Microeconomics

#2. (8 points) You want to maximize the present value of prots from the extraction and sale of a depletable resource. You are a price-taker and demand is described as p! : a0 , aqu , where p! is price, and q; is quantity. There is also a substitute for the depletable resource that is available at time T at a price pT : a where a : a0. Extraction costs increase with extraction, such that cf : Fig;f . We have T T max 2 p" (pf 73%)]! , subject to: Z q! : Q i=0 i=0 Our problem to be solved is T T mgxzmp, Jada: \"(92%) q' 1:0 (:0 a. (5 pts) Solve for the optimal extraction path, qt , and price path, pr , over time of the resource. b. (3 pts) What is the effect on quantity in each period if 05 decreases such that a