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=400−QA−QBP=400−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+110QA+QA2TCA=1,500+110QA+QA2

TCB=1,200+40QB+2QB2TCB=1,200+40QB+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

Main Answer:

For Company A, the long-run equilibrium output is QA = 50 and the selling price is PA = $300. For Company B, the long-run equilibrium output is QB = 50, and the selling price is PB = $300. At the equilibrium output, Company A earns total profits of $12,500, and Company B earns total profits of $7,500. Therefore, the total industry profits are $20,000.

Step-by-step explanation:

In the Cournot model, each firm independently determines its output quantity based on the assumption that the other firm's output remains constant. The long-run equilibrium is reached when both firms produce an equal quantity, QA = QB = 50. At this equilibrium, the selling price is determined by the demand function P = 400 - QA - QB, leading to PA = PB = $300.

To calculate the total profits, subtract the total cost function from the total revenue function for each company. For Company A, total profits (πA) at equilibrium is calculated as (PA * QA - TCA), resulting in $12,500. Similarly, for Company B, total profits (πB) at equilibrium is calculated as (PB * QB - TCB), resulting in $7,500. Adding both firms' profits gives the total industry profits of $20,000.

The equilibrium output and prices are determined by the interplay of demand and cost functions, highlighting the firms' strategic decision-making in a duopoly. Company A and Company B both aim to maximize their profits while considering the expected reaction from the other firm.