Problem set 3
EEP 102, Fall 2015
Due: (as a hard copy) November 17 (Tuesday) by 3.40 p.m. (the beginning of the
lecture). To encourage students not to wait until the last minute, no questions about
the problem set will be answered during the 24 period bef
Problem set 3
EEP 102, Fall 2015
Due: (as a hard copy) November 17 (Tuesday) by 3.40 p.m. (the beginning of
the lecture). To encourage students not to wait until the last minute, no
questions about the problem set will be answered during the 24 period bef
Problem set 2
EEP 102, Fall 2015
Due: (as a hard copy) October 6 by 5 p.m. (the end of the lecture)
To encourage students not to wait until the last minute, no questions about
the problem set will be answered during the 24 period before the problem
set is
EEP/ECON C102, Section 10
Week of November 23, 2015
In this section we will study the equilibrium under the price-taking sole owner of a fishery.
Here equilibrium means the optimal harvest rulethe harvest as a function of the stock
level. The purpose of t
Corrected answer to Proble 11, Problem set #3
11.(a) For the two types of taxes, the monopolys two objective functions
are:
unit: ( ) ( )
ad valorem: ( ) ( (1 + )
The corresponding first order conditions are
unit: + 2 = 0
ad valorem: + 2 + 2 = 0
(b) Solv
Problem set 4
EEP 102, Fall 2015
Due: (as a hard copy) December 1 (Tuesday) by 3.40 p.m. (the beginning
of the lecture). To encourage students not to wait until the last minute, no
questions about the problem set will be answered during the 24 period
befo
EEP/ECON C102
Professor Larry Karp
In-class exercise 8
November 10, 2015
a. Inverse demand is p(y) = 6 20y, and constant (average = marginal) harvest cost is
C = 1. Write the open access harvest rule and briefly (a sentence or two) explain its
derivation.
EEP/ECON C102
Professor Larry Karp
In-class exercise 9
November 19, 2015
(This exercise has TWO pages.)
a. Inverse demand is p = 5 y and
the constant average harvest cost is C = 2. The growth
x
function is F (x) = 2x 1
and the discount rate is r = 1. Ide
EEP/ECON C102
Professor Larry Karp
In-class exercise 6
October 27, 2015
Consider a competitive resource market (no backstop here) where the average (= marginal)
extraction cost is constant, C.
a. Graph the equilibrium price, in the absence of a tax, as a
EEP/ECON C102
Professor Larry Karp
In-class exercise 7
November 5, 2015
(This exercise has TWO pages.)
a. Figure 1 shows the graph of dx/dt and eight values of x, points A through H. In the
blank next to each of these points write -, 0, or + to indicate w
EEP/ECON C102
Professor Larry Karp
In-class exercise 3
September 22, 2015
Consider a two-period problem. Demand in a period is 10 y and constant (average =
marginal) extraction cost is C = 2. A competitive firm has initial stock x0 = 2 and
discount factor
Spring 2016
Environmental Economics /EEP101/ECON125
Section 1 Calculus and Econ Review
Review of Concepts:
Function:
What is a function (of real numbers):
Is a link by mathematical operator(s) between elements of a domain (inputs) and elements of a
codoma
Spring 2016
Environmental Economics
Section 7 : NPV and Inter-temporal Allocation
Discounting
What is discounting:
Scaling payoffs according to the point in time they occur.
Why do we discount:
To make quantities associated with different time periods
Spring 2016
Environmental Economics/EEP 101/ECON 125
Section 2. Solutions
Exercise
1. For each function, give the argument(s) and the value of its maximum:
a) f (x) = (x 3)2
First Order Conditions (FOC): f 0 (x) = 2(x 3)
= x = 3
= f 00 (x) = 2 = maxima
f
Spring 2016
Environmental Economics/EEP 101/ECON 125
Section 1. Calculus and Econ Review
Solutions
1
Calculus Exercise
1.What is the derivative of:
a) f (x) = 3x7 + 6x3 + 5x + 2, f (x) = 21x6 + 18x2 + 5.
b) f(x) = 4xln(3x), f (x) = 4ln(3x) + 4.
2. What ar
Spring 2016
Environmental Economics/EEP 101/ECON 125
Section 2. Optimization, Externalities and
Interventions
Optimization
Unconstrained
Find the arguments of a function that yield the maximum value for that function
If the function is differentiable an
Spring 2016
Environmental Economics/EEP101/ECON125
Section 5 Some Concepts and Uncertainty
Restoration
Full restoration may be suboptimal:
The point where MB=MC does not have to correspond to the pristine situation.
Source of Pollution
Point source pollu
Spring,2016
Environmental Economics
Section7 Valuation and Resource Economics
Solutions
Problems
1. What is the present value of a payment of $100.
a) in 2 years if the discount factor is 0.95?
PV =1000.952 =90.25
b) in 2 years if the discount rate is
PV
Spring 2016
Environmental Economics/EEP101/ECON125
Section 3 Externalities and Intervention Continued
Problems
1. Consider the following market:
Demand: = 30 2
Supply: = 3 +
Negative externality: = 7 + 2Q
a) What is the social optimum?
b) In a competitiv
Spring 2016
Environmental Economics
Section 5 Some Concepts and Uncertainty
Solutions
Problems
1. Consider a market with 2 firms (1 and 2). Firms have different marginal benefits for an
externality generating good (Q). The MEC is not known, but policymake
Spring 2016
Environmental Economics/EEP101/ECON125
Section 3 Externalities and Intervention Continued
Solutions
Problems
1. Consider the following market:
Demand: Q= 30 p
2
Supply: M P C=3+Q
Negative externality: M E C=7 +2 Q
a) What is the social optimum
Spring 2016
Environmental Economics/EEP 101/ECON 125
Section 6. Public Goods, Club Goods
Public Goods
Characteristics (of pure public goods)
Non-rival: Many agents can consume the good at the same time without
diminishing its value
Non-excludable: Agen