The market demand for a special type of wood that is essential for producing aco
ID: 1220087 • Letter: T
Question
The market demand for a special type of wood that is essential for producing acoustic guitars is given by Q = 70,000-2000P, where Q is measured in thousands of pounds per year and P is the price of a pound of wood. Suppose that there are 1000 small producers of such wood, each with marginal cost given by MC = q +5, where q is the output of the typical firm.
Now suppose a very large source of this special type of wood is discovered in California such that a firm in California that controls that resource becomes the dominant firm in the world and acts as a price leader. It sets the price in the market and produces accordingly to maximize its own profit. The “CF” continues to act as a competitive group and accepts the price set by the leader in California. The cost function of the dominant firm is given by C = 15QL +2000, where QL is output of the dominant firm. Calculate the profit maximizing output and price of the dominant firm in California. Also calculate its profit. Calculate the total output produced by the CF as well as the market output.
Explanation / Answer
Market Demand is given as Q = 70,000 - 20,000P
1000 smaller firms making a competitive fringe. MC = q + 5
Now for dominant firm, C = 15QL + 2000 is the quantity of Dominant firm.
Price is set by the dominant firm and is accepted by the frindge firms.
For dominant firm, Price is set as P = MC or MC = 15 Thus P = MC = 15
Market price is given by 15. Smaller firms take P=15 as given and tries to maximise their profits by P = MC
or 15 = q + 5 implies q =10.
One firm produces q =10, thus 1000 firms produces = 10,000 units
Putting P= 15 in Market demand curve, we have Q = 70,000 - 2,000 (15) = 70,000 -30,000 = 40,000
Total quantity produced by frindge firms = 10,000
Thus QL= 30,000
Profit of Dominant of firm = 30,000*15 - (15*30,000 + 2000) = -2000
And Total output produced by CF = 30,000 units and Market Output = 40,000
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