Question 1:

Consider the following three period extraction model in a competitive market setting. With demand given as P_t = 10 - 0.5q_t, then it can be shown that Total Benefits for a competitive market are

10q_t - .25q_t² for t = 0, 1, and 2.

Where q_t is the level of demand as well as the amount extracted from the mine and sold. Let r = 0.25.

1. Suppose the total starting stock of the resource S, is 80. Using the same procedure I used in class (i.e. that little bit of calculus and algebra I showed you), find the amount extracted and sold every year (t=0, 1, and 2). What do the results imply?What is the user cost of the resource (i.e. lamda)? What does this value imply?
2. Suppose now the total starting stock S = 40. Find the amount extracted and sold every year (t=0, 1, and 2). What do the results imply?What is the user cost of the resource (i.e. lamda)? What does this value imply?