Question

2. Suppose an industry consists of two firms that compete in prices. Each firm produces one product. The demand for each product is as follows:

q1 = 25 − 5p1 + 2p2

q2 = 25 − 5p2 + 2p1

The cost functions are C(qi) = 2 + qi for i = 1, 2.

The Nash equilibrium price is 3.75

(e) What is the percentage markup of price over marginal cost here (this is called the Lerner index)? Do the firms have market power? Why does the Bertrand paradox of zero variable duopoly profits apply here?

(f) Suppose the firms merged. What is the new price of products 1 and 2?

(g) Explain intuitively why the price is higher under monopoly than under Bertrand duopoly?

(h) Are total monopoly profits higher or lower than the sum of Bertrand duopoly profits? Why or why not?

Answer 1

yes the firms have market power. The Bertrand paradox of duopoly profits refers to the situation that if a firm choose quantities over price then the competitive outcome would occur with price equal to marginal cost. if the two firm charge the same price the demand of customers will be split into half . but also the firms cannot set the price less than the unit cost.

suppose the firms are merged the new price of the product will be the same. Which will encourage customers to choose from any of the firm based on quality and usage etc.

The price will be higher in monopoly than duopoly is because that in monopoly we have only single seller producing a unique product without any competition which results in higher price for the goods because there is no other producer producing the same goods. But in duopoly we have 2 firms producing the same kind of goods and the each firm expects the rival will set the price constant. irrespective of its own decision on pricing. which results in reduction of price of the goods in both monopoly and duopoly.

The both pofits in monopoly and duopoly changes. because in monopoly we have only single seller producing a unique product and no one else is producing the particular product which will attract all the customers towards that particular firm in monopoly which will result in increase in profits. but in duopoly there are 2 firms and the customer can choose from which firm they have to buy. which will result in decrease in profits.