of the change in the tax code is ambiguous: with higher marginal rates, he would work less, but with higher average rates, he would work more.  For the $60,000 per year earner the marginal rate has dropped (work more) and average rates have risen (work more) – This is the strongest piece of the tax reform (in terms of stimulus).  For the $110,000 a year household, marginal rates drop (work more), but average rates drops as well (work less).  Once again, the net effect is ambiguous. At the aggregate level, however, things simplify a little because the income effects cancel out.  Anyone with income over $55,000 will have the incentive to work more with the flat tax system while anyone earning less will have the incentive to work less.  To decide which group will dominate, we would need to know something about median income in the country of Fredonia.  Suppose that median income was exactly $55,000.  This means that exactly half the population earns more than $55,000 and half earn less. In this case, the conversion to the flat tax would have no aggregate effects.  Suppose that median income in Fredonia was $30,000.  This would tell us that more than half the population earned less than $55,000 and, hence would dominate the labor market.  Therefore, in this case, aggregate labor supply would drop and the pre-tax wage would rise.

2)

    1. Bill Clinton is offering to provide a service that consumers value at $720 per year ($60/month * 12) for a cost of $500. If this legislation passes, it would have the same effect as $220 worth of goods per consumer magically appearing out of thin air. However, because this legislation is under the treat of being overturned, this extra $220 worth of goods is viewed as temporary. The analysis looks exactly like a temporary increase in income. Savings increases as consumers save some of their extra income. The result is lower interest rates, and higher levels of savings and investment.
    1. If there is know threat of reversal, the yearly "gift" of $220 can be viewed an permanent. Hence, there is no reason to increase savings. Therefore, interest rates, savings and investment remain constant.
3.    The key to analyzing distortionary taxes is to recognize the fact that people tend to do less of the activities that are being taxed. (Recall, that Ricardian equivalence implies that the income effects of taxes are zero for a given level of government spending).
    1. In this case, an investment tax credit lowers the user cost of capital thereby increasing investment demand. Note that the secondary price effects act to reinforce the original policy. As interest rates rise, the incentive to save increases. The end result is that interest rates are higher, consumption is lower (hence, saving is higher) and investment is higher.
    2. With this policy, the lowering of the tax on savings gives consumers the incentive to save more. However, as the demand for consumption falls, interest rates start dropping, which lowers the effectiveness of the policy. The end result is that consumption is lower (hence, saving is higher), investment is higher, and interest rates are lower.

To decide which policy is more effective, we would need a little more information, such as the tax and interest rate elasticity of investment and consumption demand.

4.    To analyze the effects of transfers, we need to recognize that income is not being created, but simply transferred. Therefore to decide the aggregate effect, we need to compare the behavior if the "winners" with that of the "losers".
    1. In the case of social security, the "winners" are the retirees and the "losers" are those currently working. Think of aggregate consumption demand as the sum of workers and retirees. The retirees have received a gift in the form of their social security check and, hence, consume more. Those who are working just lost an amount exactly equal to the retirees gain and hence, consume less. In principle, these two effects could exactly cancel each other out, leaving all aggregate variables unchanged. However, it is my guess that the marginal propensity to consume for the retirees is higher that that of workers. In this case the increase in demand by retirees would be greater than the drop by workers resulting in higher consumption and interest rates and lower investment.
    2. If the social security system is financed by an income tax, everything from part (a) holds, but we must also consider the distortion created by the tax. With higher marginal tax rates, aggregate labor supply falls, lowering output and raising wages. Note that this loss in output magnifies the results from part (a).