AGEC 350 Dynamic efficiency and resource allocation

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AGEC 350Dynamic efficiency and resource
allocation
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Some basic questions about our non-renewable
resources

• Does it make sense to use them up as fast as
  possible?
• How fast should we use them up?
• Is this a problem we need to worry about or will
  markets take care of themselves?

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Present value

• A benefit or cost experienced in the future is
  smaller when evaluated today because of
• Opportunities to invest current amount today and
  earn interest in the future

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PV of a stream of benefits or costs

• Suppose we receive B0 dollars this year (year 0),
  B1 dollars in 1 year, B2 dollars in 2 years, etc.
  Then the PV of this stream of benefits is

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The Efficiency model for non-renewable resources
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8
NB
2
15
7
8
6
2
MNB
15
8
Current period
9
Future period
Suppose we also get (net) benefits next year.
But those benefits need to be discounted. 6/(110
)5.45
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Suppose we only have 15 units and we have to
split it between now and next period
Resource scarcity and intertemporal tradeoffs
One possible split 10 today 5 tomorrow
PV of Net Benefits of leaving 5 for next period
Net benefits of using 10 today
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Suppose we have 15 units
Benefits
Cost
Cost of consuming 10 today, reducing what can be
consumed in the future.
Net benefits of using 10 today
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Suppose we have 15 units
Marginal User Cost of 10th unitconsumed today
Marginal Net benefit of 10th unitconsumed today
Benefits
Cost
Cost of consuming 10 today, reducing what can be
consumed in the future.
Net benefits of using 10 today
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6 5.45
PV of NB if all 15 are consumed next period
consumption next period
0 15
14
6 5.45
The more we consume today, the less NB we have
in the future.
Q2
0 15
15
6 5.45
The more we consume today, the less NB we have
in the future.
Q2
0 15
16
6 5.45
The more we consume today, the less NB we have
in the future.
Q2
0 15
17
6 5.45
The decreased net benefits in the future is
called user cost
User cost
Q2
0 15
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The more we consume today (Q1) the less we can
consume tomorrow, diminishing the PV of net
benefits well get in the future. Consumption
today has a user cost.
6 5.45
User cost
User cost
Q2
Q2
15 0
0 15
Q1
0 15
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If we have 20 units
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If we have 20 units
The first 5 units could be consumed without
reducing net benefits in the next period.
So, from 0 to 5 there is no cost of consumption
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Assuming 20 units available
Marginal User Cost
6
MNB
15
5
20
22

6
Marginal User Cost
MNB
Q today
15
5
20
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6
Marginal User Cost
MNB
15
5
20
Q today
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6
Marginal User Cost
MNB
15
5
20
Q today
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PV of NB are maximized!

6
Marginal User Cost
MNB
15
5
20
Q today
Marginal net benefits (MNB) today PV of MNB
tomorrow That means that the MNB tomorrow will be
(110)?MNB today
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6
Marginal User Cost
MNB
15
5
20
Q today
A little more than 10 units consumed today
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6
Marginal User Cost
MNB
15
5
20
Q today
A little less than 10 units Left for tomorrow
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Why is more consumed in the first period?
Imagine what would happen if the discount rate
were much higher

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MNB
Marginal User Cost
height 6/(1r)
15
5
20
Q today
A lot less than 10 units Left for tomorrow
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So what prices must exist in each period so that
a little more than 10 is consumed today and a
little less than 10 is consumed next period?
P2
P2Market-clearing price in period 2
P1Market-clearing price in period 1
P1
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Scarcity rentBecause price exceeds MC, producers
make profits. This is scarcity rent i.e.,
profits (rent) that arise because the producers
are using a scarce resource
P2
P1
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General Case - many years
In this case, the price of resource increases
annually at the rate of interest.

Time
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Price of energy without backstop technology

Price of energy with backstop technology
Time
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Main lessons from the simple model of
nonrenewable resources

• Resource availability is a function of price
• As scarcity increases, there is a tendency for
  prices.
• These two effects combine so that
  catastrophically sharp increases in prices are
  avoided
• If alternatives exist, they will eventually
  become economically viable.