Two firms Layuza Ent and Martin Ltd serve the same market. They have constant average costs...

Two firms Layuza Ent and Martin Ltd serve the same market. They have constant average costs of GH₵2.5 per unit. The firms can choose either a high price (GH₵10) or a low price (GH₵5) for their output. When both firms set a high price, the total demand is 10,000 units which is split evenly between the two firms. When both set a low price, total demand is 19,000, which is again split evenly. If one firm sets a low price and the second a high price, the total market demand will be 18,000 which is shared such that the high-price firm gets a quarter of the total sales and the low-price firm gets the rest.
Analyze the pricing decisions of the two firms as a non-co-operative game.
i. In the normal from representation, construct the payoff matrix, where the elements of each cell of the matrix are the two firms' profits.
ii. Derive the equilibrium set of strategies.
iii. Explain Thoroughly why the Nash is equilibrium in this case is not Pareto Optimal.

Solutions

Expert Solution

ii) The equilibrium strategies are shown in the matrix which are circled. Here both the firm's dominant strategy is to keep a high price and hence it is also the Nash equilibrium.

iii) Here, the Nash equilibrium is Pareto Optimal, as no firms has any incentive to move to other strategy.

Rahul Sunny answered 1 year ago

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