Answers to Problem Set Number 3


    Marginal cost for each station is constant at $3.00 per gallon. Variable costs are simply equal to the constant marginal cost times gallons sold. Demand for gasoline from the two stations combined is 10,000 gallons per day at a price of $3.00 per gallon equal to marginal cost. For every $0.01 per gallon the price rises above $3.00, the quantity consumers want to buy drops by 200 gallons per day. So, for example, if both stations charge $3.20 -- equal to $.0.20 above marginal cost -- demand is 6,000 gallons per day. However, the stations split this equally, so each station sells 3,000 gallons per day.

1. Initially, the stations compete against each other to sell the most gasoline. What
is the price charged, quantity sold, and net income earned by each station? Normally, the competitive firms sells at price equals marginal cost. However, at this price, neither station can cover its fixed costs, and they are losing money. To remain in business, the stations will have to raise the price enough so that each earns $200 per day to pay for the fixed costs. At a price of $3.044, demand is 9,120 gallons per day. Each station can sell 4,560 gallons with a margin (price less marginal costs) of $0.044 per gallon, earning just over $200 per day not counting fixed cost. The competitive price would therefore be  about $3.05, with net earnings close to zero.

(This problem can be solved algebraically by recalling that there are two simultaneous equations. One is the equation for demand. If each station sells an amount Q per day, P = 3.50 - 200*2*Q. The other equation is the competitive zero-profit condition: total revenue equals total costs, or P*Q = MC*Q +FC = 3.00*Q + 200. Substitute the first equation into the second and solve for the root that yields the lower price -- the stable competitive equilibrium.)

2. If the station managers get together to fix prices, they can maximize joint profits where marginal revenue equals marginal cost. Working this out numerically, you will see that marginal revenue is $3.50 when quantity sold is zero, and drops by $0.02 per gallon for every 200 gallons sold, or twice as fast as the price. Marginal revenue equals marginal cost -- $3.00 -- at a combined sales quantity of 5,000 gallons. At that quantity, price equals $3.25 per gallon. Each station sells 2,500 gallons and earns $425 per day, net of fixed costs.

3. Station B's supplier now raises the wholesale price of its gasoline by $0.10, raising its marginal cost to $3.10 per gallon. If station A honors the agreement not to undercut B's prices, then A will keep the price at the same level of $3.25 and earn as much money as before. B will now have a margin of $0.15 per gallon and earn $175 per day net of fixed costs. If A is dishonorable, A will cut the price to $3.10 and drive B out of business, becoming a monopolist (at least for a while).