Abc of Management

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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...
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