Question

Shanice's satellite company broadcasts TV to subscribers in two cities, Luminous and Noble. The demand functions for each of these markets are

Qₗ =100−0.50Pₗ
​Qₙ =60−0.25Pₙ
​ where Q is in thousands of subscriptions per year and P is the subscription price per year. The cost of providing Q units of service is C=1,000+40Q, where Q=Qₙ +Qₗ
​. a) What are the profit-maximizing prices and quantities for the Luminous and Noble markets? b) As a consequence of a new satellite that was recently deployed, people in Luminous receive Shanice's Noble broadcasts, and people in Noble receive Shanice's Luminous 2 broadcasts. As a result, anyone in Noble or Luminous can receive Shanice's broadcasts by subscribing in either city. So Shanice can charge only a single price. What price should she charge, and what quantities will she sell in each city? c) In which of the above situations, a) or b), is Shanice better off? In terms of consumer surplus, which situation do people in Noble prefer and which do people in Luminous prefer? Why?

Answer 1

To find the profit-maximizing prices and quantities for the Luminous and Noble markets, set the marginal revenue equal to the marginal cost in each market. When Shanice can charge a single price, she should charge the price that maximizes her total revenue.

Step-by-step explanation:

To find the profit-maximizing prices and quantities for the Luminous and Noble markets, we need to set the marginal revenue equal to the marginal cost in each market. The marginal revenue is the derivative of the demand function, and the marginal cost is the derivative of the cost function. Setting the marginal revenue equal to the marginal cost will give us the profit-maximizing prices and quantities for each market.

In the second situation where Shanice can charge a single price after the new satellite deployment, she should charge the price that maximizes her total revenue. This will be the same price that maximizes the total revenue in the Noble market before the satellite deployment, as the subscribers in both cities now have access to both broadcasts.

In terms of consumer surplus, the people in Noble will prefer the situation where Shanice can charge a single price and sell in both cities, as they will have access to more programming at a lower price. The people in Luminous, on the other hand, may prefer the original situation where the markets were separate, as they may have to pay a higher price in the new situation.