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Intermediate Microeconomics
Fall 2014
Problem Set 2
Due Lecture 3 in class on paper
1. GLS Chapter 3, Question 5
(a) Equilibrium price of broadband.
224 − 4P
12.5P − 150
QS
12.5P − 150
2
P = 22
3
QD
QS
Set QD
224 − 4P
=
=
=
=
(b) Equilibrium quantity
1
2
QD = 224 − 4(22 ) = 133
3
3
2
1
QS = 12.5(22 ) − 150 = 133
3
3
Recall that the units are in 1,000s, so this is 13,333 subscribers.
(c) Consumer surplus
To find consumer surplus, we need to know where the demand curve intersects the y axis.
This is P such that QD = 0. Let 0 = 224 − 4P , which implies P = 56.
The width of the consumer surplus is the market equilibrium quantity: 133 31 . The height
is the distance from the market equilibrium price to the price at which there is no more
demand: 56 − 22 32 .
Therefore, CS = 21 (133 13 )(56 − 22 23 ) = 2222.2. Since the units are in 1,000s, consumer surplus is roughly $222,222.
(d) Producer Surplus
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Similarly to (c), we need to find the price where the quantity supplied is 0. Let 0 = 12.5P −
150, which implies P = 12.
The width of the producer surplus is the market equilibrium quantity: 133 13 . The height is
the distance from the market equilibrium price to the price at which there is no more supply:
22 23 − 12.
Therefore, P S = 21 (133 13 )(22 23 − 12) = 711.1. Since units are in 1,000s, producer surplus is
roughly 71, 111.
(e) Total surplus
Total surplus is the sum of producer and consumer surplus (there is no one else in our market
who has any surplus).
T S = P S + CS = 2222.2 + 711.1 = 2933.3, or $293,333.
2. GLS Chapter 3, Question 9
(a) Find the equilibrium wage and quantity.
We know from the problem that QS = 10W and QD = 240 − 20W . To find the equilibrium,
we set QS = QD .
QS
10W
30W
We
=
=
=
=
QD
240 − 20W
240
8
Given the equilibrium wage of 8, we can solve for the equilibrium quantity.
QD = 240 − 20W
QD = 240 − 20(8)
QD = 80
This means that, in equilibrium, the market produces 80,000 hours of work.
Remember that you can check the equilibrium price and quantity by plugging in the price
(wage) to find QS as well. If QS = QD you should become very concerned.
(b) Suppose that we set the wage equal to $10/hour. What is the new quantity of labor hired?
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At W = 10, QD = 240 − 20W = 240 − 10(10) = 40.
However, at W = 10, QS = 10W = 10(10) = 100. Workers supply 100 hours, but employers
only want 40 hours. Recall that the market equilibrium number of hours is 80. There is a
surplus of 60 hours (100 - 40).
(c) What is the deadweight loss?
I suggest that you draw a picture. We know that the width of the DWL triangle are the
trades that are not taking place – from 40 to 80 on the Q axis.
We know that at W = 10, employers demand 40,000 hours. The missing information to
calculate DWL is the wage workers (remember that they are the suppliers in this problem)
would accept for 40,000 hours of work. So we are interested in what P is when QS = 40.
We can write QS = 10W , or 40 = 10W , which implies that W = 4.
Thus, DWL = 12 (80 − 40)(10 − 4) = 20(6) = 120.
(d) What are the changes in producer and consumer surplus?
Let’s start with CS and PS before any changes. To calculate these, we need a few more
points for our picture. What is demand when QD = 0? Set 0 = 240 − 20W , which implies
W = 12. Therefore consumer surplus before is (note that I use o here for “old”; in the next
calculations we’ll use n for new), CSo = 0.5(80)4 = 160. For producer surplus, we need
to know what W is when QS = 0. Since QS = 10W , when W = 0, QS = 0. Therefore,
P So = 0.5(80)8 = 320.
Now we turn to CS and PS after the $10 minimum wage. The new consumer surplus is
above the new market price and below the demand curve, so CSn = 0.5(40)2 = 40. The
new producer surplus is to the left of the new market quantity, above the supply curve, and
below the market price. Therefore, P Sn = 0.5(40)4 + 40(6) = 320.
The change in consumer surplus is ∆CS = CSo − CSn = 40 − 160 = −120. Consumer
surplus declines. Recall that in this problem, consumers are employers. On net, employers
are worse off.
The change in producer surplus is ∆P S = P Sn − P So = 320 − 320 = 0. Producers are workers. There is no change in producer surplus, which means that low-wage workers, on net,
are no worse off. However, note that some individual workers are better off (those earning
$10/hour), and some are worse off (those not earning anything at all).
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3. Price regulations
(a) Does the US have a milk floor?
We accept any well-reasoned answer. Recall that a price floor is a price below which producers are not allowed to sell. For a price floor to have an effect, it must be above market
price. Your answer to this should explain whether this description fits (or does not) with
milk pricing in the US.
(b) Again, we accept any well-reasoned argument. In general, total surplus declines, consumer surplus declines and the change in producer surplus is ambiguous.
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