Question 4. Technological Progress (25 points + 20 bonus points) Consider the extraction of a fossil fuel resource that has endogenously increasing marginal extraction cost and stable demand over time. a. On two separate figures, depict (1) the quantity of the non-renewable resource used in each period and (2) the price of the non-renewable resource in each period along the efficient extraction path under the assumption that the resource is not exhausted along the efficient extraction path. This is "Model 5" from Lecture 9. (10 points) b. Suppose that a technological advance allows the resource to be extracted at a lower marginal cost. Further, assume that the technological advance makes it so that marginal extraction costs increase more slowly over time as the resource stock is diminished. Using the figure from part (a.), depict how the technological advance would change the following quantities assuming that the resource is not exhausted along the efficient extraction path even after the technological advance. Explain the economic intuition for each result: i. The marginal user cost in period t = 1. (5 points) ii. The quantity of the resource extracted and consumed in each period. (5 points) iii. The time that resource extraction ends. (5 points) c. Using the figures from part (a.), show how your answer to part (b.) would change if technical advance meant that the entire stock of the resource is now economic, and the resource is exhausted along the efficient extraction path. (20 bonus points)