Suppose that there are two (identical) fishermen. Let hi, where i = 1,2, denote the fishing...

  

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Suppose that there are two (identical) fishermen. Let hi, where i = 1,2, denote the fishing effort (measured, for example, as a number of standard trawler days at sea) of fisherman i. Fisherman i's catch/harvest is given by qi = 0hx, where 0 is a technology parameter and is fish stock. The fish stock grows according to the logistic growth function g(x) = (1-x/K) where is a growth parameter and K is the carrying capacity. Moreover, let P denote the constant price of fish biomass. Therefore, total revenue of fisherman i is Pq. For each fishermen, the total cost of fishing is wh?/2, where w is a cost parameter. Assume that the fisher operates in a steady-state equilibrium (i.e., the fish stock does not change). Let K = 100, y = 4,0 = 0.1, w = 25, P = 50. a- If there was only a single fisherman, the fishing effort h would be equal to Y(OKP-w) 202 KP (1) If there were two fishermen, the best-response function of fisherman i would be h = C- h = OPK(y-oh-)- wy 202 PK (2) where-i denotes the other fisherman. Using these information, calculate the co- operative, competitive, deviation effort levels and profits. b- Construct the payoff matrix (as we did for the common grazing problem in the class) and find the Nash equilibrium. Interpret. Suppose that the interactions of the two fishermen is repetitive and is expected to last for 9 periods. Supposing that the players adopt a tit-for-tat strategy and taking the discount rate as r 0.1, how would the fishermen behave in this case? Calculate and interpret the result. = Suppose that there are two (identical) fishermen. Let hi, where i = 1,2, denote the fishing effort (measured, for example, as a number of standard trawler days at sea) of fisherman i. Fisherman i's catch/harvest is given by qi = 0hx, where 0 is a technology parameter and is fish stock. The fish stock grows according to the logistic growth function g(x) = (1-x/K) where is a growth parameter and K is the carrying capacity. Moreover, let P denote the constant price of fish biomass. Therefore, total revenue of fisherman i is Pq. For each fishermen, the total cost of fishing is wh?/2, where w is a cost parameter. Assume that the fisher operates in a steady-state equilibrium (i.e., the fish stock does not change). Let K = 100, y = 4,0 = 0.1, w = 25, P = 50. a- If there was only a single fisherman, the fishing effort h would be equal to Y(OKP-w) 202 KP (1) If there were two fishermen, the best-response function of fisherman i would be h = C- h = OPK(y-oh-)- wy 202 PK (2) where-i denotes the other fisherman. Using these information, calculate the co- operative, competitive, deviation effort levels and profits. b- Construct the payoff matrix (as we did for the common grazing problem in the class) and find the Nash equilibrium. Interpret. Suppose that the interactions of the two fishermen is repetitive and is expected to last for 9 periods. Supposing that the players adopt a tit-for-tat strategy and taking the discount rate as r 0.1, how would the fishermen behave in this case? Calculate and interpret the result. =

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a To calculate the cooperative competitive and deviation effort levels and profits we need to substitute the given parameters into the equations Given ... View the full answer