# ECON 100 Tutorial: Week 13

```ECON 100 Tutorial: Week 13
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office hours: 3:45PM to 4:45PM tuesday LUMS C85
Question 1
Suppose the inverse demand function is given by P=450-2Q. And the supply curve
is given by MPC=30+2Q where MPC is the marginal PRIVATE costs. In addition
there are social costs given by MSC=Q – that is every unit of output of the
generates \$1 of additional costs to society over an above the costs of production.
The diagram below illustrates the market.
Question 1(a)
Inverse demand function: P=450-2Q
Supply Curve: MPC=30+2Q , where MPC is the marginal PRIVATE costs.
Social costs given by MSC=Q
What is the competitive level of output, Qc, and competitive price, Pc?
To find Q, set the Marginal
Private Cost equal to the
inverse demand function:
30+2Q = MPC = P = 450-2Q
30+2Q = 450-2Q
4Q = 420
Q = 420/4
Q = 105
Ps
Pc
Qs
Qc
Plug this Q into the demand
function:
P = 450 – 2 (105)
P = 450 – 210
P = 240
Question 1(b)
Inverse demand function: P=450-2Q
Supply Curve: MPC=30+2Q , where MPC is the marginal PRIVATE costs.
Social costs given by MSC=Q
What is the socially optimal output and price?
We need to find MPC+MSC:
MPC+MSC = 30 + 2Q + Q
= 30 + 3Q
Set this equal to demand:
30 + 3Q = 450 – 2Q
5Q = 420
Q = 84
Ps
Pc
Plug this into demand:
P = 450 – 2(84)
P = 450 – 168
P = 282
Qs
Qc
Complete the following table using the areas labelled in the diagram:
Social
optimum
Competitive optimum Difference
Consumer surplus
Private producer surplus, PSp
Externality cost
Social producer surplus, PSs
Social welfare W=CS+PSs
A+B+C+D
F+G+H
C+D+E+G+H
F-C-D-E
A+B+F-E
Question 1(c)
This graph shows a scenario where
there is some sort of Marginal social
cost due to a production/supply
externality.
Ps
Pc
Qs
Qc
Complete the following table using the areas labelled in the diagram:
Social
optimum
Consumer surplus
Private producer surplus, PSp
Externality cost
Social producer surplus, PSs
Social welfare W=CS+PSs
Question 1(c)
Consumer
Surplus
Competitive optimum Difference
A+B+C+D
Complete the following table using the areas labelled in the diagram:
Consumer surplus
Private producer surplus, PSp
Externality cost
Social producer surplus, PSs
Social welfare W=CS+PSs
Question 1(c)
Consumer
Surplus
Social
optimum
A
Competitive optimum Difference
A+B+C+D
B+C+D
Complete the following table using the areas labelled in the diagram:
Consumer surplus
Private producer surplus, PSp
Externality cost
Social producer surplus, PSs
Social welfare W=CS+PSs
Question 1(c)
Private
Producer
Surplus
Producer surplus is the area
under the price and above
the MPC.
Social
optimum
A
Ps
Pc
Competitive optimum Difference
A+B+C+D
F+G+H
B+C+D
Complete the following table using the areas labelled in the diagram:
Consumer surplus
Private producer surplus, PSp
Externality cost
Social producer surplus, PSs
Social welfare W=CS+PSs
Question 1(c)
Private
Producer
Surplus
Producer surplus is the area
under the price and above
the MPC.
Social
optimum
A
B+C+G+F
Competitive optimum Difference
A+B+C+D
F+G+H
B+C+D
H-B-C
Complete the following table using the areas labelled in the diagram:
Consumer surplus
Private producer surplus, PSp
Externality cost
Social producer surplus, PSs
Social welfare W=CS+PSs
Question 1(c)
Externality
Cost
Note: The cost of an
externality is actually
everything under the
marginal social cost curve, up
to the Q.
We show it this way
(MSC+MPC) because it makes
it easier to find the equilibia.
Social
optimum
A
B+C+G+F
Competitive optimum Difference
A+B+C+D
F+G+H
C+D+E+G+H
B+C+D
H-B-C
Complete the following table using the areas labelled in the diagram:
Consumer surplus
Private producer surplus, PSp
Externality cost
Social producer surplus, PSs
Social welfare W=CS+PSs
Question 1(c)
Externality
Cost
Note: The cost of an
externality is actually
everything under the
marginal social cost curve, up
to the Q.
We show it this way
(MSC+MPC) because it makes
it easier to find the equilibia.
Social
optimum
A
B+C+G+F
C+G
Competitive optimum Difference
A+B+C+D
F+G+H
C+D+E+G+H
B+C+D
H-B-C
D+E+H
Complete the following table using the areas labelled in the diagram:
Consumer surplus
Private producer surplus, PSp
Externality cost
Social producer surplus, PSs
Social welfare W=CS+PSs
Question 1(c)
Social
producer
surplus
Another way of thinking
surplus is
PSs = PSp – E
Social
optimum
A
B+C+G+F
C+G
Competitive optimum Difference
A+B+C+D
F+G+H
C+D+E+G+H
F-C-D-E
B+C+D
H-B-C
D+E+H
Question 1(c)
Social
producer
surplus
Another way of thinking
is
PSs = PSp – E
So, if we are producing at Qc
and the price is Pc, our
Producer surplus is areas
F+G+H.
The Externality cost is
G+C+D+H+E.
If we subtract one from the
other, we get:
PSs = F+G+H-G-C-D-H-E
PSs = F+G-G+H-H-C-D-E
PSs = F-C-D-E
Ps
Pc
Qs
Qc
Complete the following table using the areas labelled in the diagram:
Consumer surplus
Private producer surplus, PSp
Externality cost
Social producer surplus, PSs
Social welfare W=CS+PSs
Question 1(c)
Social
producer
surplus
Another way of thinking
surplus is
PSs = PSp – E
Social
optimum
A
B+C+G+F
C+G
B+F
Competitive optimum Difference
A+B+C+D
F+G+H
C+D+E+G+H
F-C-D-E
B+C+D
H-B-C
D+E+H
-B-C-D-E
Complete the following table using the areas labelled in the diagram:
Consumer surplus
Private producer surplus, PSp
Externality cost
Social producer surplus, PSs
Social welfare W=CS+PSs
Question 1(c)
Social welfare
Another way of thinking
W = CS + PS -E
Social
optimum
A
B+C+G+F
C+G
B+F
Competitive optimum Difference
A+B+C+D
F+G+H
C+D+E+G+H
F-C-D-E
A+B+F-E
B+C+D
H-B-C
D+E+H
-B-C-D-E
Complete the following table using the areas labelled in the diagram:
Consumer surplus
Private producer surplus, PSp
Externality cost
Social producer surplus, PSs
Social welfare W=CS+PSs
Question 1(c)
Social welfare
Another way of thinking
W = CS + PS -E
Social
optimum
A
B+C+G+F
C+G
B+F
A+B+F
Competitive optimum Difference
A+B+C+D
F+G+H
C+D+E+G+H
F-C-D-E
A+B+F-E
B+C+D
H-B-C
D+E+H
-B-C-D-E
-E
Question 2(a)
Explain what is meant by excludability and rivalry.
Excludable: A good or service is called excludable if it is possible to prevent
individuals who have not paid for it to have access to it.
Rival: A good or service is called rival if it’s consumption by one consumer prevents
simultaneous consumption by other consumers.
We use these two characteristics to divide goods into four categories:
Rival
Non-rival
Excludable
Private goods
Club good
Non-excludable
Common property
Public good
Why do we care about these distinctions?
How well markets work in providing goods depends on the characteristics of those
goods. Markets work best for private goods (which are both rival and excludable).
But they do not work as well for other types of goods. In such cases government
policy is used to remedy market failure and raise economic well-being.
Question 2(a)
Give two examples of rival, non-rival, excludable, and non-excludable goods.
Excludable: A good or service is called excludable if it is possible to prevent
individuals who have not paid for it to have access to it.
Rival: A good or service is called rival if it’s consumption by one consumer prevents
simultaneous consumption by other consumers.
Rival
Non-rival
Excludable
Private goods:
food, clothing,
cars
Club goods:
cinema, private
park, satellite
telly
Non-excludable
Common property:
fish stocks, timber,
coal
Public goods:
television, air,
national defence
Question 2(b)
Security guards protect the two tenants of a shopping mall (it's a US story).
Guards cost a wage of W=\$10 per hour.
Store 1 with Demand D1 , such that W=18-2G, is willing to hire 4 guards an hour
(it's a big-box store).
The market for guards is competitive and will supply as much as required at \$10 an
hour.
Store 2, with Demand D2, such that W=7-G, and so is not willing to hire any guards
(it's a small boutique) at the going wage.
The services that a guard provides is a public good - so the boutique can benefit
from whatever the big-box store hires. The social demand is the vertical sum of the
demand curves for the two stores.
Draw a diagram to capture this problem. Show what the social and the competitive
private optima are.
Question 2(b)
Guards wage: W=\$10 per hour.
The market for guards is competitive and will supply as much as required at \$10 an
hour.
That gives us our supply curve. Horizontal at MC = 10.
Then we can re-arrange the following two demand curves into Y = mX + c form:
Store 1’s Demand D1 , such that W=18-2G, is willing to hire 4 guards an hour.
Store 2’s Demand D2, such that W=7-G, is willing to hire 0 guards an hour.
This is what we have so far:
Next, we’ll graph the Social
Demand curve so that we can
Find the social optimum.
Question 2(b)
Guards wage: W=\$10 per hour.
The market for guards is competitive and will supply as much as required at \$10 an
hour.
Store 1’s Demand D1 , such that W=18-2G, is willing to hire 4 guards an hour.
Store 2’s Demand D2, such that W=7-G, is willing to hire 0 guards an hour.
The services that a guard provides is a public good. The social demand is the
vertical sum of the demand curves for the two stores.
Draw a diagram to capture this
problem.
What is the social optimum?
G* = 5
What is the competitive private
optimum?
Gc = 4
Note: If 5 guards are hired, store
1’s demand implies it is willing to
pay 18 – 2(5) = \$8 and store 2 is
willing to pay 7-5 = \$2
Question 3(a)
Suppose the demand for oil is Qt = 200 – Pt in each year, t=1,2. All the oil is
extracted and sold by the end of the two periods. Suppose the marginal cost of
extraction is zero. Show how the price of oil at time t depends on the interest rate,
i, and on the total supply of oil.
Total supply is given by:
Q = Q1+Q2
Q = (200 – P1) +(200 – P2)
The Hotelling Rule says P2 = P1 (1+i).
So Pt = (400 – Q)/(2 + i)
Here’s how to get there:
Q = (200 – P1) +(200 – P1 (1+i))
Q = 400 – P1 – P1 (1+i)
Q = 400 – (P1 + P1 (1+i))
Q = 400 – P1 (1+1+i)
Q = 400 – P1 (2+i)
Q – 400 = -P1 (2+i)
400 – Q = P1 (2+i)
(400 – Q)/(2+i) = P1
Question 3(b)
Show that the lower is i the more oil is conserved until year 2.
Ian’s Answer: Since P2 = P1 (1+i),
It follows that at a higher i the difference in prices across time will be
larger.
So with high i P2 will be large relative to P1.
Consumers react to this bigger price differential by buying more in
period 1 and leaving less for period 2.
Exam 2 notes:
Tutors have to turn in marked exams on Feb. 10th, so you’ll receive your marks
sometime soon after that date.