Natural Resource Economics
Academic year: 2016-2017
Prof. Luca Salvatici
[email protected]
Lesson 3: Discounting
Natural Resource Economics - Luca Salvatici
(2016-17)
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Natural Resource Economics - Luca Salvatici
(2016-17)
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TED
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https://www.ted.com/talks/paul_gilding_the_earth
_is_full#t-69955
Natural Resource Economics - Luca Salvatici
(2016-17)
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Outline
1. Definitions
2. Discounting
Natural Resource Economics - Luca Salvatici
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K* = optimal capital stock
K* is a function of which variables?
• rm = (opportunity) cost
• rc = profits (micro view)
GDP (macro view)
Possible K adjustment models:
• rigid: K(t) - K(t-1) = K*(t) - K(t-1)
• flexible (“adjustment costs”):
K(t) - K(t-1) = (1-a) [K*(t) - K(t-1)]
Graph in (K,t) space
Natural Resource Economics - Luca Salvatici
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Adjustment paths
Natural Resource Economics - Luca Salvatici
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Admissible time paths: graph 1
Natural Resource Economics - Luca Salvatici
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Control variable
• The variables chosen in any given period in
time are called the control variables.
• These are not stock, but flow variables. A
flow variable is measured over an interval
of time and therefore a flow would be
measured per unit of time (say a year)
Examples:
I = investiments (capital theory)
Y = harvest/extraction
Natural Resource Economics - Luca Salvatici
(2016-17)
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State variable
The information about the current situation which is
needed to make a correct decision is called the state
• Variable(s) describing the state of the stock(s) are
state variables
Examples:
capital (K) in the investment theory
X = resource stock
• State equation: it describes the dynamics of the state
variable
Example:
X t 1  X t  F  X t   Yt
Natural Resource Economics - Luca Salvatici
(2016-17)
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Renewable resources dynamics
y(t) = harvest in period t
X(t) = stock at the beginning of period t
F(Xt) = net growth function
X t 1  X t  F  X t   yt
Escapement: 𝑋𝑡 − 𝑦𝑡 ≥ 0
𝑦𝑡 < 𝐹 𝑋𝑡
𝑋𝑡+1 − 𝑋𝑡 > 0
Natural Resource Economics - Luca Salvatici
(2016-17)
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Nonrenewable resources
dynamics
R(t): remaining reserves in period t
q(t): rate of extraction
R(t+1) – R(t) = – q(t)
Natural Resource Economics - Luca Salvatici
(2016-17)
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Discounting I
Two explanations for discounting:
• money could be invested for a greater future return (the
opportunity cost of capital), and
• people are impatient (time preference).
If we think in terms of the market for investment funds, the
opportunity cost rationale says what firms are willing to pay
for new funds, while the impatience rationale identifies the
amount that individuals require as compensation for delaying
consumption by investing their funds.
In the economists’ ideal world – fully competitive markets,
no distortionary taxes, perfect information, and complete
rationality –these rates would be identical. In point of fact,
most economists agree that the discount rate suggested by
the impatience explanation – the “social” discount rate – is
substantially lower than the rate indicated by the opportunity
cost of alternative investments.
Natural Resource Economics - Luca Salvatici
(2016-17)
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Discounting II
• In general, individuals have positive time
preferences over consumption (money): this is
the ‘pure’ rate of time preference r
• Market interest rates also reflect risk, inflation,
taxation, etc.
• We will use ‘discount rate’ and ‘interest rate’
interchangeably
• The discount rate also reflects the opportunity
cost of investment (saving)
• High discount rates heavily discount future
benefits and costs
Natural Resource Economics - Luca Salvatici
(2016-17)
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