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University of Victoria
Economics 312
Urban Land Economics
Martin Farnham
Problem Set #0 (optional: based on optional micro review notes)
Note that this problem set is for students who’ve been away from 103 for a while and
want to brush up on their micro theory and welfare analysis (or anyone who wants to
brush up). It’s excellent review material for other elective courses (many of these
problems are used in Public Economics, for example, and it would be good review for an
Environmental Economics course). And it’s material all econ majors should know. I will
not explicitly test any of this material in 312 though, as this is a third-year elective with a
103 prereq, I can assume that you understand this material as I proceed with the course.
1) Practice calculating individual welfare with an individual demand curve.
Consider the individual demand equation Q=120-P.
a) Draw this demand curve.
b) At a price of $100, how much does this individual choose to consume? Why do they
choose that quantity?
c) How much is the consumer willing to pay (per unit) for a tiny bit more of the good, at
this quantity?
d) How much is the consumer willing to pay (in total) for the quantity they choose to
consume at a price of $100?
e) What are the net benefits the consumer gets at this quantity?
f) Suppose, instead, she chooses the quantity 10 at a price of $100. What are the net
benefits the consumer gets at this quantity? Show your answer numerically and
graphically. What is the relationship between marginal benefit and price at this quantity?
What should the consumer do to make herself better off? Why?
g) Now suppose she chooses the quantity 30 at a price of $100. What are the net benefits
the consumer gets at this quantity? Show your answer numerically and graphically. What
is the relationship between marginal benefit and price at this quantity? What should the
consumer do to make herself better off? Why?
2) Practice calculating individual firm welfare with an individual supply curve.
Consider the individual supply equation Q=P-2.
a) Draw this supply curve.
b) At a price of $100, how much does this firm choose to produce? Why do they choose
that quantity?
c) How much does it cost the firm (per unit) to produce a tiny bit more of the good, at this
quantity?
d) What are the firm’s variable costs of producing the quantity they choose to produce at
a price of $100?
e) What are the net benefits the producer gets at this quantity? Now assume the firm faces
fixed costs of $10. What are the firm’s profits at this quantity?
f) Suppose, instead, the firm chooses the quantity 90 at that price. What are the net
benefits the firm gets at this quantity? What are the profits they get at this quantity? Show
your answer numerically and graphically. What is the relationship between marginal cost
and price at this quantity? What should the firm do to make itself better off? Why?
g) Now suppose the firm chooses the quantity 110 at that price. What are the net benefits
the producer gets at this quantity? What are the profits they get at this quantity? Show
your answer numerically and graphically. What is the relationship between marginal cost
and price at this quantity? What should the producer do to make itself better off? Why?
3) Practice Calculating Social Welfare with Supply-Demand diagram.
Consider the market demand equation Q=1200-2P.
a) Draw this demand curve.
b) What is the total benefit to consumers associated with consuming 200 units of the
good? How much would total benefit go up by if they switched from consuming 200
units of the good to 300 units of the good? Shade this area in a diagram.
c) Suppose the price of this good is $100. What is the consumer surplus associated with
the quantity of goods that will be consumed at this price? Shade this area in a diagram.
d) Now assume the market supply curve is given by Q=P. Add this supply curve to your
diagram.
e) What is the equilibrium quantity of goods produced and consumed in this market?
f) What is the producer surplus at this equilibrium? Shade this area in a diagram.
g) What is social welfare at this equilibrium? Assume there are no externalities or other
market failures.
h) Why is this equilibrium efficient?
i) By how much would social welfare change if the government imposed a binding quota
at Q=300? Shade total social welfare (net benefits) in a diagram.
j) What is the deadweight loss resulting from implementing the quota?
Problems 4-6 give a partial tour of equilibrium, market success, and market failure
4) Consider the market for slices of pizza. Suppose that the market is perfectly
competitive. There are 4 consumers and 2 producers (but each acts as price taker).
Consumers are identical and producers are identical. Assume that partial slices of pizza
may be produced and consumed.
individual demand curve: q=6-P
individual supply curve: q=P
a) Write an equation for the market demand curve. Why does the demand curve slope
down?
b) Write an equation for the market supply curve. Why does the supply curve slope up?
c) Find equilibrium price and quantity in the market for pizza slices. How many slices
does each person consume? How many does each producer make?
d) Calculate the total benefit derived from the equilibrium consumption of pizza. Draw a
picture and shade in the area representing total benefit.
e) Calculate the total variable cost of the equilibrium quantity of slices produced. Draw a
picture and shade in the area representing total variable cost.
f) Calculate consumer surplus. Draw a picture and shade in the area representing CS.
g) Calculate producer surplus. Draw a picture and shade in the area representing PS.
h) Is the equilibrium quantity efficient? Why?
i) Using the efficiency criterion, could the government do any better than the market in
allocating goods in this case?
5) (Using the setup from problem 4) Now suppose there is an externality associated with
pizza slices. Consumers of the pizza have a nasty habit of dropping their paper plate on
the sidewalk after eating. This presents a form of visual pollution to everyone else in the
area.
Assume that, on average, ½ plate is dropped on the sidewalk per slice of pizza consumed.
Each plate on the sidewalk causes $2 of collective unhappiness to society.
a) Is this a positive or a negative externality?
b) Is it a consumption externality or a production externality?
c) What is the marginal external cost of a slice of pizza?
d) Draw the marginal social benefit curve.
e) Does equilibrium production of pizza change in the face of the externality.
f) Calculate the total external cost of pizza consumption in equilibrium.
g) Calculate the total social benefit of pizza consumption in equilibrium.
h) Calculate total welfare in equilibrium.
i) What is the efficient level of pizza production, in light of the externality?
j) How much would total social benefit decline by moving to that efficient level?
k) How much would total social cost decline by moving to that efficient level?
l) What would total social welfare be at the efficient level? Compare that with total
social welfare in equilibrium.
m) What is the deadweight loss associated with the pizza market?
n) What are some policy instruments the government could use to eliminate the
deadweight loss?
6) Now suppose the externality occurs in the following form. The consumers don’t dump
their plates on the ground. Instead, the pizza parlors dump their trash (tomato cans,
cheese wrappers, etc.) on the street at the end of the day. How would your analysis differ
from in problem 2? Which curve would you alter now, to reflect the externality.
Supposing the marginal external cost is the same per slice as above, does the efficient
equilibrium differ?
7) (Using setup from problem 5) Suppose the Victoria town council wants to apply a tax
on pizza, in order to induce the efficient level of pizza consumption.
a) Suppose the tax will be imposed on consumers. That is, each consumer must pay
amount $t per slice of pizza they buy. Draw a picture showing how the tax affects the
marginal private benefit curve.
b) What is the level of tax (per slice) that should be chosen in order to induce an efficient
equilibrium?
c) What is the new equilibrium quantity? Price paid by consumers? Price received by
producers?
Now suppose the tax will be imposed on producers of pizza instead of on consumers.
That is, for each slice produced, the pizza parlor must pay $t.
d) What is the level of tax (per slice) that will induce efficiency?
e) What is the new equilibrium quantity? Price paid by consumers? Price received by
producers?
f) Calculate total social welfare (consumer surplus+producer surplus+government
revenue-total external cost).