L4: Sustainability II

Question 1

the intertemporal welfare function is written as:

Answer 1

the intertemporal welfare function is written as:

𝑊 = 𝑊(𝑈0, 𝑈1)

U0 - utility in period 0

Question 2

The specific form in utilitarianism can be written as:

What do each of the terms represent?

Answer 2

𝑊 = 𝜑0𝑈0 + 𝜑1𝑈1

where 𝑊 is the weighted average of utilities for the time periods, so that 𝜑0 and 𝜑1 are
the weights used in aggerating utility over the time periods to obtain SW

Question 3

The implications of discounting is that, for 𝜌 __ 0 future utility counts for less.

For 𝜌 = 0 current and future utility are ____ ____

Answer 3

The implications of discounting is that, for 𝜌 > 0 future utility counts for less. For 𝜌 = 0
current and future utility are equally weighted

Question 4

Why, if the discount rates are fixed, do the weights of the utility still fall as t increases?

Answer 4

Because t (the number of time periods is increasing) and the amount that an individual cares in decreasing because the consequences of their consumption become so far removed. This is in part due to non-renewable resources

Question 5

▪ Let us now consider another approach or perspective to addressing the intertemporal problem in which we are concerned about production, the shifting of consumption, and hence utility, over time via the accumulation and use of ____.

The alternative optimal growth approach therefore models the interaction between
_____ and _____

Answer 5

Capital

The alternative optimal growth approach therefore models the interaction between
impatience and productivity

Question 6

In this simple optimal growth model production uses a ___-_______ _______

We want to find the path of _____ and hence, _____ and ____ accumulation over time that results in:

How do we write this?

Answer 6

In this simple optimal growth model production uses a non-renewable resource

We want to find the path of consumption and hence, savings and capital accumulation over time that results in:

W = Integral U (Ct)e^ρt dt (see slide optimal growth 3)

Question 7

In the Optimal Growth Model:

Ct = 
Q = 
R = 
K (dot) = 
S bar =
S dot =

Answer 7

Ct = is aggregate consumption at time t
Q = is the output
R = is the non-renewable resource
K (dot) = is the time derivative of K
S bar = is the stock of the non-renewable resource
S dot = is the rate of extraction of the non-renewable resource

Question 8

2) says that output, Q, can either be used for ____, or ____,
▪ (3) says that the natural resource is ______ so it ____ with the amount being
used
▪ (4) says that the total cumulative use cannot exceed the ___of the resource

Answer 8

2) says that output, Q, can either be used for consumption, C, or investment,
▪ (3) says that the natural resource is non-renewable so it decreases with the amount being
used
▪ (4) says that the total cumulative use cannot exceed the stock of the resource

Question 9

In the utilitarian approach, we have focused on a _____/_____ perspective where
the main challenge is ______ (in preference satisfaction utilitarianism, people prefer
consumption now than in the ____)

Answer 9

In the utilitarian approach, we have focused on a consumption/utility perspective where
the main challenge is impatience (in preference satisfaction utilitarianism, people prefer
consumption now than the future)

Question 10

▪ Output may be ___, used to acquire ____ or used to extract a natural ____ _____.

From the +ve marginal products we can see that pay-off from ___ and ____ is +ve.

▪ Must remember that a small amount of output invested today carries a cost in terms of ___ ___ foregone , but adds an amount larger than to ____ ____possibilities.

Answer 10

▪ Output may be consumed, used to acquire capital or used to extract a natural nonrenewable resource.

From the +ve marginal products we can see that pay-off from accumulation and extraction is +ve.

▪ Must remember that a small amount of output invested today carries a cost in terms
of current consumption foregone , but adds an amount larger than to future
consumption possibilities.

Question 11

Which author introduced how capital should be accumulated?

Answer 11

Hartwick 1977, 1978

Question 12

Hartwick outlined conditions to achieve what?

What did they suggest be added to the SWF to achieve this?

Answer 12

What Hartwick did was to identify conditions under which constant consumption
could be maintained indefinitely. Hartwick suggested a savings and investment
constraint be added to the SWF in (1).

Question 13

What conditions did Hartwick assume to achieve constant consumption

What did he show the outome would be?

Answer 13

Conditions (2)-(4)

A Cobb-Douglas production function (represent the technological relationship between the amounts of two or more inputs and the amount of output that can be produced by those inputs)

alpha > beta
ie. the MP of capital is greater than the MP of non-renewable resources

Under such conditions he showed that constant consumption would be the outcome if a particular savings/investment rule was adopted assuming efficient depletion

Question 14

The constraint proposed by Hartwick is that, at every point in time, all the ___ arising
from the extraction of the resource must be saved and invested in ____ capital ,
i.e., must be equal to the total ___ arising in the resource extraction industry

Answer 14

The constraint proposed by Hartwick is that, at every point in time, all the rent arising
from the extraction of the resource must be saved and invested in reproducible capital ,
i.e., must be equal to the total rents arising in the resource extraction industry

Question 15

What is the unit rent/tax for extraction.?

ie. how is the rent of extraction measured?

Answer 15

The unit rent is the scarcity value which rises as the resource is depleted

Question 16

The Hartwick rule is ___ but not ____ for efficient capital ____.

Following it will realise ____ ____ if the resource is depleted efficiently and if sustainability is feasible i.e. plenty of substitution possibilities

Answer 16

The Hartwick rule is necessary but not sufficient for efficient capital accumulation.
Following it will realise constant consumption if the resource is depleted efficiently and if sustainability is feasible i.e. plenty of substitution possibilities

Question 17

What are the intertemporal Efficiency conditions?

Answer 17

Intertemporal efficiency conditions: Equivalent to assuming that firms are in PC with perfect foresight and the whole economy is PC.

Question 18

The difference between weak and strong sustainablists centres on substitution possibilities.

____ sustainabilists think that production should be represented by a C-D prod function where ___>___,

whereas ____ sustainabilists argue in favour of a prod function where the _____ problem is unsolvable

Answer 18

The difference centres on substitution possibilities.

Weak sustainabilists think that production should be represented by a C-D prod function where alpha>beta,

whereas strong sustainabilists argue in favour of a prod function where the sustainability problem is
unsolvable

Question 19

What is human capital composed of ? 3

Answer 19

human-made capital is defined to be the sum

of physical, human and intellectual capital

Question 20

___ sustainabilists argue that KN should be non-declining

while ____ sustainabilists
argue that the sum of KN
and KH must be non-declining

Need to be able to measure the size of the ____ ___ stock.

Answer 20

Strong sustainabilists argue that KN should be non-declining while weak sustainabilists
argue that the sum of KN
and KH must be non-declining

Need to be able to measure the size of the natural capital stock.

Question 21

What is the Hartwick rule?

Answer 21

In resource economics, Hartwick’s rule defines the amount of investment in produced capital that is needed to exactly offset declining stocks of non-renewable resources. This investment is undertaken so that the standard of living does not fall as society moves into the indefinite future.