4. Consumers consume two goods, pineapples (x1) and fish (x2). There are n consumers in the...

 

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4. Consumers consume two goods, pineapples (x1) and fish (x2). There are n consumers in the economy. Every consumer has income m and a preference ordering represented by the utility function U(x₁, x₂) = 1/2 1/2 The price of pineapples is p1 and the price of fish is p2. The farmers who produce pineapples have the technology given by x₁ = AK¹/²1¹/²where x₁ is the quantity of pineapples produced, K is the amount of land used, L is the amount of labour used in production and A is the productivity parameter. The cost of a unit of land is the rental rate r and the cost of a unit of labour is the wage rate w. There are t farmers currently producing pineapples in a perfectly competitive market. Each farmer currently uses Ko units of land and in the short-run, it is prohibitively expensive to change the amount of land utilized. 5. For the same consumer preferences and the production function from question 4, suppose that the parameters of the model have the following values: n = 100, A = 1, m= 100, w = 4, t = 20, Ko = 5, and r = 1. a. What is the equilibrium price and equilibrium quantity of pineapples? How many pineapples does each farm supply? How many pineapples does each consumer purchase? (3 marks) b. What are the profits of a single farm? On two clearly labelled diagrams, illustrate the equilibrium found in part (a). In the first diagram illustrate the market equilibrium. In the second diagram show the equilibrium position of a representative farm. On this second diagram make sure you indicate the profit maximizing output for the farm and the total profit earned. (4 marks) c. Is the industry in short-run or long-run equilibrium or both in part (b)? Explain your answer. If the industry is not in long-run equilibrium, explain the adjustment process that will occur. (3 marks) 4. Consumers consume two goods, pineapples (x1) and fish (x2). There are n consumers in the economy. Every consumer has income m and a preference ordering represented by the utility function U(x₁, x₂) = 1/2 1/2 The price of pineapples is p1 and the price of fish is p2. The farmers who produce pineapples have the technology given by x₁ = AK¹/²1¹/²where x₁ is the quantity of pineapples produced, K is the amount of land used, L is the amount of labour used in production and A is the productivity parameter. The cost of a unit of land is the rental rate r and the cost of a unit of labour is the wage rate w. There are t farmers currently producing pineapples in a perfectly competitive market. Each farmer currently uses Ko units of land and in the short-run, it is prohibitively expensive to change the amount of land utilized. 5. For the same consumer preferences and the production function from question 4, suppose that the parameters of the model have the following values: n = 100, A = 1, m= 100, w = 4, t = 20, Ko = 5, and r = 1. a. What is the equilibrium price and equilibrium quantity of pineapples? How many pineapples does each farm supply? How many pineapples does each consumer purchase? (3 marks) b. What are the profits of a single farm? On two clearly labelled diagrams, illustrate the equilibrium found in part (a). In the first diagram illustrate the market equilibrium. In the second diagram show the equilibrium position of a representative farm. On this second diagram make sure you indicate the profit maximizing output for the farm and the total profit earned. (4 marks) c. Is the industry in short-run or long-run equilibrium or both in part (b)? Explain your answer. If the industry is not in long-run equilibrium, explain the adjustment process that will occur. (3 marks)