Dr. Westerhold
Econ 432
Summer 2010
Final Exam Review Questions: Taxation
1. Price Elasticity and Burden of a Tax. Suppose you are selling movie tickets to two different groups
of individuals: adults and senior citizens. Adults are relatively price inelastic with Ed= - 0.50;
whereas seniors are relatively more price sensitive with Ed= - 2.25. If the price elasticity of supply
is 1.30 and an excise tax of $1.50 per unit is imposed then determine the relative burden for
adults and seniors. Which group pays a larger burden of the tax? Which will result in greater tax
revenue? Briefly explain.
2. Ad Valorem Taxes: Suppose there is a market that has market demand characterized by demand
and supply of:
Qd =30 – 1/3P and Qs = – 2 + 1/2P.
(A) Graph the market with y intercepts (and x intercept for demand).
(B) Find the equilibrium price and quantity in this market and show on your graph.
(C) Suppose an ad valorem tax of 30 percent is imposed on good X. Show the new demand equation
on your graph (to find the new equation, re-arrange the given demand equation of Qd=30-1/3P
and solve for P such that P=90-3Qd. Now price will be increased by 30% so use the new effective
after-tax price of 1.30P in the demand equation given (set 1.30P=90-3Qd) and re-solve for Q.
a. Check your answer for this equation: the x intercept should remain the same (if price is
zero then a 30% tax on zero is still zero).
b. Use the original equilibrium quantity and determine the new effective price for the seller
(basically their net price) then add on the 30% tax and you should get something close to
your original equilibrium price---slight differences due to rounding.
(D) Now find the new equilibrium price, quantity and tax revenue in the market.
OMITQuestion 3: Excess Burden and Equivalent Variation
(A) Assume we have a consumer with I=$20,000 and the price of cigarettes is $8 per pack. Currently,
the consumer maximizes utility by consuming 520 packs of cigarettes per year (point A). Show
the consumer’s budget line and consumer choice.
(B) Now assume the government implements a $2 tax per unit on cigarettes. Create the new budget
line faced by the consumer on your graph above showing a consumption level of 480 packs of
cigarettes (point B). Determine total tax paid by the consumer and show on your graph as point c.
(C) Calculate the price elasticity of demand for cigarettes.
(D) Show on your graph a lump sum tax which results in the same loss of utility (to I2) as point D.
Show on your graph the equivalent variation. Is the cigarette tax efficient?
Question 4: Measuring Excess Burden
Assume that taxes on utilities are 8% and last year $10 million of tax revenue was generated from
utilities. If the price elasticity of demand for utilities is approximately -0.85 then determine the excess
burden of this tax. If the price elasticity of demand was more elastic, would the excess burden be
higher or lower?
Answers:
Question 1: elasticity and revenue generation
Adults—movie tickets burden of the tax: (1.30)/(1.30- - 0.5) * 1.50 or $1.08 of the tax; leaving the
remaining $0.42 for the seller to bear. With seniors --movie tickets (1.30) (1.30- -2.25) * $1.50= $0.55
of the tax; leaving the remaining $0.95 for the seller to bear. Since seniors are more price elastic they
will pay a lower relative burden of the tax. As for tax revenue, tax revenue generated is equal to the
tax of $1.50 * quantity sold with the tax. Given that seniors are more price sensitive we would expect
a larger reduction in quantity due to the tax (2.25% decrease in Qd for every 1% change in price vs
adults with a 0.50% reduction in quantity demanded for a 1% change in price) and hence lower tax
revenue from seniors.
Question 2: Ad Valorem Tax
(A) Y intercept demand is $90; x intercept demand is 30; y-intercept supply is $4
(B) Setting supply equal to demand and solving yields approximately Pe = $38.40 and Qe= 17.2.
(C) The after-tax demand curve is now Qnew= 30 -0.433P.
Note: the x intercept is still 30 and at Q=17.2 the effective retail price would be $26.90. Once
you add on 30% tax to this you get the original equilibrium price of $38.40. This is how I know
the equation is correct!
(D)Setting after-tax demand (Qd=30-0.433P) equal to supply you find P* = $34.30 for suppliers,
quantity supplied is 15.15 units, and P* = $44.60 for consumers (including the tax).
Note that the consumer’s price of $44.60 is 30% higher than the sellers’ net price of $34.30
because of the 30% tax. Your numbers could be slightly off due to rounding.
Tax revenue is difference between gross price paid by consumers and net price earned by sellers
times the amount of units sold or tax revenue: (44.60-34.30)*15.15 = $156.05.
OMITQuestion 3: Equivalent Variation
A. X intercept will be 2500 units; y intercept is $20,000 or 20,000 units. Consumer choice, point A, is
(x=520; y=15,840).
B. BL2 has x intercept of 2000 units; y intercept of 20,000. Consumer choice, point B is (x=480;
y=15200). Total tax paid is $2*480=960 or coordinates of point C are (x=480; y on BL1 would be
16,160) resulting in tax paid of 16,160-15,200=$960.
C. Ed =
or -0.42 inelastic
Shift BL1 in parallel until tangent with I2 to create point D. EV is the vertical distance between point D
and BL1 (point E). The cigarette tax is not efficient because the tax revenue generated (vertical
distance BC) is less than the EV (vertical distance DE). Hence, there is an excess burden.
Question 4: Excess Burden
EB= ½ (-0.85)(10,000,000)(.08)2 = $27,200
More elastic demand results in greater excess burdens—as people are more price sensitive we see
greater distortions in quantity as a result of the tax and therefore higher burdens. Verify by creating a
more elastic Ed say of 2.0 to see this mathematically: EB=1/2(-2)(10,000,000)(0.08)2= $64,000