Question

A monopolist faces the following demand curve: \[ Q=144 / P^{2} \] where $Q$ is the quantity demanded and $P$ is price. Its average variable cost is \[ \mathrm{AVC}=Q^{1 / 2} \] and its fixed cost is 5 a. What are its profit-maximizing price and quantity? What is the resulting profit? b. Suppose the government regulates the price to be no greater than $\$ 4$ per unit. How much will the monopolist produce? What will its profit be? c. Suppose the government wants to set a ceiling price that induces the monopolist to produce the largest possible output. What price will accomplish this goal?

   A monopolist faces the following demand curve:
\[
Q=144 / P^{2}
\]
where $Q$ is the quantity demanded and $P$ is price. Its average variable cost is
\[
\mathrm{AVC}=Q^{1 / 2}
\]
and its fixed cost is 5
a. What are its profit-maximizing price and quantity? What is the resulting profit?
b. Suppose the government regulates the price to be no greater than $\$ 4$ per unit. How much will the monopolist produce? What will its profit be?
c. Suppose the government wants to set a ceiling price that induces the monopolist to produce the largest possible output. What price will accomplish this goal?

Microeconomics

Robert S. Pindyck,… 9th Edition

Chapter 10, Problem 18

Instant Answer

Step 1

To do this, we need to set marginal cost equal to marginal revenue. The total cost can be found by adding variable costs and fixed costs together. The fixed cost is given as 5 and the variable cost is $Q^{3/2}$. So, the total cost is $5 + Q^{3/2}$. Show more…

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A monopolist faces the following demand curve: \[ Q=144 / P^{2} \] where $Q$ is the quantity demanded and $P$ is price. Its average variable cost is \[ \mathrm{AVC}=Q^{1 / 2} \] and its fixed cost is 5 a. What are its profit-maximizing price and quantity? What is the resulting profit? b. Suppose the government regulates the price to be no greater than $\$ 4$ per unit. How much will the monopolist produce? What will its profit be? c. Suppose the government wants to set a ceiling price that induces the monopolist to produce the largest possible output. What price will accomplish this goal?

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