ECON 3C03 Public Sector Economics: Taxation

Instructions
You may discuss the assignment with your classmates but the
assignment you submit must be original (and not copy the work of others).
1 Excess Burden [25 marks]
Consider an economy with two goods, consumption c and leisure l, and a
representative consumer. The consumer is endowed with 24 hours of time
in a day. A consumer’s daily leisure hours are equal to l = 24 − h where
h is the number of hours a day the consumer chooses to work. The price
of consumption p is equal to 1 and the consumer’s hourly wage is w. The
consumer faces an ad valorem tax on their earnings of τ percent. The consumer also receives some exogenous income Y that does not depend on how
many hours she works (e.g. an inheritance). The consumer’s preferences over
consumption and hours of work can be represented by the utility function
U(c, h) = c − h1+ 1

1+ 1

.
(a) What is this consumer’s budget constraint? [1 marks]
(b) Solve for the consumer’s utility maximizing hours of work h∗(w, 1−τ ) and consumption c∗(w, 1 − τ, Y ). [2 marks]
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(c) What is the compensated own-price elasticity for the supply of hours of work? [3
marks]
For parts (d) – (h), assume the following: w = $10, Y = $100 and = 0.25.
(d) Suppose the income tax rate is initially zero (i.e. τ = 0). Calculate the consumer’s
utility at their utility maximizing consumption and labour supply bundle. [2 marks]
(e) Suppose now that the income tax liability is increased to τ = 0.3. Calculate the
consumer’s utility at their new utility maximizing consumption and labour supply bundle
after the tax change. [2 marks]
(f) Calculate the change in the consumer’s surplus (i.e. utility) following the tax change
[2 marks]
(g) Calculate the revenue generated by the income tax increase. [2 marks]
(h) Using the excess burden formula, calculate the excess burden from this tax. [3 marks]
(i) Now suppose that = 0.5 (instead of = 0.25). Re-calculate the excess burden from
this tax. Is your answer different than in part (h)? Explain why or why not in 2-4
sentences. [4 marks]
(j) Suppose instead that the consumer’s utility function was U(c, h) = min(c, −h).
Would the EB from a unit excise tax be larger or smaller compared with the original
utility function. Explain your answer in 2-4 sentences. [4 marks]
2 Tax Incidence and Excess Burden [15 marks]
The market for smart phone applications is characterized by the following demand and
supply curves.
QD = D(P) = 5 × P−2
QS = S(P) = 1280 × P2
(a) Calculate the equilibrium price and quantity for this market. [2 marks]
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(b) The government is concerned with the amount of time that youth are on their phones
and is considering introducing a per unit tax of t on each smartphone application that is
purchased. Sellers of the tax are legally required to pay the tax. Using the equilibrium
conditions, D(P∗) = S(P∗ − t) = Q∗, derive an equation for the effect of this tax on the
equilibrium price in this market in terms of the elasticity of demand ed and the elasticity
of supply es. [3 marks]
(c) Suppose that the unit excise tax is set at t = 1. What is the excess burden of this
tax per dollar of revenue raised? [5 marks]
(d) Suppose that we incorrectly assumed that supply was perfectly elastic and there was
no impact of the tax on the equilibrium price. Would EB/Tax Revenue be higher or
lower than what you calculated in part (c)? In 1-2 sentences, explain your answer. [5
marks]
3 Income Taxation [25 marks]
As part of Budget 2018, the Government of Canada introduced the Canada Workers
Benefit (CWB) that will take affect starting on January 1, 2019. The CWB is a tax
credit that supplements the earnings of low-income workers. For a single individual, the
structure of the CWB is as follows.
• No credit for earnings less than or equal to $3,000
• A 26% credit on each dollar of income earned over $3,000 up to a maximum of
$1,355
• The maximum credit is reduced by 12% for each dollar eared above $12,820
Based on these parameters, please answer the following.
(a) What is the “phase in” region for the CWB? In other words, what is the income
range over which workers receive a CWB subsidy? You may answer using a graph, an
equation or using words. If you choose to characterize the phase-in region using words,
then your answer must be very precise. [6 marks]
(b) What is the “break even” level of earnings above which a single worker no longer
receives a CWB subsidy? [6 marks]
(c) Based on your answers to parts (a) and (b) and the parameters of the CWB, draw
a figure showing the budget constraint of a single worker under the CWB. Your figure
should clearly label the x-axis, y-axis and the income cutoffs B1, B2 and B3. [6 marks]
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(d) In one paragraph or less, explain how the CWB affects the incentive to work for (i)
individuals with earnings below B1, (ii) individuals with earnings between B1 and B2,
(iii) individuals with earnings between B2 and B3, and (iv) individuals with earnings
above B3. [7 marks]
4 Multiple Choice and True/False [15 marks, 1 mark each]
(a) Excess burden is sometimes referred to as
1. deadweight less of taxation
2. welfare cost of taxation
3. both of the above
4. neither of the above
(b) Equivalent Variation is
1. the vertical distance between the original/pre-tax budget constraint and the posttax budget constraint
2. the vertical distance between the post-tax budget constraint and the “shifted”
budget constraint that is parallel to the original/pre-tax budget constraint
3. the vertical distance between the original/pre-tax budget constraint and the “shifted”
budget constraint that is parallel to the original/pre-tax budget constraint
4. None of the above
(c) Price-distorting taxes differ from lump-sum taxes in that they lead to
1. both substitution effects and income effects
2. only substitution effects
3. only income effects
4. neither substitution nor income effects
(d) If the uncompensated demand for a commodity does not change when it is taxed,
does that mean there is no excess burden?
1. Yes
2. No
3. Uncertain
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(e) Goods whose compensated demands are less elastic generate a larger excess burden.
1. True
2. False
3. Both True and False
4. Uncertain
(f) The additional excess burden arising form increasing an existing tax is larger than
the excess burden arising from introducing a new tax on the same good, all else equal.
1. True
2. False
3. Neither True nor False
4. Uncertain
(g) Consider an economy with two goods that consumers view as close substitutes: pizza
and hot dogs. Hot dogs face an ad-valorem tax of 13 percent but pizza is initially not
taxed. Introducing a 5 percent tax on pizza is expect to
1. Increase the overall excess burden in the economy
2. Decrease the overall excess burden in the economy
3. Have no impact on the overall excess burden in the economy
4. Not enough information to tell
(h) The elasticity of taxable income measures
1. the percentage change in taxable income when a person’s marginal tax rate increases by 1 percent
2. the percentage change in taxable income when a person’s net-of-marginal tax rate
increases by 1 percent
3. the percentage change in earnings when a person’s marginal tax rate increases by
1 percent
4. the percentage change in earnings when a person’s net-of-marginal tax rate increases by 1 percent
(i) Public economists measure the progressivity of a tax system by
1. Observing how marginal tax rates change with income
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2. Observing how marginal tax rate change over time
3. Observing how average tax rates change over timeUncertain
4. Observing how average tax rates change with income
(j) The Canadian tax system has become more progressive since 1990.
1. True
2. False
3. Uncertain
(k) Suppose an individual receives an income of $75,000 per year and pays $14,500 per
year in federal income taxes, $3,500 per year in provincial income taxes and $2,000 per
year in payroll taxes. Their average tax rate is
1. 19.3 percent
2. 4.6 percent
3. 2.7 percent
4. 24 percent
5. 26.7 percent
6. 22 percent
7. 7.3 percent
(l) Is the tax system given by the function: T(I) = −B + tI
1. Progressive
2. Regressive
3. Proportional
(m) Is the tax system given by the function: T(I) = tI
1. Progressive
2. Regressive
3. Proportional
(n) The economic incidence of a tax on the profits of a monopolist is borne by consumers
who have to face higher prices.
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1. True
2. False
3. Uncertain
(o) In recent years, renting a 2-bedroom apartment in Hamilton has become more expensive as rents have been increasing at a rate of 5 percent per year. The City of Hamilton
is considering a policy that would limit increases on rent to be no more than 2 percent
per year. It is expected that this policy will cause
1. Apartment prices to rise
2. Apartment prices to fall
3. Apartment prices to neither rise nor fall (i.e. remain stable)