Priceleade 91) The market for an industrial chemical has a single dominant compr

Question

Priceleade 91) The market for an industrial chemical has a single dominant comprised of many firms that behave as price takers. The dominant firm has recently begun firm and a competitive frings benaving as a price leader, setting price while the competitive fringe folows. The market demand curve and competitive fringe supply curve dominant firm is $0.75 per gallon. follows. The market are given below. Marginal cost for the QM = 140,000-32,000P QF= 60,000 + 8,000P, marke«Quachtaderna,JM where QM- market quantity demanded, and QF the supply of the competitive fringe. Quantities are measured in gallons per week, and price is measured as a price per gallon. a. Determine the price and output that would prevail in the market under the conditions described above. Identify output for the dominant firm as well as the competitive fringe. b. Assume that the market demand curve shifts rightward by 40,000 units. Show that the dominant firm is indeed a price leader. What output (leader and follower) and market price will prevail after the change in demand?

Explanation / Answer

a. QM= 140,000 - 32,000P

QF= 60,000 + 8,000P

dominant firm demand curve(QD):

QD= QM-QF

QD= 140,000 - 32,000P - (60,000 + 8,000P)

QD= 80,000 - 40,000P

QD- 80,000 = -40,000P

P = 2 - 0.000025QD

MRD= 2 - 0.00005QD

Hence, MRD=MCD

MCD= 2 - 0.00005QD

As, MC= $0.75

2 - 0.00005QD= 0.75

or, QD= 25,000

Therefore, P = 2 - 0.000025(25,000)

P = 1.375 per gallon

dominant firm price :

QF= 60,000 + 8,000(1.375)

QF= 71,000

QT= 25,000 + 71,000 = 96,000

b. 40,000 increase in demand curve :

QM= 180,000 - 32,000P

QF= 60,000 + 8,000P

QD= 180,000 - 72,000P - (60,000 + 8000P)

QD= 120,000 - 40,000P

Now, the inverse demand function,

PD= 3 - 0.000025QD

MRD=3 - 0.00005QD

As, MRD=MCD

3 - 0.00005QD= 0.75

QD= 45,000

PD= 3 - 0.000025(45,000) = $1.875

Fringe again follows

QF= 60,000 + 8,000(1.875)

QF= 75,000

QT= 45,000 + 75,000 = 120,000

Now, it is sen that a change in demand leads to increase in price by the dominant firm .The competitive fringe took the new priceand adjusted output accordingly.

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