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. 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 form a cartel to act as a monopolist and maximize total industry profits (sum of Firm A and Firm B profits). In such a case, Company A will produce units and sell at .Similarly, Company B will produce units and sell at . At the optimum output levels, Company A earns total profits of and Company B earns total profits of . Therefore, the total industry profits are . At the optimum output levels, the marginal cost of Company A is and the marginal cost of Company B is . The following table shows the long-run equilibrium if the firms act independently, as in the Cournot model (i.e., each firm assumes that the other firm’s output will not change). Cournot Equilibrium Price Output Profits ($) (units) ($) Company A 290 60 5,700 Company B 290 50 6,300 Total Industry 110 $12,000 Compare the optimal solutions obtained in this exercise with the Cournot equilibrium given in the preceding table. What happens to the optimal selling price, total industry output, and total industry profits when the two firms form a cartel instead of acting independently? Increase Decrease No change Selling price Total industry output Total industry
Assume that two companies (A and B) are duopolists who produce identical products. Demand for the products is given by the following linear demand function:
P=400−QA−QBP=400−QA−QB
where QAQA and QBQB are the quantities sold by the respective firms and P is the selling price. Total cost functions for the two companies are
TCA=1,500+110QA+QA2TCA=1,500+110QA+QA2
TCB=1,200+40QB+2QB2TCB=1,200+40QB+2QB2
Assume that the firms form a cartel to act as a monopolist and maximize total industry profits (sum of Firm A and Firm B profits). In such a case, Company A will produce
units and sell at
.Similarly, Company B will produce
units and sell at
.
At the optimum output levels, Company A earns total profits of
and Company B earns total profits of
. Therefore, the total industry profits are
.
At the optimum output levels, the marginal cost of Company A is
and the marginal cost of Company B is
.
The following table shows the long-run equilibrium if the firms act independently, as in the Cournot model (i.e., each firm assumes that the other firm’s output will not change).
Cournot Equilibrium
|
Price |
Output |
Profits |
|
|---|---|---|---|
|
($) |
(units) |
($) |
|
| Company A | 290 | 60 | 5,700 |
| Company B | 290 | 50 | 6,300 |
| Total Industry | 110 | $12,000 |
Compare the optimal solutions obtained in this exercise with the Cournot equilibrium given in the preceding table. What happens to the optimal selling price, total industry output, and total industry profits when the two firms form a cartel instead of acting independently?
|
Increase |
Decrease |
No change |
||
|---|---|---|---|---|
| Selling price |
|
|
|
|
| Total industry output |
|
|
|
|
| Total industry |
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