1. Imagine a two period model of the market for diamonds - a non-renewable, non-

Question

1. Imagine a two period model of the market for diamonds - a non-renewable, non-recyclable resource. The marginal cost of extracting diamonds is constant at $20. The demand curve in each period is: P = 200 – 0.5q.
Suppose the discount rate is 15% and the total quantity of diamonds to be harvested is 250.
a. Determine the optimal quantity of diamonds to be extracted in each period and the optimal price of diamonds in each period.
b. Suppose the discount rate is 10% and everything else is the same. Calculate the new dynamically efficient allocation of oil across the two periods.
c. How would the price path for diamonds be affected by the decrease in discount rate from part b?

Explanation / Answer

P= 200-0.5Q

TR = PxQ

TR = (200-0.5Q)Q = 200Q-0.5Q2

MR= 200-Q

Now, MR = MC

200-Q = 20

Q = 180

P = 200-(0.5x180) = 110

a) now there is a discount of 15%

So new price = 85/100 x 110 = 93.5

For quantity, 93.5= 200-0.5Q

0.5Q = 200-93.5

Q= 213

b) Discount rate is 10%

New price = 90/100 x 110 = 99

Quantity : 200-0.5x99 = 150.5

c) Due to the discount rate the prices are $99 and $93.5

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