Agricultural Business 450 Natural Resource Economics

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Agricultural Business 450 Natural Resource
Economics

• Chapter 4
• Resource Allocation
• Over Time
• Dr. Susan Watson

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Goals for Chapter 4

• Be able to discover equilibrium in the current
  time period
• Be able to balance present and future periods
• Understand dynamic equilibrium over two periods
• Be able to explain user costs and resource
  depletion
• Be able to use Hotellings Rule time discounting

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Types of Resources

• Renewable resources if properly managed, can
  last indefinitely
• Nonrenewable resources cannot last forever
  and may be in relatively short supply
• Examples high-grade deposits of copper ore or
  crude oil supplies

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Equilibrium Current Time Period

• Marginal Net Benefit derived from supply and
  demand curve
• See Figure 4-1a next slide
• Graphically, marginal net benefit is the vertical
  difference between the supply curve and the
  demand curve

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Figure 4-1a Supply, Demand, and Marginal Net
Benefit for Copper
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Figure 4-1a Supply, Demand, and Marginal Net
Benefit for Copper
Vertical Distances between Demand and Supply
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Figure 4-1b Supply, Demand, Marginal Net
Benefit for Copper
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Marginal Net Benefit -- Algebraically

• Demand Pd 150 - 0.25 Q1
• Supply Ps 50 0.25 Q1
• Marginal Net Benefit
• MNB Pd Ps 100 0.5 Q1
• At supply demand equilibrium Q1 200
• Marginal Net Benefit 0
• additional units provide no additional benefit

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Static Equilibrium

• Analysis corresponds to the ordinary supply and
  demand equilibrium for the 1st period, at a
  quantity of 200 and a price of 100
• This is the market equilibrium that will prevail
  if only present costs and benefits are considered

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Balancing Present Future Periods Initial
Set-up

• A fixed quantity of the resource is divided
  between two time periods
• Use horizontal axis to measure the total quantity
  available
• Put the Marginal Net Benefit curve for the first
  period on graph in the usual way
• Put the Marginal Net Benefit curve for the second
  period in mirror-image fashion

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Figure 4-2 Allocation of Copper Over Two Time
Periods
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Balancing Present Future Periods Analysis
Completion

• We must translate future values into present
  values by using a discount rate
• Example ? Interest 7.25 Future Value after 10
  years 1,000 Present Value 500.
• Formula PV MNB2 MNB2 / ( 1 r ) n
• Example ? MNB2 / (1.0725) 10 MNB2 / 2

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Dynamic Equilibrium for Two Periods

• The special graphical format now becomes apparent
• Note where the MNB1 and PVMNB2 curves cross
• At this point the present value of both curves is
  the same
• This is the optimum economic allocation

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Figure 4-3 Different Inter-temporal Resource
Allocations
Optimal Allocation
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Dynamic Equilibrium for Two Periods
Algebraically

• MNB1 PV MNB2 and Q1 Q2 250
• 2nd equation is Supply Constraint tells us that
  quantities used must SUM to 250
• MNB1 100 -0.5Q1 MNB2 (100 0.5Q2)/2
• 100 0.5Q1 50 0.25Q2

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Dynamic Equilibrium for Two Periods
Algebraically CONTINUED

• Because Q1 Q2 250 Q1 250 Q2
• Therefore,
• 100 0.5 (250 Q2) 50 0.25 Q2
• 0.75 Q2 75
• Q1 150 Q2 100

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Figure 4-3 Different Inter-temporal Resource
Allocations
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User Costs Resource Depletion

• We imposing costs on future consumers of a
  resource by using that resource today
• The user costs are also known as externalities
  in time
• The vertical distance to the intersection point
  MNB1 and PVMNB2 shows the user cost at
  equilibrium

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User Costs Resource Depletion Calculations

• Where Q1 150 and Q2 100
• User Cost MNB1 100 0.5(150) 25
• Or
• PVMNB2 50 0.25 (100) 25
• The User Cost at Equilibrium is thus 25

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User Costs Resource Depletion What does this
mean?

• Consider original supply demand curves for
  Period 1 redrawn in next slide
• If we dont consider Period 2 at all, market
  equilibrium will be 200 units of copper _at_ 100
• Now, add the user cost Figure 4-2
• Result is Social Cost schedule S new
  equilibrium of copper consumption at 150 units _at_
  112.50

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Figure 4-4 Market for Copper in Two Periods
User Cost at this new equilibrium is 25
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Figure 4-4 Market for Copper in Two Periods
With 1st period consumption of 150 units, 100
units will remain for consumption in the 2nd
period _at_ 125
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Resource Depletion Tax

• Imposed on ore production and sales
• Will raise the effective supply schedule to the
  real social cost S
• Alternative policy mechanisms include
• Direct government control of resource
  exploitation
• Setting aside resource deposits
• Maintaining stockpiles

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Hotellings Rule Time Discounting
Discount rate is critical
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Figure 4-5 Intertemporal Resource Allocation
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Hotellings Rule Time Discounting

• The owner of a resource will consider the net
  price available today against a possible higher
  future net price
• If present net price interest exceeds the
  probable future net price ? will profit more by
  extracting resource today and investing the
  proceeds
• If expected future net price is higher than
  present net price interest, will wait sell at
  some future date

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Hotellings Rule Time Discounting

• If all resource owners follow this logic, the
  quantity of the resource supplied today will
  increase until todays resource price falls low
  enough to encourage resource owners to conserve,
  hoping for a better future price

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Hotellings Rule Time Discounting

• At this point Hotellings rule will hold
• the expectations of future price
• increases will exactly follow an ex-
• potential curve P1(1r)n, where P1
• is todays price, r is the discount
• rate, n is the number of years from
• the present see fig. 4-6 on next slide

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Figure 4-6 Hotellings Rule on Equilibrium
Resource Price
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Can you

• Discover equilibrium in the current time period?
• Balance present and future periods?
• Understand dynamic equilibrium over two periods?
• Explain user costs and resource depletion?
• Use Hotellings Rule time discounting?

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Questions?