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.

B)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.

Answer 1

The marginal cost curve of a typical competitive firm is its supply curve above the average total cost. Multiply the individual firm supply curve with number of firms to get market supply curve:

MC=Q+5

MC=P=Q+5

P=Q+5

Qs=P−5

Qs=1000(P−5)

Qs=1000P−5000

The demand curve of dominant firm is given by the horizontal difference between the market demand curve and competitive fringe's supply curve:

QDM=70,000−2,000P

Qscf=1000P−5000

Qddf=65,000−1000P

The dominant firm will act like monopoly with respect to residual demand curve and produces where marginal revenue equals marginal cost to maximize profit.

Use 'twice-as-steep' rule to get marginal revenue from inverse demand function:

Q−65,000=−1000P

P=65−0.001Q

MR=65−0.002Q

MR=MC

MC=∂C/∂Q:15

65−0.002Q=15

0.002Q=40

Q=20,000

P=65−0.001(20,000)

P=$45

Profit is the difference between Total revenue and Total cost:

∏=TR−TC

TR=P⋅Q=$45×20,000=$900,000

TC=15(20,000)+2000=$302,000

∏=$900,000−$302,000=$598,000

Plug in the value of price in the market supply curve of the competitive firm and solve for their output:

Qs=1000(45)−5000

Qs=40,000 units

Market output is dominant firm output plus the competitive firms output:

Market output =40,000+20,000=60,000 units