税收学 罗森课后讨论题和答案

一、税收与收入分配

1、根据Goolsbee的估计，网上购物对税率的敏感度很高，如果对这类购物按现行销售税征税，就会大

大降低在线购物者人数和在线支出数额。如何认识网上销售征税的税收归宿？

These reports about demand sensitivity suggest that there is a very elastic demand curve for goods sold over the Internet. Because of this high elasticity, the incidence of a tax levied on Internet sales is primarily borne by producers, not consumers.

2、在任一产量水平上，物品X的平均成本都等于其边际成本，假定X的市场是竞争的，且需求曲线是

线性的。试分析对X课征单位税u美元的影响。假定X的市场是垄断的，征同样的税会有何影响。

讨论两种情况的差异。

3、用一般均衡框架，讨论对香烟征税的可能归宿。

One expects that those factors that are used intensively in tobacco production will bear the burden of the tax.

Assuming, for example, that tobacco production is capital-intensive, one expects owners of all capital (not just those with investments in tobacco) to bear some of the burden.

4、假定在某一理想的国家里，香烟的需求为：Q D=2000-200P，式中Q D是需求的数量（包），p是每包烟

的价格。香烟的供给是Q S=200P。

（1）假定市场是竞争的，找出香烟的价格和数量。

（2）为了减少吸烟，政府对每包烟课以2美元的税。计算出征税后香烟的数量、消费者支付的价格以及生产者得到的价格。这种税为政府筹措了多少收入？

a. Set 2000 – 200P = 200P, so P = $5 and Q = 1000 packs

b.Consumer price = Producer Price + $2. Let P be the producer price.

2000 – 200 (P + 2) = 200 P.

Producer receives $4 per pack; consumer pays $6 per pack.

Quantity sold = (200)(4) = 800 packs.

Tax revenue = (tax/pack) (no. of packs) = (2) (800) = $1600.

5、假定某种商品的需求曲线是：Q D=a-bP。该商品的供给曲线是：Q S=c＋dP。找出做为常数a、b、c、d

函数的均衡价格和产量。

现假定对这种商品征收u美元的单位税。证明：不管这种税是对该商品的生产者课征，还是对其购买者课征，新的均衡点是一样的。

The equilibrium price can be calculated by setting the quantity supplied equal to the quantity demanded:

(i) Q D = a - bP

(ii) Q S = c + dP

If Q D = Q S , then the equilibrium price can be determined as follows:

The equilibrium output can be determined by substituting the equilibrium price into either the supply or demand equation.

Substituting into the demand equation:

Substituting into the supply equation:

If a unit tax of u dollars is impos ed on the commodity, then it doesn’t matter which party it is imposed upon (the consumer or producer); the new equilibrium will be the same in either case. If the unit tax is

imposed upon the consumer, then the price the consumer pays is u higher than the price received by the supplier. The consumer’s price without the tax, P C , and price that includes the tax, P CT , are:

Similarly, the price received by the producer in the absence of the tax, P P , is u lower than the price received with the imposition of the tax, P PT . These prices are expressed below:

The equilibrium that prevails after the imposition of the tax can be found by setting P CT = P P or P C = P PT -- in the end, both approaches will yield the same answer. First, we can derive the solution setting P CT = P P :

d

b c a P P

d b c a dP

c bP a +-=+=-+=-)(??

? ??+--=-=d b c a b a Q bP

a Q ??

? ??+-+=+=d b c a d c Q dP

c Q Q b b a P C ??

? ??-=1d c Q d P P -??

? ??=1u d c Q d P PT --??

? ??=1u Q b b a P CT +??? ??-=1

Next, setting P C = P PT :

Therefore, both approaches lead to the same outcome.

9、假定在某一国家，税收收入（T ）取决于收入（I ），其函数形式为T=a ＋tI 。其中，a 和t 是数字（例如，a ＝－4000，t ＝0.2）。以收入水平的函数形式，写出平均税率公式。证明：如果a 是负数，则该税制是累进的；如果a 是正数，则该税制是累退的。（提示：平均税率是T/I ）

The equation T=-4000+.2I is somewhat similar to the exercise in Table 12.1 on page 277 of the textbook. If we follow the text and define progressivity with respect to average tax rates rather than marginal tax rates, then the average tax rate equal ATR=(-4000/I)+.2 for any income level. Clearly this average tax rate converges to ATR=20% as income gets large, and is lower for lower income levels. Replicating Table 12.1 for the tax system given here, we get:

10、2002年，纽约市把香烟税率从每包8美分提高到1.5美元。一个月之后，市长发言人说：“香烟的销量少了，而本市赚的钱多了”。出于简化而假定纽约市的香烟供给是完全弹性的。

d

b dbu b

c da Q Q db

d b db dbu bc da Q d b u d c b a d c Q d u Q b b a P P P

CT +++=??

? ??+=++??

? ??+=++-??

? ??=+??? ??-=1111d

b dbu b

c da Q Q db

d b db dbu bc da Q d b u d c b a u d c Q d Q b b a P P PT

C +++=??

? ??+=++??

? ??+=++--??

? ??=??? ??-=1111

（1）假定该发言人说的是事实，在纽约市香烟需求弹性的真实情况是什么？

（2）回想一下，该发言人的话是在税率上调之后一个月说的。随着时间的推移，你认为需求曲线的弹性会发生什么情况？这对纽约市的税收收入将产生怎样的影响？

a. After New York City increased the tax from $0.08 to $1.50 per pack of cigarettes, t he quantity demanded went down and revenues went up. Define TR1 as the total revenue after the tax, and TR0 as the total revenue before the tax. Then TR0=QP and TR1=(Q-dQ)(P+dP)=QP+QdP-PdQ-dQdP.Ignore the last term, dQdP, which is of second order importance. Then dTR=QdP-PdQ. If this change in revenue is positive, then dTR=QdP-PdQ>0, or QdP/PdQ>1. Thus (1/εD)>1 or εD<1. Thus, the absolute value of the elasticity of demand is less than 1, or demand must be inelastic in this case.

b. The spokesman’s comment was made just one month after the tax increase was enacted. As more time passes and consumers are able to adjust (e.g., by quitting smoking, substituting to other forms of tobacco that are not taxed in the same way, et

c.), it is expected that the long-run elasticity of demand for cigarettes will be larger in absolute value (e.g., become relatively more elastic), and revenues will likely fall.

11、2003年，香港对雇佣来自其他国家的家庭佣人的雇主，每月课税51美元。这些工人很多都来自菲律宾，菲律宾总统阿罗约称这种税是不公正和不公平的。在这种税对雇主征收的情况下，阿罗约总统的这种不安是正确的吗？勾画出与她的被证明是正确的关注相一致的模型。

Even though the statutory incidence of the $51 per month per domestic-help tax is on the employers, the tax may very well be borne primarily by the foreign domestic-help workers. This could happen if the demand for the foreign domestic-help workers is relatively elastic and/or the supply of foreign domestic-help workers is relatively inelastic. One might imagine, for example, that native domestic-help is a good substitute for foreign domestic-help, and thus, demand for foreign domestic-help is quite elastic. Thus, wages of foreign workers are likely to fall, assuming there is no minimum wage in Hong Kong (if there was a minimum wage, it is likely that employment would fall). Thus, the Philippine president was correct to be disturbed, because the economic incidence falls on his countrymen. The figure below illustrates the likely situation with relatively inelastic labor supply and relatively elastic labor demand.

二、税收与效率

1、下列那种情况可能产生较大的超额负担？

（1）土地税

（2）对手机的使用课征24%的税

（3）对高新技术的投资给予补贴

（4）经济利润税

（5）对所有计算机软件课征10％的税

（6）只对Excel 电子表格程序征税

a. Since land is fixed in supply, we expect no excess burden when it is taxed. The supply curve is inelastic.

b. There are fairly good substitute for cell phones. Therefore, their demand is quite elastic, and a

tax on them will have a substantial excess burden, relative to the size of revenues collected.

c. Without knowing exactly what “high -tech” means, it is likely that many companies could re label

themselves as high-tech in order to receive the subsidy. Thus, the supply is quite elastic, and

there will be substantial excess burden.

d. A tax on economic profits does not affect behavior, and hence has no excess burden.

e. &

f. A tax on all computer software will have a smaller excess burden (relative to revenues collected)

than a tax on one particular type of software like the Excel spreadsheet. This is because it is

easier to substitute away from one type of software than software in general.

2、根据2001年通过的立法，最高收入档次（年收入100万美元以上）的个人，其工资的边际税率从39.9％下降到34.0％。用等式13.4近似估计这种变化将减少这一收入群体的个人承担的超额负担比例。

Q 0

Q FOREIGN

FIGURE 12.11 – Economic incidence of tax

Q 1