Question

Consider a non-renewable resource with a demand function Q = 500 – 4P. The marginal cost of extraction is constant over time at $50. The discount rate is 0.10. There are 800 units of resources available.

a) Construct the optimal extraction path for this resource. How many periods does it take to exhaust the resource? (Hint: Start by using the choke price to determine the price in the “final” time period, calculate the rent, use the fact that the rent increases at the rate of interest to solve for the price in the period before the final time period, and so on to fill in the table that was discussed in class. Use a spreadsheet – unless you really like writing out all these calculations. ). (10 points)

b) What if the discount rate increases to 20%? What is the impact on the optimal extraction path (price path, quantity path, time to exhaustion)? (10 points)

Answer 1

Quantity Demand Function Q= 500- 4P. Q represent the demand of Quantity and .P represents the price.

Q= Demand =Quantity demand for the Product of non-renewable resource=500-4P

P= Price of the Commodity.

Q= 500- 4(125)= Demand is 0 when the price at 125.

Q=500-4(100)=Demand is 100 when the price at 100.

you can Graph X as Demand and Y as Price slope line represents the change in Demand in effect of price.

So when the price reaches 125 demand becomes Zero or otherwise no demand for that Product

Marginal Cost is constant over time at $50.

Discount Rate is $0.10

Marginal Cost is the Total cost incurred for the Additional Good Produced .

Formula : Marginal Cost = Change in Total Cost/Change in Quantity.

For Example : 100 Units costs $1000 and the production increases to 150 units and costs $1500 Marginal Cost = 1500-1000/50=10

Marginal Cost is $10 for each units .