Consider a market with linear market demand curve p = 250 - Y. Each firm supplying...

 

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Consider a market with linear market demand curve p = 250 - Y. Each firm supplying the market uses the same technology with constant average and marginal costs of $10 per unit. From the formulas derived in class we know that a monopolist will produce 120 units and the market price will be $130; but if the market is a Cournot duopoly, then each firm will supply 80 units and the market price will be $90. (You do not need to verify these claims; just take them as given.) (a) The generalised inverse-elasticity rule says that 1 ne p-c P = where p is the market price, n is the number of firms in the market, is the elasticity of demand at the market price and quantity, and is the absolute value of a (i.e., the value of a without the negative sign). Show that the Cournot duopoly market satisfies this rule. (b) How much does each firm earn in the Cournot duopoly? (c) Suppose the market is a duopoly but the duopolists collude, with each agreeing to supply half of the monopoly output (i.e., 60 units each). i. If the firms keep to this agreement, then how much profit will each firm earn? ii. Suppose Firm 1 believes that Firm 2 will keep its side of the bargain and supply 60 units. If Firm 1 decides to ignore the agreement and produce the quantity that maximises its own profit, then how much will it produce? (You may assume that Firm 1 also ignores any future consequences it may suffer from breaking the agreement and aims to maximise its current profit.) iii. What are the firms' profits in the outcome described in (ii)? Consider a market with linear market demand curve p = 250 - Y. Each firm supplying the market uses the same technology with constant average and marginal costs of $10 per unit. From the formulas derived in class we know that a monopolist will produce 120 units and the market price will be $130; but if the market is a Cournot duopoly, then each firm will supply 80 units and the market price will be $90. (You do not need to verify these claims; just take them as given.) (a) The generalised inverse-elasticity rule says that 1 ne p-c P = where p is the market price, n is the number of firms in the market, is the elasticity of demand at the market price and quantity, and is the absolute value of a (i.e., the value of a without the negative sign). Show that the Cournot duopoly market satisfies this rule. (b) How much does each firm earn in the Cournot duopoly? (c) Suppose the market is a duopoly but the duopolists collude, with each agreeing to supply half of the monopoly output (i.e., 60 units each). i. If the firms keep to this agreement, then how much profit will each firm earn? ii. Suppose Firm 1 believes that Firm 2 will keep its side of the bargain and supply 60 units. If Firm 1 decides to ignore the agreement and produce the quantity that maximises its own profit, then how much will it produce? (You may assume that Firm 1 also ignores any future consequences it may suffer from breaking the agreement and aims to maximise its current profit.) iii. What are the firms' profits in the outcome described in (ii)?