Numerical Exam Questions for Environmental Economics
Numerical exam questions for Environmental Economics
Spring 2006
Krister Hjalte
Question 2. (29/3 1998)
The inverse demand function for a non-renewable resource is Pt = a- bRt, where Pt is the market price and Rt the extraction in period t. The total gross benefit from extracting this resource can be written as an integral
The extraction cost Ct= cRt, where c is a constant. Total available amount of the resource is denoted by S. From a social point of view we want to maximise the net benefits from extracting this resource subject to the general constraint that the sum of extraction in different time periods must equal the total available amount. Start by formulating an expression for the net benefits. Your problem is then to estimate how much that will be extracted in each period under the following assumptions
a= 8 b= 0.4 c= 2 r= discount rate
S = 30
T= 0,1,2 (three periods)
Use the Lagrange multiplier method for the maximisation and denote the multiplier by (.
a) How much is extracted in each of the three periods if the discount rate is 10%? What is the value of ( and give an economic interpretation of it.
b) How will your answer in a) change if the discount rate r is 0 in stead?
c) If the discount rate r is 20%?
d) How much of the total stock must be available for the extraction not to give rise to an economic intertemporal allocation problem? In what way does the assumption of different discount rates influence your answer to this? Explain carefully.
e) Imagine that the resource would have been a renewable resource, say fish or mammals. In what principle way will the analysis of an intertemporal welfare maximisation harvesting policy change the optimality conditions?
Question 1. (29/3 2000)
An important issue focuses on the consequences of uncertainty for the efficiency loss arising from use of various instruments when wrong information is used. In situations with certainty where decision makers know the pollution abatement cost and the pollution damage
Spring 2006
Krister Hjalte
Question 2. (29/3 1998)
The inverse demand function for a non-renewable resource is Pt = a- bRt, where Pt is the market price and Rt the extraction in period t. The total gross benefit from extracting this resource can be written as an integral
The extraction cost Ct= cRt, where c is a constant. Total available amount of the resource is denoted by S. From a social point of view we want to maximise the net benefits from extracting this resource subject to the general constraint that the sum of extraction in different time periods must equal the total available amount. Start by formulating an expression for the net benefits. Your problem is then to estimate how much that will be extracted in each period under the following assumptions
a= 8 b= 0.4 c= 2 r= discount rate
S = 30
T= 0,1,2 (three periods)
Use the Lagrange multiplier method for the maximisation and denote the multiplier by (.
a) How much is extracted in each of the three periods if the discount rate is 10%? What is the value of ( and give an economic interpretation of it.
b) How will your answer in a) change if the discount rate r is 0 in stead?
c) If the discount rate r is 20%?
d) How much of the total stock must be available for the extraction not to give rise to an economic intertemporal allocation problem? In what way does the assumption of different discount rates influence your answer to this? Explain carefully.
e) Imagine that the resource would have been a renewable resource, say fish or mammals. In what principle way will the analysis of an intertemporal welfare maximisation harvesting policy change the optimality conditions?
Question 1. (29/3 2000)
An important issue focuses on the consequences of uncertainty for the efficiency loss arising from use of various instruments when wrong information is used. In situations with certainty where decision makers know the pollution abatement cost and the pollution damage