Question

Ms. Aura is a psychic. The demand for her services is given by Q-2000 10P, where Q is the number of one-hour sessions per year and P is the price of each session. Her marginal revenue is MR = 200-0.2Q Ms. Aura's operation has no fixed costs, but she incurs a cost of 150 per session (going to the client's house).

a. What is Ms. Aura's yearly profit?
b. Suppose Ms. Aura becomes famous after appearing on the Psychic Network. The new demand for her services is Q = 2500-5P. Her new marginal revenue is MR = 500-0.4Q. What is her profit now?
c. Advances in telecommunications and information technology revolutionize the way Ms. Aura does business. She begins to use the Internet to find all relevant information about clients and meets many clients through teleconferencing. The new technology introduces an annual fixed cost of 1,000, but the marginal cost is only 20 per session. What is Ms. Aura's profit? Assume the demand curve is still given by Q-2500 -5P.
d. Summarize the lesson of this problem for the superstar phenomenon.

Answer 1

To calculate Ms. Aura's yearly profit, we need to find the quantity and price that maximize her profit. The profit is calculated as total revenue minus total cost. The lesson from this problem is that profit-maximization requires comparing marginal revenue and marginal cost.

Step-by-step explanation:

To calculate Ms. Aura's yearly profit, we need to find the quantity and price that maximize her profit.

The profit is calculated as total revenue minus total cost.

Total revenue is the product of quantity and price, and total cost is the sum of the cost per session multiplied by the quantity.

To maximize profit, we can compare the marginal revenue and marginal cost. The profit-maximizing level of output occurs where marginal revenue equals marginal cost.

For part a, we have the demand function Q-2000-10P and the marginal revenue MR=200-0.2Q.

The marginal cost is the cost per session, which is 150. By setting MR equal to MC, we can solve for Q and P. Once we find the values of Q and P, we can substitute them into the profit equation to find the yearly profit.

In part b, the demand function changes to Q=2500-5P and the marginal revenue becomes MR=500-0.4Q.

The rest of the steps are the same as in part a to find Ms. Aura's profit under the new demand and marginal revenue functions.

In part c, the new technology introduces an annual fixed cost of 1,000 and a marginal cost of 20 per session.

The demand curve remains the same as in part b. We can use the same steps as before to find the profit.

The lesson from this problem is that profit-maximization requires comparing marginal revenue and marginal cost.

The optimal level of output occurs where marginal revenue equals marginal cost.

Additionally, changes in demand, costs, and technology can affect a firm's profit.