Question

a. An oil producer drills for oil on the high seas by renting oil rigs. Each rig rents for 1 rig-dollar. No other input is required for production. The production technology is linear and 1 additional oil rig can “produce” 10 units of oil. What is the cost function of the oil producer? Denote amount of oil produced by y.

b. Oil production harms nearby marine life. Each additional unit of oil produced causes an estimated environmental loss of 0.8 rig-dollars. What is the marginal social cost of oil production?

Answer 1

1. 1 oil rig produce 10 units of oil and cost 1 rig-dollar. This means each unit of oil produced require 1/10 = 0.1 rig-dollar as cost.

Linear cost function can be expressed as:

C(y) = 0.1y + a

(Where C(y) is the cost, y is amount of oil produced and a is a constant representing fixed cost of production)

2. Every unit of oil produced causes 0.8 rig dollar of cost to environment. Marginal Social Cost (msc) can be calculated as:

msc = marg. private cost + marg. external cost

In the previous part, we found the expression for marginal private cost function as: 0.1y + a. Taking marginal external cost as 0.8 y, we have marginal social cost (MSC) as:

MSC(y) = 0.9y + a