The topic of exhaustible resources often comes up in every-day conversations, and we constantly hear ads on the
radio and on TV that urge us, the general public, to conserve natural resources. Those campaigns sound very
encouraging and praise-worthy because they tell us that by conserving resources today, we will be able to make a
better future for the next generation. However, economic analysis of conservation of exhaustible resources provides
us with a completely different angle than the media presents. In order to see what happens when we decide to
conserve a certain amount of a particular exhaustible resource, we first need to learn about a few things:


Present Demand and Present Value of Future Demand
Adding Demand Curves
Present Demand and Present Value of Future Demand
Price
65 D0
Market for Coal in the U.S
50 D1
interest rate
40
PV(D1)
55
70
Quantity
Figure 19.f.1. D0 represent demand of this year’s people (or it could be today’s people). D1 represents demand of
next year’s people (or it could be tomorrow’s people). PV(D1) represents the present value of demand of next year’s
people. Present value of demand means demand of the future (be it next year or tomorrow) in today’s money. The
difference between next year’s demand and the present value of next year’s demand is the interest rate.
If we know that the interest rate (R) is 25%, we can find out today’s value of next year’s demand. We always have
to do this step before adding the demand curves:
P1=P0*(1+R)
P0 is the price this year
50=P0*(1+0.25)
P1 is the price next year
50=P0*(1.25)
40=P0
We have two demand curves now, but we cannot calculate the equilibrium point using a supply curve and two
demand curves. Therefore, we need to add this year’s demand and the present value of next year’s demand in order
to obtain Aggregate Demand.
We horizontally add the two demand curves:
Price
65
Market f or Coal in the U.S.
D0
Supply
50 D1
40
PV(D1)
∑ Do+PV(D1)
35
7
32
55
70 125
Quantity
Figure 19.f.2. The red line represents the horizontal sum of D0 and PV(D1). The aggregate demand curve is
identical with D0 up to the point where PV(D1) starts (point of the y-intercept of PV(D1)). The blue dot is at the
intersection of the aggregate demand curve and our supply curve. This point is the equilibrium point. Consequently,
the equilibrium price is $35 and the equilibrium quantity is 125 gallons. The quantity this year’s people want to
consume is 32 and the quantity next year’s people want to consume is 7. Notice that in order to see how much next
year’s people want to consume, we disregard D1 and look at PV(D1).
Now, suppose that the government was concerned that next year’s people will not have enough coal and therefore
made this year’s people conserve 5 tons. That means that this year’s people will now be able to consume only 27
tons (32-5), but next year’s people will have 12 tons instead of 7 tons. That sounds like fair game. However, let’s see
what happens when we put these changes on the above graph:
Price
65
Market f or Coal in the U.S.
D0
Supply
50 D1
40
PV(D1)
∑ Do+PV(D1)
35
benefit
B
7 12
A
27 32
55
70 125
Quantity
loss
Figure 19.f.2. Area A represents the loss for this year’s people. Area B represents the gain for next year’s people.
We immediately see that the loss is bigger than the gain, meaning that the society as a whole is worse off because of
forced conservation of exhaustible resources. That seems counter-intuitive, but what is really happening here is this:
next year’s people value their resources less because they now have more of them, and this year’s people value their
resources more because they have less of them.
Practice Problems
1.
Suppose the equation for D1 is P=300-Q
Suppose the interest rate is 20%.
 What is the PV(D1)?
 Is the x- intercept of D1 the same as the x-intercept of PV(D1)? Will this always be the case?
Why?
2.
The interest rate is 5%. Looking at the diagram below, answer the following questions:
a)
b)
c)
d)
e)
Find PV(D1)
Draw PV(D1) on the graph
Draw aggregate demand
Show quantity demanded today on the graph
Show quantity demanded tomorrow on the graph
Market for oil in the U.S
Price
65
Supply
D1
30 D0
1000
3.
2000
Quantity
Looking at the diagram below, explain what happens if we force today’s people to consume 100 units less
so that next year’s people can consume 100 units more and we know that Q0=300 , Q1=800 , and the
equilibrium price=$18. If we enforce this measure in order to save oil for the future generation, will the
society as a whole benefit or lose? Show this on the diagram and calculate the net benefit or the net loss to
society.
Market for oil in the U.S.
Price
Supply
48 PV(D1)
30
D0
1000 1100
2000
Quantity
Solutions
1.
P1=P0(1+R)
D1: P=300-Q
R=0.20
X
intercept
Therefore, the x-intercept of D1 and
PV(D1) is always going to be the same
300-Q = P0 (1+0.20)
300-Q = P0 (1.2)
250- (Q/1.2) = P0
250-1/1.2 Q = P0
PV(D1)
X
intercept
2.
a)
65-(65/2000)Q=P0(1+0.05)
65- 0.0325=1.05 P0
64.9675=1.05P0
61.87≈62=P0=PV(D1)
Market for oil in the U.S.
Price
65
62
30
Supply
D1
D0
∑ Do+PV(D1)
Q0
1000 Q1
PV(D1)
3.
2000
Quantity
Market for oil in the U.S.
Price
Supply
48
30
D0
18
∑ Do+PV(D1)
loss
200 300
900 1000 1100
800
gain
2000
PV(D1)
From the graph, we can clearly see that the gain is smaller than the loss.
Loss: 18(100)+(1/2)(100)(24-18)=2100
Gain: 16.5(100)+(1/2)(18-16.5)(100)=1725
Net Loss: 2100-1725=375
Quantity