Question

Assume that two companies (A and B) are duopolists who produce identical products. Demand for the products is given by the following linear demand function:

P=200−QA−QBP=200−QA−QB

where QAQA and QBQB, are the quantities sold by the respective firms and P is the selling price. The total cost functions for the two companies are

TCA=1,500+55QA+QA2TCA=1,500+55QA+QA2
TCB=1,200+20QB+2QB2TCB=1,200+20QB+2QB2

Assume that the firms act independently as in the Cournot model (i.e., each firm assumes that the other firm’s output will not change).

For Company A, the long-run equilibrium output is - and the selling price is.
For Company B, the long-run equilibrium output is- , and the selling price is.
At the equilibrium output, Company A earns total profits of- and Company B earns total profits of- . Therefore, the total industry profits are- .

Answer 1

To find the long-run equilibrium output and selling price for companies A and B, we need to calculate their maximum profits and use the demand function to determine the equilibrium selling price. By plugging in the equilibrium quantities into the revenue and cost functions, we can find the total profits for each company and the total industry profits.

Step-by-step explanation:

To find the long-run equilibrium output and selling price for companies A and B, we need to find the quantities at which their profits are maximized. In a Cournot duopoly model, each firm assumes that the other firm's output will not change.

For company A, we can find the equilibrium output by maximizing its profit function, which is given by P(A) * QA - TC(A). Taking the derivative of this function concerning QA and setting it equal to zero, we can solve for QA. Similarly, we can find QB for company B.

Once we have the equilibrium quantities, we can plug them into the demand function to find the equilibrium selling price. The total profits for each company can be calculated by subtracting the total cost function from the revenue function at the equilibrium output.

Using these calculations, we can determine the long-run equilibrium output and selling price for companies A and B, as well as their total profits and the total industry profits.