Please help with this

Assume the following conditions for a natural resource:

A.Marginal Willingness to pay function = 38 - 4Q

B.Marginal Cost = 6 (constant)

C.Discount Rate = 10%

D.11 Units of the natural resource are available

1. State the assumptions we implement to calculate the optimal extraction of a limited natural resource in a two time period setting.

2. Find the optimal extraction quantity when the resource is unlimited in quantity available (show work and graphs).

3. Find the optimal extraction quantities in a two time period model (assume we will extract some quantity this year and the following year) when the quantity of natural resources available is limited to 11 (show work and graphs).

4. Show graphically that benefits are maximized when extracted at the optimal extraction rates from question (3) (you do not need to calculate the total benefits) and show that benefits are not maximized when extracted at any other quantity. Shade in the benefits areas for the two time periods and label the MNB intercepts (q₀, q₁, and prices) (show work and graphs).

5. Assume that instead of extracting the resources in this year and the following year, we now extract the resources this year and two years out (second extraction is year 3). What is the change in total net benefits in each time period from extracting today and two years out rather than today and one year out?

6.Find the marginal user costs of quantities calculated from question (3) (show work and graph).