Question

electricité de france (edf) operates nuclear plants in france. suppose it decides to own uranium mines, a competitive industry, and faces demand p300 – 10 q, where q is tons of uranium and p is €/ton. marginal extraction cost is €30. the discount rate is 20%. assuming there are only 40 tons of uranium remaining in the mine, how much should edf extract today, and how much a year from now? what will be the price of uranium today and one year from now?

Answer 1

To determine the optimal extraction strategy for EDF, we need to consider the present and future value of uranium extraction. We can use the Hotelling's rule, which states that the optimal extraction rate is where the marginal extraction cost equals the discount rate.

Given:

• Demand function: p = 300 - 10q

• Marginal extraction cost: €30

• Discount rate: 20%

• Remaining uranium in the mine: 40 tons

First, let's find the optimal extraction rate for today:

Marginal extraction cost = Discount rate €30 = 20% * p

Solving for p: €30 = 0.2 * (300 - 10q) €30 = 60 - 2q 2q = 60 - €30 2q = €30 q = €15

Therefore, EDF should extract 15 tons of uranium today.

To determine the price of uranium today, substitute the value of q into the demand function: p = 300 - 10q p = 300 - 10(15) p = 300 - 150 p = €150

Hence, the price of uranium today is €150/ton.

Now let's calculate the optimal extraction rate for one year from now. Since we're considering a competitive industry, we assume that the demand function remains the same. However, the remaining uranium in the mine will decrease by the amount extracted today (15 tons) and the annual discount rate.

Remaining uranium in the mine one year from now: 40 tons - 15 tons = 25 tons

Discounted remaining uranium in the mine: 25 tons / (1 + 0.2) = 20.83 tons (approx.)

The optimal extraction rate for one year from now is when the marginal extraction cost equals the discount rate:

Marginal extraction cost = Discount rate €30 = 20% * p

Solving for p: €30 = 0.2 * (300 - 10q) €30 = 60 - 2q 2q = 60 - €30 2q = €30 q = €15

Therefore, EDF should extract 15 tons of uranium one year from now.

To determine the price of uranium one year from now, substitute the value of q into the demand function: p = 300 - 10q p = 300 - 10(15) p = 300 - 150 p = €150

Hence, the price of uranium one year from now is €150/ton, which remains the same as today due to the assumption of constant demand.

In summary:

• EDF should extract 15 tons of uranium today.

• The price of uranium today is €150/ton.

• EDF should extract 15 tons of uranium one year from now.

• The price of uranium one year from now is also €150/ton.