1. in the long run if there are
1. The market demand for a type of carpet known as A12 has been estimated as P = 75 1. 5Q, where P is price ($/yard), and Q is output per time period (thousands of yards per month). The market supply is expressed as P = 25 + 0. 50Q. A typical competitive firm that markets this type of carpet has a marginal cost of production of MC = 2.
5 + 10q. a. Determine the market equilibrium price for this type of carpet. Also determine the production rate in the market. b.
Determine how much the typical firm will produce per week at the equilibrium price. c.If all firms had the same cost structure, how many firms would compete at the equilibrium price computed in (a) above? d. Determine the producer surplus the typical firm has under the conditions described above.
(Hint: Note that the marginal cost function is linear. ) e. What is the number of firms that would be in the long run if there are no fixed costs.
a. Market equilibrium price is found by equating S and D. 75 – 1.
5Q = 25 + 0. 50Q 50 = 2Q Q = 25 (thousand yards per month) The equilibrium selling price is P = 75 – 1. 5(25) = $37. 5/yard. b.Since the firm’s supply is based on its MC curve, we can use MC to determine production rate. P = 37.
5 = MC = 2. 5 + 10q c. Since each firm produces 3. 5 thousand yards per month and total production is at 25 thousand yards per month, a total of 7. 14 firms would be needed. d. Producer surplus is the area between the price of $37.
5 and MC, bounded by zero and 3. 5 units of output for the typical firm. The bounded area is a triangle. 2. The market demand and supply functions for imported beer are: and To encourage the consumption of domestic beer, Congress has imposed a quota of 25,000 units of imported beer.Calculate the change in producer surplus from this legislation. Solution:First we must determine the market equilibrium quantity and price before the quota.
To do this, we set quantity demanded equal to quantity supplied and solve for equilibrium price. At a price of $32, the quantity exchanged will be: 35,000. The choke price (lowest price such that no units are transacted) is $118. 15. The highest price such that no beer will be imported is $12.
35. Consumer surplus is Producer surplus is If a quota of 25,000 units is implemented, consumers will bid the market price up to $56. 2 for each of the units.
The new producer surplus is: In this example, the producer surplus has increased by $208,250 or 60. 6%. 3. The Metro Electric Company produces and distributes electricity to residential customers in the metropolitan area. This monopoly firm is regulated, as are other investor owned electric companies. The company faces the following demand and marginal revenue functions: P = 0. 04 – 0.
01Q MR = 0. 04 – 0. 02Q Its marginal cost function is: MC = 0. 005 + 0.
0075Q, where Q is in millions of kilowatt hours and P is in dollars per kilowatt hour.Find the deadweight loss that would result if this company were allowed to operate as a profit maximizing firm, assuming that P = MC under regulation. Solution: Find the area between the average revenue curve and the marginal cost curve that is bounded by the rates of production chosen first by the profit maximizing monopoly and second by the regulated industry having the same cost structure. Monopoly output is denoted QM and is found where MC = MR. 0. 04 – 0.
02Q = 0. 005 + 0. 0075Q QM = 1. 2727 (in millions of KWH) The regulated industry output takes place where average revenue equals marginal cost.The area representing deadweight loss is the area under the AR curve minus the area under the MC curve between Q = 2 and Q = 1. 2727.
Area under AR is computed by first finding the heights of AR at the two quantities. At Q = 2, AR = 0. 04 – 0. 01(2) = 0. 04 – 0.
02 = 0. 02 At Q = 1. 2727, AR = 0. 04 – 0.
01(1. 2727) = 0. 04 – 0. 012727 = 0. 02727. Area = (2 – 1. 2727)(0.
023636) = 0. 01719 The area under MC is At Q = 2, MC = 0. 005 + 0. 0075(2) = 0. 02 At Q = 1.
2727, MC = 0. 005 + 0. 0075(1.
2727) = 0. 014545 The area under MC is