Question

1

1. Consider two Cournot competitive firms – with the following market demand function P=100-Q. The firms face constant marginal costs, MC₁ = 5 whereas MC₂ = 25.

However, if they merge then the marginal production costs would fall to 5.

1. Calculate the costs and benefits due to the merger for either firm.   
2. Is this merger Pareto improving for the economy? Explain.   

2. A Bertrand competition does not necessarily gravitate towards competitive prices in the equilibrium, with imperfect substitutes.

1. In this context, derive the Lerner’s Index and explain why the market power of the Bertrand competitive firm is identical to that of the Monopolist, at the equilibrium.
2. Consider the Bertrand competition with imperfect substitutes, if the firms decide to coordinate in prices. Explain with the help of the relevant Lerner’s index, the factors that affect the firms’market power under Monopoly relative to Bertrand competitive market.   

Answer 1

Given market demand function is P=100-Q, firm1 has marginal cost MC1= 5 firm2 has MC2=25

after merger marginal cost is MC=5

Following working shows when firms compete under cournot model. Firm1 able to sell quantity = 38.33 and firm2 can sell q2= 18.33, both at price= 43.34. After merger firm2 benefits as its marginal cost reduces to 5 from 25.

A(ii) quantity after merger has reduced and price level has increased as can be seen from the above calculation, thus it is not pareto optimal.

B (i)

Above is the derivation of lerner's index. Under Bertrand model, having product differentiation (imperfect substitutes) firms sell goods at prices more than marginal cost at equilibrium and this aligns with of the character of monopoly. As per lerner's index firm can charge prices more than marginal cost upto the point where MC=0 i.e. lerner index =1.

B(ii) Since lerner index is inverse of the elasticity of demand (which is an indicator of market power) it can be said if elasticity of demand is low then firm can charge higher prices.

In monpoly with no close substitutes elasticity of demand is low i.e.market power is high then firms are in position to charge higher prices