Monopoly

The monopolistic technology firm Goople faces a market described by the demand function $p = 20 − q$, where p is the price the firm receives if it sells quantity q of advertisement. The firm’s cost function is given by $C(q) = 64 + \frac{q^2}{4}$.

1. Using the slider in the above graph, find the advertisement quantity $q$ that maximizes the firm’s profit. What is the profit of the firm if they sell this quantity? What is the relationship between marginal revenue and marginal cost at this choice?
2. Using the demand and cost functions above, derive the firm’s total revenue, marginal revenue, and marginal cost functions.
3. Set up and solve Goople’s profit maximization problem, and show that the quantity chosen, the price charged, and the profit made match what you found using the graph.
4. If Goople could sell more advertising at this price, would they? How much advertising would they optimally sell at this price? Explain briefly why this doesn’t happen.
5. Using the graph, find the quantity Goople would sell if they acted like a perfect competitor. How much money would they lose in this case? Explain briefly why they would choose to lose money.
6. Compare the total surplus when Goople acts as a monopolist to the total surplus when Goople acts as a perfect competitor.