Consider a duopoly with homogeneous products, where two competing firms pick price (Bertrand duopoly). In this chapter you learned that both firms will choose price equal to the marginal cost (MC). But what happens if the the two firms have unequal marginal costs? Suppose that Dogwood has MC = $40andRosePetalhasMC = $25. Assume firms can set prices such as $29.99.
A. Explain why it is not a Nash equilibrium for both firms to set a high price such as $60.
B. Explain why it is not a Nash equilibrium for both firms to set a price equal to the lower marginal cost of $25.
C. Explain why it is not a Nash equilibrium for each firm to set a price equal to their respective marginal costs.
D. What is a Nash equilibrium? Which firm sells? At what price?
Duopoly with a homogenous product - This is a Bertrand model which examines price competition among various firms with homogenous products or highly substitutable products like tea and coffee
So earlier P=MC where P = price and MC = marginal cost.
Now Dogwood has Mc1 = $40 , Rose = MC2 = $25
This is to be assumed that firms can set Price = $29.99
(a) Since both the firms sell homogenou products so if one firm charges a price higher, then the firm with a higher price will have no customers and hence at equilibrium both the firms should set a price which is equal.
(b) Now it will be not a Nash Equilibrium if the firms set price lower to the MC = 25 because then in that care one firm can slightly raise its price and lower the profit will fall. Most importantly it is to remember that Bertrand Equilibrium will occur when P=MC1=MC2.
(c) If the prices set by both the firsm are same but lower than the Marginal cost or equal to it, there will be an incentive for both the firms to deviate and lower the prices and capture more customers in the market. The only equilibrium where none of the firms would be willing to deviate would be at P=MC. But since MC are not equal, the outcome will not be Pareto Efficent.
(d) SO we can see that Rose has a lower price than Dogwood and hence Rose Petal would see. This is an asymmetric case where MC1>MC2
P rice = MC1 and Rose would capture all the market and get positive profit by $ (40-25)= $15 and Dogwood would earn 0 profit.
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