Benefit-cost analysis and supply of crude oil

Question

Part 1: True/False questions. Explain your answer fully.

1. The risk treatment in the benefit-cost analysis assumes risk neutrality. This assumption cannot be justified for large projects.

2. In a market with positive externalities, monopolies can be better than competitive firms from the society’s point of view.

3. The supply of a good in a private market is given by Q = -2 + P. However, the production process of this good is damaging the environment. Given the social marginal cost MC_S = 3 + 2Q you have found that the socially optimal quantity (i.e., when taking the externality effect into consideration) of that good is Q* = 5 units. Therefore, a corrective measure against this negative externality is a Pigouvian tax of t_P = $1.

4. A property rights system that satisfies exclusivity and enforceability does not guarantee good maintenance of the resources.

Part 2: Analytical questions. Do the problems in the order given.

1. The demand for and supply of crude oil from Alberta oil sands are given by P = 120 - 0:5Q_D and P = 1:5Q_S + 10. Although these equations express the private marginal benefits and private marginal costs, they fail to incorporate the external costs associated with the production process and consumption of oil. These external costs are estimated to be given by
MC_E = 5 + Q.

(a) What is the market solution (market price and quantity)? What is the total surplus of the society under the market solution?

(b) What is the socially optimal solution (optimal quantity and price)? What is the total surplus of the society under the socially optimal solution?

(c) What is the optimal effluence tax that will lead the market on producing the socially optimal quantity?

2. The following equations describe the willingness to pay of Amanda, Brian, and Carol for a non-excludable and indivisible good:

Amanda’s WTP: P_A = 5 - Q_A
Brain’s WTP: P_B = 8 - 2Q_B
Carol’s WTP: P_C = 4 - Q

The marginal cost function is

MC = 3 + 3Q

(a) What is the market demand for this public good? What is the socially efficient provision of this public good?

(b) What are the two possible reasons why the market fails to provide the socially efficient quantity of this public good? Fully explain your answer.

3. An oil refinery is considering three alternative production processes. Although the resulting benefits will be the same (the resulting gasoline, diesel fuel, asphalt base, heating oil, kerosene from the three different methods are of the same quality and quantity), the marginal costs associated with each method are different. More specially, the marginal cost of method 1 is MC₁ = 28, the marginal cost of method 2 is MC₂ = 12 + q₂, and the marginal cost of method 3 is MC₃ = 2q₃.

(a) If the factory wants to produce 100 units in total, how many units will be produced using each different method?

(b) Repeat part (a) when the factory wants to produce 18 units in total.