The Hull Petroleum Company and Inverted V are retail gasoline franchises that co

Question

The Hull Petroleum Company and Inverted V are retail gasoline franchises that compete in a local market to sell gasoline to consumers. Hull and Inverted V are located across the street from each other and can observe the prices posted on each other’s marquees. Demand for gasoline in this market is Q = 100 -4P, and both franchises obtain gasoline from their supplier at $2.75 per gallon. On the day that both franchises opened for business, each owner was observed changing the price of gasoline advertised on its marquee more than 10 times; the owner of Hull lowered its price to slightly undercut Inverted V’s price, and the owner of Inverted V lowered its advertised price to beat Hull’s price. Since then, prices appear to have stabilized. Under current conditions, how many gallons of gasoline are sold in the market, and at what price?

Gallons sold:

Price: $

Explanation / Answer

Under the equilibrium ie when the prices have stablized, the following holds true as per Bertrand Duopoly condition

P=MC

=> 25 - Q/4 = 2.75 => 25-2.75 = Q/4 => 22.25 = Q/4 => Q = 89 Gallons are sold at equilibrium price of $2.75/Gallon

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