for parts (l) - (o), assume the following: All existing firms and potential entrants have indetical cost structure where LR average cost is minimized at 15 units of output. The minimum average cost is $5 per unit (the assignment question says $10 / unit).

Part 3: Comprehensive Problem 1. Consider the HealthyCity. There are m inhabitants of HealthyCity and they wish to consume only two kinds of goods, fruits () and vegetables (y). The preference ordering for each consumer can be represented by the utility function U(r. y) = x+yl-4. Each consumer has weekly income M. The price of fruits per basket is pr. that of vegetables, per basket, Py. The production function for fruits is 2 = AK4/21/2, where I is the quan- tity of fruits produced every week, measured in baskets, K is the amount of land used, L is the amount of labour used and A is a productivity parameter. Let w represent the wage rate and r the rental rate of land. There are n firms currently producing fruits. Each currently uses K, units of land. In the short-run it is prohibitively expensive to change the amount of land utilized. Assume perfect competition. (a) Find the demand curves for fruits for a representative consumer. (b) Find the market demand curve for fruits. Suppose that the parameters of the model have the following values: m = 1000, n = 200, a = 1/2. A = 1. M = 90,w = 10, K = 5, and r = 1. (h) (i) What is the equilibrium price and equilibrium quantity of baskets of the fruits? (ii) How many baskets does each firm supply? (mi) What are the profits of each firm? (iv) How many baskets of fruits does each consumer purchase? (1) With care and precision, graph the equilibrium found in (h) using two diagrams. In one diagram illustrate the market equilibrium. In the second diagram show the equilibrium position of a representative firm. On this second diagram make sure you indicate the profit maximizing output for the firm and the profit earned. () is the industry in short-run or long-run equilibrium or both in part (h)? WHY? If the industry is not in long-run equilibrium, explain the adjustment process that will occur. (k) Find the price at which existing firms will earn zero profit in the short run. All existing firms and potential entrants have identical cost structure where the long-run average cost is minimized at output of 15 units. The minimum average cost is $10 per unit. (1) What is the industry's long run supply curve? (m) What is the long-run equilibrium price? The total industry output? The output of each firm? How many firms operate under such market conditions? (n) With care and precision, graph the short run marginal and average costs with information from part (k), firm's profit as you found in part (h) and the long run average cost with properties described above. (o) Based on the graph from the previous part (n), how you think the firm will adjust in the long run? Part 3: Comprehensive Problem 1. Consider the HealthyCity. There are m inhabitants of HealthyCity and they wish to consume only two kinds of goods, fruits () and vegetables (y). The preference ordering for each consumer can be represented by the utility function U(r. y) = x+yl-4. Each consumer has weekly income M. The price of fruits per basket is pr. that of vegetables, per basket, Py. The production function for fruits is 2 = AK4/21/2, where I is the quan- tity of fruits produced every week, measured in baskets, K is the amount of land used, L is the amount of labour used and A is a productivity parameter. Let w represent the wage rate and r the rental rate of land. There are n firms currently producing fruits. Each currently uses K, units of land. In the short-run it is prohibitively expensive to change the amount of land utilized. Assume perfect competition. (a) Find the demand curves for fruits for a representative consumer. (b) Find the market demand curve for fruits. Suppose that the parameters of the model have the following values: m = 1000, n = 200, a = 1/2. A = 1. M = 90,w = 10, K = 5, and r = 1. (h) (i) What is the equilibrium price and equilibrium quantity of baskets of the fruits? (ii) How many baskets does each firm supply? (mi) What are the profits of each firm? (iv) How many baskets of fruits does each consumer purchase? (1) With care and precision, graph the equilibrium found in (h) using two diagrams. In one diagram illustrate the market equilibrium. In the second diagram show the equilibrium position of a representative firm. On this second diagram make sure you indicate the profit maximizing output for the firm and the profit earned. () is the industry in short-run or long-run equilibrium or both in part (h)? WHY? If the industry is not in long-run equilibrium, explain the adjustment process that will occur. (k) Find the price at which existing firms will earn zero profit in the short run. All existing firms and potential entrants have identical cost structure where the long-run average cost is minimized at output of 15 units. The minimum average cost is $10 per unit. (1) What is the industry's long run supply curve? (m) What is the long-run equilibrium price? The total industry output? The output of each firm? How many firms operate under such market conditions? (n) With care and precision, graph the short run marginal and average costs with information from part (k), firm's profit as you found in part (h) and the long run average cost with properties described above. (o) Based on the graph from the previous part (n), how you think the firm will adjust in the long run