# Upcoming in Class Homework #5 Due Today Homework #6 Due Oct. 25

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Upcoming in Class Homework #5 Due Today Homework #6 Due Oct. 25
Quiz #3 Oct. 27th Writing Assignment Due Oct. 27th Exam #3 Thursday Nov. 3rd

HW #5 Suppose a market demand schedule for a resource is P = Q and the market supply schedule is P = Q. What is the equation for the marginal net benefit curve? Disregarding future time periods, how much of the resource would be produced? What is the marginal net benefit at this level of production?

HW #5 What is Hotelling’s rule?
Include an explanation of how a change in the interest rate will affect the price of a resource over time.

The Dynamically Efficient Allocation

Chapter 5 - A Two-Period Model
Assumptions Fixed supply of oil Consider two time periods only Total supply is 20 tons Demand (marginal WTP) is constant: Calculate NB = P – MC = 6 – 0.4 Q

Chapter 5 - Problem Assume the demand conditions are the same, but let the discounted rate be 0 and the marginal cost of extraction be \$4. Total supply available = 20. How much would be produced in each period in an efficient allocation? What would be the marginal user cost in each period? Would the static and dynamic efficiency criteria yield the same answers for this problem? Why? Efficient allocation is 10 and 10. the static and dynamic models are the same. User cost = 0

Chapter 5 - Problem Assume the demand conditions are the same, but let the discounted rate be 0 and the marginal cost of extraction be \$4. Total supply available = 10. How much would be produced in each period in an efficient allocation? What would be the marginal user cost in each period? Would the static and dynamic efficiency criteria yield the same answers for this problem? Why? Efficient allocation is 5 and 5. the static and dynamic models are not the same. User cost = \$2

Marginal User Cost The opportunity cost caused by intertemporal scarcity is called the marginal user cost (MUC). The marginal user cost for each period in an efficient market is the difference between the price and the marginal extraction cost.

Change in discount rate
A higher discount rate will favor the present. The amount allocated to the second period falls as the discount rate rises.

Discount Rate The annual rate at which future benefits or costs are discounted relative to current benefits or costs. PV = NB2/(1+r)n

Chapter 5 - Problems Assume the demand conditions are the same, but let the discounted rate be 0.10 and the marginal cost of extraction be \$4. Total supply available = 20. How much would be produced in each period in an efficient allocation? Assume the discount rate is What happens to the efficient allocation? Assume the discount rate is What happens to the efficient allocation? R= q R= q R= q R= q

Discount Rate and Marginal User Cost
A higher discount rate will favor the present. The amount allocated to the second period falls as the discount rate rises. Marginal user cost rises over time at the rate of discount causing efficient prices to rise over time and thus reflecting scarcity. Scarcity rent is producer surplus that exists in the long run due to the fixed supply of resources.

The Efficient Market Allocation of a Depletable Resource: The Constant-Marginal-Cost Case. (a) Period 1 (b) Period 2

Efficient Intertemporal Allocations
The Two-Period Model Revisited Dynamic efficiency is the primary criterion when allocating resources over time. An n-period model presented uses the same numerical example as before, but extends the time horizon and increases the recoverable supply from 20 to 40.

The N-Period Constant-Cost Case
With constant marginal extraction cost, total marginal cost (or the sum of marginal extraction costs and marginal user cost) will rise over time. The graph shows total marginal cost and marginal extraction cost. The vertical distance between the two equals the marginal user cost. The horizontal axis measure time. Rising marginal user cost reflects increasing scarcity and the intertemporal opportunity cost of current consumption on future consumption.

FIGURE 7.2 (a) Constant Marginal Extraction Cost with No Substitute Resource: Quantity Profile. (b) Constant Marginal Extraction Cost with No Substitute Resource: Marginal Cost Profile

Chapter 6 – Discount Rate
Accounts for the time value of money Rate at which a dollar value increases over time Present Value – The value of money in the future, put in terms of the value of money today.

Present Value of \$1,000 at Different Discount Rates

Discounting For the ith period PV [Bi] = Bi/(1+r)i
For the sum across all period PV [B] = ∑i=1n Bi/(1+r)i

Discounting & Environmental Policies
The discount rate affects policies that have long term consequences. For example, consider the construction of a dam. 3 years to build 50 years of operation 50+ years of environmental damage

Costs and Benefits of a Dam Project

Discount Rate If r is set high The short run is favored.
Poor societies where struggle for today is impossible Developed countries where the term of office for policymakers is short Benefits of dam will be stated as smaller But so will the cost environmental damage For example, imagine the construction of a nuclear power plant. We benefit from that plant for 40 years, but the environmental damage from hazardous wastes sticks around for hundreds of years. So a high discount rate is going to severely discount the cost of environmental damage in future periods.

Discount Rate If r is set low
Weights long term environmental damage heavier. If the damages extend beyond the life of the project, then it is likely that the project will be canceled.

Discount Rate and Policy
Neither a high or low discount rate is better for environmental valuation. Low discount rates are often advocated on the needs of future interests Global Climate Change Soil Erosion

Discount Rates Utilized
OMB = rate of return on government bonds (1.6 to 3.5) World Bank often uses 10 Sensitivity Analysis is an analytical tool that studies how the outputs of a model changes as the assumptions of the model changes. Assumption that changes is the discount rate. At what rate does the discount rate have to be for the policy to have a net benefit? At what rate does the discount rate have to be for the policy to have a net loss?

Future Outcomes Risk – the probability that an event will happen
Uncertainty – different outcomes may occur Consider a person who smokes

Expected Values EV [X] = p[X] C[X]
p is the probability of event X occurring C is the cost of event X

Expected Values Risk aversion is the tendency to prefer certainty instead of risky outcomes, particularly in cases where actions may cause significant negative consequences Precautionary principle is the view that policies should account for the uncertainty by taking steps to avoid damaging outcomes, especially when the outcomes are irreversible

Chapter 12 – Non-renewable Resources
Physical supply - available reserves measured in physical terms without regard for cost and value Economics supply – the amount of a resource that is available based on current prices and technology

Classification of Nonrenewable Resource

Reserves Identified reserves – the identified quantity of a resources; includes both economic and subeconomic reserves Indicated or inferred – resources that have been identified but whose exact quantity is not known with certainty

Undiscovered Reserves
Hypothetical – the quantity of a resource not identified with certainty but hypothesized to exist Speculative – the location and quantity of a resource has not been identified but is hypothesized to exist

Resource lifetime Subeconomic resources – resources whose costs of extraction are too high to make production worthwhile Economic reserves – resources of high enough quality to be profitably produced and are identified

Resources Changes to reserves
The resources is extracted and used => diminished reserves New resource deposits are discovered => increasing reserves Changing price and technology can make more or less of the known reserves economically viable

“Limits to Growth” http://en.wikipedia.org/wiki/The_Limits_to_Growth
Written in 1972, predicting over use of resources Written in 1968, predicting a population crash due to resource scarcity The wager : rlich_wager

Price Trends for Selected Minerals

Optimal extraction R=P-MC PV [R] = R0 + R1/(1+r) + R2/(1+r)2 +…
Optimal extraction quantity R0 = R1/(1+r) = R2/(1+r)2 =… Hotelling’s Rule - net price rises over time with the rate of interest.

Resource Rent for the Competitive Firm

Marginal Cost of Extraction
Technology Decreases marginal cost of extraction Higher quality resources will be extracted first. => subeconomic resources may become economic when the price rises or technology improves

Exhaustion of a Mineral Stock

Resource Extraction Choke price – the minimum price of a good or service that would result in a zero quantity demanded Price path – the price of a resource over time Extraction path – the extraction rate of a resource over time

Change in World Reserve Base for Selected Minerals

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