1. The incidence of the subsidy depends on the elasticities of the supply and demand curves.
Here the price received by sellers increases from P0 to P1. Buyers also benefit – their price falls from P0 to P2. In evaluating the claims that energy subsidies to low-income families do not benefit industry, the figure below could be modified by shifting the demand curve rather than the supply curve. Nonetheless, what is clear from the diagram is that demand is relatively inelastic, while supply is more elastic. Thus, the subsidies to low-income families do benefit the industry.
2. 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.
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3.
4. 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.
5. 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.
6. The equilibrium price can be calculated by setting the quantity supplied equal to the quantity demanded:
(i) QD = a - bP
(ii) QS = c + dP
If QD = QS, 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.
d b
c P a
P d b c a
dP c bP a
+
= −
+
=
−
+
=
−
) (
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Substituting into the demand equation:
Substituting into the supply equation:
If a unit tax of u dollars is imposed 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, PC, and price that includes the tax, PCT, are:
Similarly, the price received by the producer in the absence of the tax, PP, is u lower than the price received with the imposition of the tax, PPT. These prices are expressed below:
The equilibrium that prevails after the imposition of the tax can be found by setting PCT = PP or PC = PPT -- in the end, both approaches will yield the same answer. First, we can derive the solution setting PCT = PP:
Next, setting PC = PPT:
+
− −
=
−
=
d b
c b a a Q
bP a Q
+ + −
= +
=
d b
c d a c Q
dP c Q
b Q b PC a
−
= 1
d Q c PP d −
=1
d u Q c PPT d − −
=1
d b
dbu bc Q da
db Q d b db
dbu bc da
d Q u b
d c b a
d Q c u d
b Q b a
P PCT P
+ +
= +
= + +
+
+
= + +
−
=
+
−
=
1 1
1 1
u b Q b
PCT a +
−
= 1
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Therefore, both approaches lead to the same outcome.
7. Equation (12.1) relates progressiveness, v1, to average tax rates. Assume throughout that I1>I0>0. Then progressivity is measured by v1=[(T1/I1)- (T0/I0)]/(I1-I0). With a $300 lump sum tax refund for all earners, the progressivity changes to v1’=[((T1-300)/I1)- ((T0- 300)/I0)]/(I1-I0). Rearranging, we have v1’= v1+[(300/I0)-(300/I1)]/(I1-I0). Thus, the progressivity differs only by the second term, [(300/I0)-(300/I1)]/(I1-I0). This second term is positive because (300/I0)>(300/I1). Thus, v1’>v1, and average tax rates increase with income by more when a $300 lump sum tax refund is given. Intuitively, the average tax rate falls by more for a low-income person from a lump sum tax reduction. Equation (12.2) relates progressiveness, v2, to the elasticity of tax revenue with respect to income.
Then progressivity is measured by v2=[(T1-T0)/T0]/[(I1-I0)/I0]. With a $300 lump sum tax refund for all earners, the progressivity changes to v2’=[(T1-300-T0+300)/(T0-300)]/[(I1- I0)/I0]= [(T1-T0)/(T0-300)]/[(I1-I0)/I0]. Note that v2’ differs from v2 only by the term (T0- 300). Thus, the numerator of v2’ is larger than v2, while the denominator is the same.
Thus, v2’>v2, and the tax system is more progressive under the second measure as well when the lump sum tax refund is given.
8. 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:
Income Tax Liability Average Tax Rate Marginal Tax Rate
$2,000 $-3,600 -1.80 0.2
3,000 $-3,400 -1.13 0.2
5,000 $-3,000 -0.60 0.2
10,000 $-2,000 -0.20 0.2
30,000 $2,000 0.066 0.2
d b
dbu bc Q da
db Q d b db
dbu bc da
d Q u b
d c b a
d u Q c Q d
b b a
P PC PT
+ +
= +
= + +
+
+
= + +
−
−
=
−
=
1 1
1 1
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9. With the schedule T=a+tI, the average tax rate as a function of income is ATR=T/I=(a+tI)/I=(a/I)+t. A progressive tax system, using equation (12.1), means that the average tax rate goes up with income, or dATR/dI>0. Taking derivatives, dATR/dI=- a/I2>0, which implies –a>0 or a<0. Thus, with a linear tax schedule, a negative intercept, a, implies progressivity. Similarly, a regressive tax system implies dATR/dI<0 or dATR/dI=-a/I2<0, which implies –a<0 or a>0. Thus, with a linear tax schedule, a positive intercept, a, implies regressivity.
10. a. After New York City increased the tax from $0.08 to $1.50 per pack of cigarettes, the 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, etc.), 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. 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. www.elsolucionario.net