Answer to Question #271081 in Economics for pau

Question

suppose that the demand curve facing OPEC is given by P=120-2Q and that each members cost of producing oil is AC=MC=$20.Find the cartels profit maximizing total output and price. Of instead of keeping to this output, all members overproduced their quotas by 20 percent,what would be the effect on OPEC's total profit?

Answer 1

$$120-2Q=20$$

$$2Q=100$$

$$Q=50$$

$$p=20$$

$$\pi=TR-TC=120Q-2Q^2-20Q=100Q-2Q^2$$

$$\frac{\delta \pi}{\delta Q}=100-4Q$$

$$Q=25$$

$$\pi=1250$$

$$Q^/=1.2\times25=30$$

$$\pi^/=1200$$