Mr. Peanutbutter proposes that Hollywood should reseed the pasture to make it greener. Since only Bojack and Todd are actively using the pasture, Mr. Peanutbutter thought it would be a great idea to ask Bojack and Todd to contribute to the reseeding effort. Let R denote the total amount of reseeding, which raises the value per goat only when R > 1: D(G, R) = In (R x G). The marginal cost or reseeding is also a constant k = 2. Let y and r denote the number of goats that Bojack and Todd choose contribute to the reseeding effort, respectively. d. What is the amount of reseeding that Bojack and Todd each contribute? How many goats does Bojack and Todd now each graze? Underline your answer. Hint: Bojack and Todd face symmetric problems, and Bojack would choose g and r to maximize the following: 8Bv (gB + g],B +rT) -cgB - krB. (5 points) e. What is the socially optimal reseeding and the socially optimal number of goats grazing on the pasture? (5 points) f. Explain in one sentence why Bojack and Todd are under-contributing to the reseed- ing effort. (5 points) Comment: Notice how the under-contribution to the reseeding effort has both Bojack and Todd under-grazing (instead of over-grazing)!3. Tragedy of the Commons and Free Riding: 30 points In Hollywood are only two goat farmers: Bojack Horseman and Todd Chavez. Both Bojack and Todd graze their goats on the same green pasture in Hollywood This pasture is very large so it can accommodate many goats. However, as the number of goats grazing on the pasture increases, the amount of grass available for each goat decreases, i.e., the marginal value of goats is decreasing. More specifically, if there is a total of G goats grazing on the pasture, then the value per goat is v(G) = In G. 4 The marginal cost of caring for the goat is constant c = 3.5. Let g and g denote the num- ber of goats that Bojack and Todd choose to raise, respectively. (Please provide answers accurate to the second decimal point.) a. How many goats does Bojack and Todd each graze? Underline your answer. Hint: Bojack and Todd face symmetric problems, and Bojack would choose go to maximize the following: go (8 + g?) - cg. (5 points) b. What is the socially optimal number of goats grazing on the pasture? (5 points) c. Explain in one sentence why Bojack and Todd are over-grazing the pasture. (5 points) Mr. Peanutbutter proposes that Hollywoodshould reseed the pasture to make it greener. Since only Bojack and Todd are actively using the pasture, Mr. Peanutbutter thought it would be a great idea to ask Bojack and Todd to contribute to the reseeding effort. Let R denote the total amount of reseeding, which raises the value per goat only when R > 1: D(G, R) = In (R x G)
