You are endowed with 100 pounds of unobtanium which you can costlessly bring to market. There are no other sellers. The market demand each year is Dt = 100 Pt. The interest rate is 5%

a) Suppose you sell all of the products today. What is the net present value of your profits.?

b) Now suppose you can split your sales between today and next year, but still sell all of your products.

i-How much should you sell each year and what prices will you charge?

ii-What is the NPV of your profits?

c) Still imagine you can split your sales between today and next year, but your endowment is only 80 pounds of unobtanium.

i-How much should you sell each year and what prices will you charge?

ii-What is the NPV of your profits?

d) Design a sequence of quantities to sell for all time {qt} t=1 that maximizes the NPV of your firm's profits. What would be the path of prices, and what is the NPV of your unobtanium.