In: Economics
he market for lawn mowers has 13 small firms and one dominant market leader. The total market demand is given by QD = 1900 - 3P. The total market supply for the 13 small firms is given by QS = 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.
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.