Calculate the outcomes of a group of fishers who harvest a renewable resource. The resource X is defined by X_t+1 =X_t +r*X_t * (1- X_t / K) - q*E*X_t

b. Attached is an Excel model Threescenarios.xlsx download that shows profit and resource size over time. You can fill in 3 scenarios. Have scenario 1 for no harvesting, scenario 2 for maximum sustainable harvesting, and scenario 3 for open access.

c. Why do we see the profits of scenario 3 going to 0 over time?

d. Why is the resource size higher in scenario 2 compared to scenario 3?

e. What happens if you put the resource size for timestep 0 to 10,000?

P Scenario 2 10,000 0.004 100,000 9 K r c E Scenario 2 Theoretical equilibria Scenario 3 Theoretical equilibria Resource_MSY = = Harvest_MSY - Effort_MSY - 50000 2000 10 Resource_OA Harvest_OA : Effort_OA = 25000 1500 15 0 0 0 0 0 0 0 0 0 100,000 90,000 80,000 Scenario 1 70,000 Scenario 2 Scenario 3 60,000 Resource site 50,000 40,000 30,000 20.000 10.000 100000 0 Time step Scenario 1 10,000 0.004 100,000 0.08 1,000,000 0 Resource Profit 0 100,000 1 100000 2 100000 3 100000 4 100000 5 5 100000 6 100000 7 100000 8 100000 9 100000 10 100000 11 100000 12 100000 13 100000 14 100000 15 100000 16 100000 17 100000 18 100000 19 100000 20 100000 21 100000 22 100000 23 100000 24 100000 25 100000 26 100000 27 100000 28 100000 29 100000 30 100000 31 100000 32 100000 33 100000 34 100000 35 100000 36 100000 37 100000 38 100000 39 100000 40 100000 41 100000 42 100000 43 100000 44 100000 45 100000 46 100000 47 100000 48 100000 49 100000 50 100000 51 100000 52 100000 53 100000 Scenario 3 10,000 0.004 100,000 0.08 1,000,000 0 Resource Profit 0 100,000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0.08 1,000,000 0 Resource Profit 0 100,000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 0 100000 0 100000 0 100000 0 100000 1 0.9 0.8 0.7 Scenario - Scenario 2 -Scenario 3 0.6 0.5 0.4 0 0 0 o 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 o 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.3 0.2 0.1 0 Time step 100000 P Scenario 2 10,000 0.004 100,000 9 K r c E Scenario 2 Theoretical equilibria Scenario 3 Theoretical equilibria Resource_MSY = = Harvest_MSY - Effort_MSY - 50000 2000 10 Resource_OA Harvest_OA : Effort_OA = 25000 1500 15 0 0 0 0 0 0 0 0 0 100,000 90,000 80,000 Scenario 1 70,000 Scenario 2 Scenario 3 60,000 Resource site 50,000 40,000 30,000 20.000 10.000 100000 0 Time step Scenario 1 10,000 0.004 100,000 0.08 1,000,000 0 Resource Profit 0 100,000 1 100000 2 100000 3 100000 4 100000 5 5 100000 6 100000 7 100000 8 100000 9 100000 10 100000 11 100000 12 100000 13 100000 14 100000 15 100000 16 100000 17 100000 18 100000 19 100000 20 100000 21 100000 22 100000 23 100000 24 100000 25 100000 26 100000 27 100000 28 100000 29 100000 30 100000 31 100000 32 100000 33 100000 34 100000 35 100000 36 100000 37 100000 38 100000 39 100000 40 100000 41 100000 42 100000 43 100000 44 100000 45 100000 46 100000 47 100000 48 100000 49 100000 50 100000 51 100000 52 100000 53 100000 Scenario 3 10,000 0.004 100,000 0.08 1,000,000 0 Resource Profit 0 100,000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0.08 1,000,000 0 Resource Profit 0 100,000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 100000 0 0 100000 0 100000 0 100000 0 100000 1 0.9 0.8 0.7 Scenario - Scenario 2 -Scenario 3 0.6 0.5 0.4 0 0 0 o 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 o 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.3 0.2 0.1 0 Time step 100000