Monopoly n One firm only in a market n Persistence of such a monopoly: – huge cost advantage – secret technology (Coca-Cola) or patent – government restrictions to entry (deliveries of letters in Germany) n But what is a market?

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The demand function: how many units of a good do consumers buy? n price n properties n availability of substitutes n quality n information n compatibility n timely delivery n...

Revenue, costs and profits n Revenue: n Cost: n Profit: n Linear case:

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Demand analysis for X=f(p, m,... ) n Satiation quantity = f(0, m,... ) n Prohibitive price = price p such that f(p, m,... ) =0 n Slope of demand curve dX/dp n Price elasticity of demand n...

Demand analysis for X(p) = d - ep n Satiation quantity: d n Prohibitive price: d/e n Slope of demand curve: dX/dp = - e n Price elasticity of demand

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Marginal revenue with respect to price n revenue goes up by X (for every unit sold, the firm receives one Euro), n but goes down by p dX/dp (the price increase diminishes demand and revenue). When a firm increases the price by one unit,

Marginal revenue w.r.t. price and price elasticity of demand marginal revenue w.r.t. price is zero when a relative price increase is matched by a relative quantity decrease of equal magnitude

n If the demand elasticity is smaller than 1, a price (in relative terms) increase is followed by a smaller quantity decrease (in relative terms. Hence, revenue goes up. n Therefore, a price increase increases revenue and decreases costs. n Answer: No. Can a demand elasticity < 1 be optimal?

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Unities of measurement n length: units of distance (e.g., kilometers) n velocity: units of distance per unit of time (e.g. miles per hour) n quantity X: units of quantity (e.g. pieces) n price p: units of money per unit of quantity (e.g. DMs per piece) n revenue R: units of money (e.g. Euros) For comparisons, units of measurement have to be the same!

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How to find the monopolist`s profit maximizing price n Profit function: n Setting the derivative of the profit function with respect to the price equal to 0:

Marginal cost with respect to price n the price increase diminishes demand, n the demand decrease decreases costs. When a firm increases the price by one unit, the costs of production go down:

Consider a monopoly selling at a single market. The demand and the cost function are given by a) Demand elasticity? Marginal-revenue function with respect to price? b) Profit maximizing price? c) How does an increase of unit costs influence the optimal price? (Consequence for tax on petrol?) (Industrial Organization; Oz Shy) Exercise (monopoly in the linear case)

Solution (monopoly in the linear case)

Consider a monopoly selling at a single market. The demand and the cost functions are given by a) Demand elasticity? Marginal-revenue function with respect to price? b) Price charged with respect to  ? c) What happens to the monopoly’s price when  increases? Interpret your result. (Industrial Organization; Oz Shy) Exercise (monopoly with constant elasticity)

Solution (monopoly with constant elasticity)

Price discrimination First degree price discrimination: Second degree price discrimination: Third degree price discrimination: Every consumer pays a different price which is equal to his or her willingness to pay. Prices differ according to the quantity demanded and sold (quantity rebate). Consumer groups (students, children,...) are treated differently.

Exercise (third degree price discrimination) n A monopolist faces two markets: x 1 (p)=100-p 1 x 2 (p)=100-2p 2. Unit costs are constant at $20. n Profit-maximizing prices with and without price discrimination? (Intermediate Microeconomics; Hal R. Varian)

Price discrimination: Without price discrimination: Solution (third degree price discrimination)

Exercises (inverse elasticities rule) n Demand elasticities in two markets: n Suppose that a monopoly can price discriminate between the two markets. n Prove the following statement: “The price in market 1 will be 150% higher than the price in market 2.“ (Industrial Organization; Oz Shy)

Solution (inverse elasticities rule)

Complements and substitutes n Goods are called substitutes if a price increase of one increases demand for the other (butter and margarine, petrol and train tickets). n Goods are called complements if a price increase of one decreases demand for the other (hardware and software, cars and gas, cinema and popcorn).

Exercise (complements) n A monopolist sells two complements: x 1 (p 1, p 2 )=100-p 1 -p 2 x 2 (p 1, p 2 )=100-2p 2 -p 1 Unit costs are constant at $20. n Profit-maximizing prices? n Now assume there are two monopolists selling the complements independently.

Solution (complements) Two monopolists: