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ECON4410
Environmental and Resource Economics

Lab Assignment 3: Non-market valuation (DCE)

and mining economics

Question 1 (50%)

You have completed a stated preference study to identify the values that people hold for increasing the area of public parks that are available to people in Perth.  You conducted a discrete choice experiment, with the following attributes:

Play: The area of recreational playing fields in the local area, ranging from 10 to 50 hectares

Green: The area of green open space in the local area, ranging from 5 to 70 hectares

Cost: The additional cost to respondents of changing the area of public parks ($)

You also measured some sociodemographic variables of the sample, including:

Inc: Their income level which ranged from $20k to $100k, mean =$50k.

Child: Whether they had children, 0=no, 1=yes.

In Table 1 below are the results from a simple conditional logit model.  All parameters estimated were significant.

Table 1  Parameter estimates from a conditional logit model.  All parameters are statistically significant

 

Coefficient

Cost

-0.05

Cost x Inc

+0.0002

Play

+0.3

Play x Child

+0.06

Green

+0.6

Status Quo

-1.0

a) (10%)  

Provide a brief summary statement, explaining your interpretation of what these coefficients imply about peoples preferences.

b) (10%)

Provide a table showing the Willingness to Pay for an additional hectare of Playing fields (Play) and an additional hectare of green open space (Green).

You should report these values for someone who has children, and someone who does not, and for people at the lowest, highest, and average income levels, and provide a brief commentary on these values.

You decide to repeat your statistical analysis, but using a latent class analysis.  The preferred structure was 2 classes, and the estimates are reported in Table 2 below.

Table 2  Parameter estimates from a latent class model.  All parameters are statistically significant

 

Class 1

Class 2

Cost

-0.04

-0.03

Play

+0.4

+0.5

Green

+0.2

+0.5

Status Quo

-1.0

+1.5

 

Percentage in each class

 

35%

 

65%

c) (10%)  

Provide a brief summary statement, explaining your interpretation of what these coefficients imply about people’s preferences.

d) (10%)

Provide a table of the willingness to pay for an additional hectare of playing fields and green open space for the two classes, and the status quo effect.  What do you thing these values imply for the acceptability of providing an increase in public open space?

e) (10%)

Currently there is 20 hectares of playing fields, and 10 hectares of green open space in the region.  The local council think they could increase that to 25 hectares of playing fields and 17 hectares of green open space, but it would require an additional cost of $147 per year from people.  Do you think that the council will get support for this proposal?  Why?

Question 2 (50%)

This assignment is about economics of mining, like the one you have done in the lab. In answering the questions, provide economic reasoning in your answer for each question which will tell us what you are doing and why you do so. The marks allocated to each question (and sub-questions) are given in the parenthesis. Logical interpretation of answers carries higher proportion of marks!

Assume a competitive resource market for a 60-year planning horizon with an inverse demand function Pt= 8 +98e-aRt - Ct where

· ‘Pt’ is the net price of the resource at time ‘t’,

· Ct is the per unit cost of resource extraction at time ‘t’ (note: it does not include the damage cost). Assuming the cost of resource extraction increases at the social utility discount rate, the discounted extraction cost per unit of resource remains same at $10/unit throughout the planning horizon.  

· ‘Rt’ is the quantity of extracted resource at time ‘t’,

· ‘e’ is the mathematical constant used to represent the exponential function,

and

· ‘a’ is the model parameter that represents the nature of the demand.

The given demand function implies that the social welfare function (W) in a discrete time (t) is given as:

where  is the social utility discount rate and ‘T’ is the resource exhaustion time. The model parameters relevant to this problem are given in the table below.

Model parameter (a)

0.15

Social utility discount rate ()

0.06

Initial resource stock (S)

220 units

However, resource extraction has negative externalities that impose costs on society. So consider that there is an external damage cost (D) per unit of resource extracted in each time.  As a social planner you want to incorporate this damage cost in the social welfare function and aim to maximize the social welfare from resource extraction and consumption.

Based on the information provided, answer the questions below.

a) Using Excel Solver find the optimal net present value of social welfare when damage cost per unit of resource extracted in each time is zero. Show your results in graphs showing the rates of extraction and net price against time. (7%) 

b) Argue whether resource extraction follows Hotelling’s rule in the above case (a) using net price of the resource over time. Provide an intuitive explanation to support your argument. (7%)

c) Assume that due to exploration initial resource stock increases to 330 units. Determine the optimal solutions (present value of social welfare, price and extraction paths) using all other model parameters as given in the problem description except increased resource stock. Show your results in graphs showing the rates of extraction and net price against time. (7%)

d) Now consider the original specification of the problem for resource stock and other model parameters with non-zero damage cost. Consider the damage costs D= $8 per unit of resource being extracted. Determine the optimal solutions in this case (present value of social welfare, net price and extraction paths). Show your results in graphs showing the rates of extraction and net price against time. (7%)

With damage cost, Pt increases at a rate lower than the discount rate.

e) Further consider the original specification of the problem except a lower social utility discount rate of 4%. Determine the optimal solutions (present value of social welfare, net price and extraction paths) with increased social utility discount rate. Show your results in graphs showing the rates of extraction and net price against time. (7%) 

f) Discuss the effects of changes in (i) available stock, (ii) damage cost and (ii) social utility discount rate on net present value of social welfare, net price path, and extraction path and resource exhaustion time. (15%)