Question

In: Economics

he market for lawn mowers has 13 small firms and one dominant market leader. The total...

he market for lawn mowers has 13 small firms and one dominant market leader. The total market demand is given by Q_D = 1900 - 3P. The total market supply for the 13 small firms is given by Q_S = 25 + 2P. The dominant firm has a constant marginal cost of $55 per lawn mower. At the profit-maximizing price chosen in question 4 above, the dominant firm will produce __________ lawn mowers and the total output of all 13 small firms together will be_____________ lawn mowers.

Solutions

Expert Solution

Demand curve faced by the dominant firm = Market demand - Market supply for 13 small firms

=> Q = QD - Qs

=> Q = 1900 -3P - (25 + 2P)

=> Q = 1900 - 3P - 25 -2P

=> Q = 1875 - 5P ----------------------- (demand function of dominant firm)

=> P = (1875 - Q) / 5

=> P = 375 - 0.2Q

TR = PQ

=> TR = (375 - 0.2Q) Q

=> TR = 375Q - 0.2Q² ----------------- (TR function of dominant firm)

=> MR = ΔTR / ΔQ

=> MR = 375 - 0.4Q ---------------------- (MR function of dominant firm)

A dominant firm maximize profit at , MR = MC

=> 375 - 0.4Q = 55

=> 375 - 55 = 0.4Q

=> 320 = 0.4Q

=> Q = (320 /0.4)

=> Q = 800

The output produced by dominant firm is 800 units.

P = 375 - 0.2Q

=> P = 375 - 0.2(800)

=> P = 215

The profit maximizing price is 215

Qs = 25 + 2P

=> Qs = 25 + 2(215)

=> Qs = 455

The total output of all 13 small firms together will be 455 lawn mowers.

At the profit-maximizing price , the dominant firm will produce 800 lawn mowers and the total output of all 13 small firms together will be 455 lawn mowers.

Rahul Sunny answered 1 year ago

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