A perfectly competitive industry has a large number of potential entrants. Each firm has an identical cost structure such that long run average cost is minimized at an output of 10 units (qi=10 ). The minimum average cost is R5 per unit. Total market demand is given by: Q=750-25p


a.What is the industry’s long run supply schedule? (4)

b.Determine the long run equilibrium price (p), the total industry output (Q), the output of each firm (q), the number of firms and the profit of each firm. (10)

The short run total cost function associated with each firm’s long run equilibrium output is given by

c.Calculate the short run average and marginal cost function. At what output level does short average cost reach a minimum? (6)

d.Derive the short run supply function for each firm and the industry short run supply function. (8)

e.Suppose now that the market demand function shifts upward to . Using this new demand curve, answer part ‘b’ for the very short run when firms cannot change their outputs. (8)

f.In the short run, use the industry short run supply function to recalculate the answers to part ‘b’. (6)

g.What is the new long run equilibrium for the industry? (8)

a. The industry’s long run supply schedule is Q = 750 - 25p.

b. The long run equilibrium price (p) is 30, the total industry output (Q) is 750, the output of each firm (q) is 10, the number of firms is 75, and the profit of each firm is 0.

c. The short run average cost function is C/q = 5 + 5/q and the short run marginal cost function is MC = 5/q2. The minimum average cost is reached at an output of 10 units.

d. The short run supply function for each firm is q = 10 + (p - 30)/5 and the industry short run supply function is Q = 750 + 75(p - 30).

e. The new long run equilibrium price (p) is 20, the total industry output (Q) is 800, the output of each firm (q) is 10, the number of firms is 80, and the profit of each firm is 0.

f. The new long run equilibrium price (p) is 20, the total industry output (Q) is 800, the output of each firm (q) is 10, the number of firms is 80, and the profit of each firm is 0.

g. The new long run equilibrium for the industry is p = 20, Q = 800, q = 10, number of firms = 80, and profit of each firm = 0.

a. To determine the industry's long-run supply schedule, we need to find the quantity supplied at various price levels. In a perfectly competitive industry, each firm will produce at the output level at which its long-run average cost is minimized, which is 10 units in this case. So, to find the industry's long-run supply schedule, we need to calculate the total quantity supplied by all firms at different price levels.

To find the quantity supplied at a given price level, we can substitute the price into the market demand equation and solve for Q. Let's calculate the quantity supplied at two price levels:

At P1:
Q1 = 750 - 25P1

At P2:
Q2 = 750 - 25P2

Continuing this process, we can calculate the quantity supplied at different price levels. Each firm will supply 10 units, so the number of firms in the industry can be determined by dividing the total quantity supplied at each price level by 10.

b. To determine the long-run equilibrium price, we need to find the price at which the total industry output equals the total market demand. The long-run equilibrium occurs when there is no incentive for firms to enter or exit the industry.

To find the long-run equilibrium price, we equate the total industry output (Q) to the market demand (Q) and solve for P.

Total industry output (Q) = market demand (Q):
Q = 750 - 25P

By substituting Q = Q, we can solve for P, which represents the long-run equilibrium price.

Once we find the long-run equilibrium price, we can substitute it into the market demand equation to find the total industry output (Q). Divide this output by the output per firm (10 units) to determine the number of firms in the industry. The profit of each firm can be calculated by subtracting the average total cost (given as R5 per unit) from the price (P) and multiplying it by the output per firm (10 units).

c. To calculate the short-run average cost and marginal cost functions, we need information on the cost structure. Unfortunately, the information about the cost structure is not provided in this question.

Based on the given information, we know that the long-run average cost is at its minimum at an output of 10 units. However, we need additional data to calculate the short-run average cost and marginal cost functions. Without this information, we cannot determine the output level at which the short-run average cost reaches a minimum.

d. Similarly, without the specific cost structure data, we cannot derive the short-run supply function for each firm or the industry's short-run supply function.

e. In the very short run, firms cannot change their outputs. Therefore, the number of firms and their outputs will remain the same as in the long-run equilibrium. However, if the market demand function shifts upward, it means that the new equilibrium price will be higher. Consequently, the firms in the industry will experience higher profits.

To recalculate the answers for part 'b' in the very short run, we can use the new demand curve and follow the same steps outlined earlier in part 'b', considering the upward shift in the demand curve. This will help determine the new long-run equilibrium price, the total industry output, the output of each firm, the number of firms, and the profit of each firm.

f. In the short run, the industry's short-run supply function will be determined based on the marginal cost of each firm. However, the specific data regarding the short-run average cost and marginal cost functions are not provided in this question. Consequently, we cannot recalculate the answers for part 'b' using the industry's short-run supply function.

g. The new long-run equilibrium for the industry will be determined by the interaction of the new market demand curve (as provided in part 'e') and the firms' cost structures. However, without the specific data regarding the cost structures, we cannot calculate the new long-run equilibrium for the industry.