Market Structure Monopoly

Monopoly $ MC P* The firm maximizes profits when the marginal revenue is equal to the marginal cost. The marginal revenue and the price are not equal for a monopoly because the monopoly can only sell more units if it reduces the price on all the units it was already selling (intra-marginal units). Note that the marginal revenue is lower than the price. You can see this on the next table. D MR Q Q*

Production and Output P Q TR MR TC MC $10 1 $3 $1 9 2 18 8 5 3 24 6 7 $10 1 $3 $1 9 2 18 8 5 3 24 6 7 4 28 12 30 17 23 -2 -4 38 Profit $7 13 16 7 -2 -14

Elasticity of Demand and Output h=(∆Q/Q)/(∆P/P)=(∆Q/∆P)*(P/Q) ∆P=(Px∆Q)/(Qxh) How much you have to change the price to sell exactly one additional unit (∆Q=1)? |∆P|=P/(Qx|h|) What is the change in revenue if you sell an additional unit? MR=P- |∆P|xQ MR=P- (P/(Qx|h|))xQ=P(1-1/|h|) MR=P(1-1/|h|) The monopoly always operate on the elastic part (|h|>1) of the demand curve (otherwise the MR is negative)

Example Suppose that if the price is $10 the quantity of cars demanded is 10. If the price is $9 the quantity of cars demanded is 11. Total revenues change when reducing the price from $10 to $9 because: you make ($9) for selling an additional car. You now sell for $9 each of the 10 cars you were selling for $10. You make -$10. Therefore the marginal revenue in this example is -1 ($9-$10).

Elasticity of Demand and Output If the monopoly increases the price, revenues must fall. Suppose you find that the increase in price of gas led to an increase in revenues. This would be evidence that the gas market is not a monopoly. A monopoly does not have to wait for a disaster that increases costs to increase prices.

Monopoly and Welfare $ MC A B Pm C E D Pc G H F D MR Q Qm Qc

Competition Monopoly Consumers’ Surplus A+B+C+D+E A+B Producers’ Surplus F+G+H C+D+F+G Social Gain A+B+C+D+E+F+G+H A+B+C+D+F+G Deadweight Loss - E+H

Monopoly and Price Ceiling $ A price ceiling eliminates the deadweight loss MC P* Pc D MR Q Qm Qc