Suppose there are only two producers, A and B, in a market producing the same good with the same total cost function
TC=0.05 Q^2 +100.
The market demand is given by
a) Find the equilibrium price and total output in the Bertrand model.
b) Find the equilibrium price and total output in the Cournot model.
Can someone please teach me how to compute these? If the marginal cost were constant, then I think I know how to answer these; for this problem, it's the cost function that is confusing me.
For the Bertrand model, we set P=MC, and solve for the output, but what is the MC in this case? There are two firms, so do we have to add them to get the MC? But how to add them? What is the equation that I have to solve?
I hope someone can be kind enough to help me out! Thank you so much!
The MC for EACH FIRM is MC=0.1q.
The trouble is that the two equations have different context, the MR is for the whole industry, but the MC is for each firm.
I am not sure how to bring this to a common footing. How can we add the MC?
What is the equation that we have to solve to get the Bertrand equilibrium price and total output in this case?
Since both firms have the same price, then the demand for each firm will just be half of the total demand. Their products are identical, so we assume that consumers will be indifferent between then two and thus, there's a 50% chance that a consumer will buy the product from firm A.
Therefore, if Q is the total quantity demanded, then Q/2 is the quantity demanded from each firm.
This is the true for the Cournot Equilibrium as well. Again, the consumers are indifferent so in both markets each firm has 50% of the market share.