1 Mushroom hunting in the Czech Republic (from 2016 midterm) Mushroom picking is a national pastime in the Czech Republic. Every weekend, hordes of Czechs ock to the country to nd fungi. One of the best place to go is Sumava National Park in southern Bohemia. Although relatively remote, a direct train runs daily from downtown Prague to the park entrance for just $10 (ie M0 = 10 per person). As the park gets more crowded and overpicked, it becomes harder for each individual to nd mushrooms. Thus, the total number of mushrooms (M) that can be sustainably harvested per day is a concave function of the number of daily mushroom hunters (H), M=90HH2 1. What is the maximum number of mushrooms that can be sustainably harvested per day? How how many hunters per day does that imply? Label these values M M and H M (M for maximum). Hint: Here we're not considering costs. Just nd the number of H that maximizes the daily yield of mushrooms M. 2. If Czechs get $1 of utility for each mushroom harvested, how many will venture to Sumava each day? How many mushrooms will be harvested per day? Label these values Mo and Ho (O for open access). Hint: Assume that every mushroom hunter gets the same share of M. Since this is an open access resource, people will enter as long as private net benets are positive. Example: So if two people visit (H = 2), then the collect M = 90(2) 22 = 176 total mushrooms. And each takes home 88, which gives them $88 of total benets. Since it costs $10 to get there on the train net benets are $78. 3. What is the socially eicient level of H and M? Label these values M E and H E (E for eicient). 4. Calculate the net benets associated with each of the previous three outcomes (ie nd N BM, N BO, and N B E) In words, explain why (conceptually) H M and H0 are not socially optimal. 5. The Czech government is considering taxing the train ride to Sumava. What tax (per rider) would ensure that the e'icient number of hunters go to Sumava each day? Hint: Find a tax t such that the cost of the ticket 10 + it exactly offsets the expected per person utility from M /H at the eicient point H E