6. Spreadsheet simulation (more advanced): Suppose that demand is given by the equation P = 200 – Q, and supply is given by the equation P = 10.
Suppose that the total resource stock Qtot = 100, and that it can be consumed over two periods (0 and 1). Place these equations and other information into a spreadsheet.

a. Solve for the dynamically efficient resource allocation for r = 0, 0.05, 0.10, 0.2, and 0.5. Note that from the exact solution we have q0 = (bQtot + r(a – c))/b(2 + r), and q1 = Qtot – q0.
Build a table with columns showing “r,” “q0,” “q1,” “PV of marginal profit period 0” and “PV of marginal profit period 1.” There will be five rows, one for each “r” value above. Confirm that Hotelling’s rule is satisfied in each case. Provide a brief interpretation of the impacts of rising discount rates on the dynamically optimal price and quantity path over time.

b. Now suppose that Qtot = 70. Build a second table like the one in 6a above. Provide a brief narrative economic interpretation of the impact of a smaller resource stock on the dynamically efficient allocation of the resource, as well as prices and marginal profit.