ANSWERS TO PROBLEM SET 6 - Public Finance J. Wissink - Cornell University

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1 ANSWERS TO PROBLEM SET 6 - Public Finance J. Wissink - Cornell University 1. a. See diagram below. On the left, the tax is levied on the suppliers and on the right, demanders. (Note: T=true and M=market) The price demanders pay and the price suppliers receive, after imposition of the tax, is independent of how the tax is collected. b. False. See the graph below. The economic price incidence will still depend on the elasticity of the demand curve relative to the shape of the marginal cost curve. Notice I didn't say "supply curve" because a monopolist really has no well-defined supply curve. Note that in this graph, the increase in the monopolist's price to demanders is less than the amount of the tax. c. Not quite. The young are saving to smooth out their own consumption including their own consumption when they retire. By giving their savings to the current old we may not have a welfare improvement, especially if economic and demographic conditions have changed for the worse by the time the current young are retired. If the system crashes or there are not enough working people

2 producing enough national income to support these now retired people at levels equal to what their savings would have allowed had their savings not been given to the current old at the time, then there would not be a Pareto improvement. 2. If X D =100-2P and X S =3P, then the equilibrium is where demand=supply. Setting the two quantity functions equal we get: 100-2P*=3P* so that 5P*=100 or that P*=$20 and therefore X*=60. Now if you have a $4 per unit tax, collected equally from suppliers and demands you factor the statutory responsibility into the respective demand and supply curves. Demand will shift vertically down by $2 and supply will shift vertically up by $2. Go back to the original demand and supply equations and get the inverse demand and supply: P D =50-(1/2)X and P S =(1/3)X. Now introduce the tax and calculate the correct market demand and supply curves: P Dmarket =48-(1/2)X and P Smarket =(1/3)X+2. Now get the equilibrium by setting P Dmarket =P Smarket. 48-(1/2)X* = (1/3)X*+2 or (5/6)X* = 46 or X* = From this we get the following: P market =$20.4 and P D =22.40 and P S = Note: the increase in price for demanders is $2.40 ($22.40-$20) where the decrease in price received by suppliers is only $1.60. So, demanders bear relatively more of the true economic price incidence of the tax, even though they pay only half of it. This stems from the fact that the demand curve is more price inelastic as compared to the supply curve. 3. a. Doesn't matter. Since both supply curves are completely elastic, demanders in each market pay all the price incidence of the tax. b. Doesn't matter. Collection does not determine economic price incidence. c. Tax "X" since there is no quantity adjustment at all. d. For (a) should tax "X" now. For (b) it still doesn't matter how you collect the tax. For (c) you still want to tax "X". 4. Notice that the origin for Food is the bottom left and the origin for Manufacturing is the top right and that (w/r) gets flatter as the economy moves from E 0 to E 1. Since food is the taxed commodity and food is relatively more labor intensive, there is an economy-wide reduction in the return to labor relative to capital; i.e., (w/r) declines. 2

3 5. a. Since capital is highly elastic under the stated assumption, then capital will flow out of the county if it is forced to bear any of the burden - so capital will not bear the incidence in the end. But someone must - so it will either be labor (which is now less productive after the flight of capital, and hence receives a lower relative wage) or the demanders of what capital is used to produce (via higher consumer prices), or both - depending on how you write the model. The bottom line is that it will not be borne by capital - it will be shifted one way or another. b. This is just the monopoly problem restated. See the answer to question 1b. 6. This claim is based on examining the implied average tax rate for these taxes. If you examine the average tax rate, and use the knowledge that the goods that are usually subject to sales and excise taxes are normal goods with low income elasticities (income elasticities less than one) you find that as income rises, the taxes paid relative to income is higher for lower income people than it is for higher income people. 7. This claim is based on the fact?/assumption? that the demand for hotels rooms in New York City is far more price inelastic than the supply of hotel rooms. If that s the case, then the economic price incidence falls on demanders, who happen to be from outside NYC (otherwise why would they need to stay in a hotel?). Would it work for Ithaca? Well...is the demand for hotel rooms in Ithaca more price inelastic than the supply of hotel rooms? And are outsiders the ones staying in these hotels paying the bill? You d have to find out the answers to such types of questions before making a prediction. 3

4 8. The following tax function has a decreasing marginal tax rate throughout income and an increasing average tax rate for income up to Y#. Taxes Y# Income 9. One could argue that OASDI is not horizontally equitable in that it favors women over men, due to the fact that it is gender neutral with respect to contributions and benefit calculations, but women live, on average, longer than men. You could also point to other redistributions that exist as a consequence of the structure and claim they introduce horizontal inequities. This is just one example. Likewise, you could argue that unequals are not treated fairly to the extent that you disagree with the amount of redistribution that takes place over income levels and/or generations, etc. 10. Since the tax function is getting steeper all the time, it is progressive with respect to marginal tax rate. It is also progressive with respect to the average tax rate. If you look at the slope of rays drawn from the origin to a point on the function, you see that these rays get steeper all the time so that the average tax rate is increasing in taxable income. 11. First find the $CE. Note that the Eu =.25* *200 = 275 so that $CE=$ Now construct the contract. Consider the good state: = 250,000 - Prem, so that Prem = 174,375. Now consider the bad state: = 40, ,375 + Ben, so that Ben = 210,000. Note that expected profit = 174, * = Social Security benefits do not change with changes in the value of assets held by the beneficiary. The formula used to calculate benefits under Social Security is based on earned income only. Your grandma s Social Security benefits will not be affected by the sale of her house. 13. A big problem with private UI is that the risk across people the market insures is correlated. It s a social risk. When the economy goes into a recession, lots of people will become involuntarily unemployed and then eligible for their benefits. This is very hard for a private firm to cover. Or when one sector in an economy decline for some reason, lots of people (say auto workers) will find themselves involuntarily unemployed at the same time. Also, government provision of unemployment insurance pools all types of risks; privately provided insurance accounts for variances in risk by requiring higher risk people to pay a higher premium. The private insurance market is most likely to work well that is, will be able to avoid market failures like adverse selection and moral hazard when any behavior that would tend to increase risk is observable by the insurance company. In situations in which private insurance markets are more susceptible to market failure, the government is more likely to directly 4

5 provide the insurance. The government is also more likely to provide insurance when there are strong equity arguments for covering everyone. While it is true that some people are at a higher risk for making claims for UI benefits, lots of that risk is not in their control. In a recession both good and bad workers get laid off. When good and bad workers are pooled, those who are fortunate enough to keep their jobs subsidize the less fortunate. Driving habits seem less a function of luck. Individuals who have a record of traffic violations or multiple claims pay higher premiums. In that way, private insurance markets require poorer drivers to bear more of the cost of their bad driving. By differentiating among driver types, insurance companies reduce the problem of adverse selection and, to some degree, the problem of moral hazard. A person who knows his premium will increase with each accident or ticket may not engage in more risky behavior. 5