Suppose that a monopolist faces the following inverse demand curve for its product:

p = 50 - 2q

where p is the price of the product and q is the quantity of the product. The monopolist incurs a constant marginal cost of $10 per unit of output.

1. What is the monopolist's profit-maximizing output level and price?

2. What is the monopolist's total profit or loss at the profit-maximizing output level?

3. Suppose that the monopolist can engage in price discrimination by segmenting its market into two groups: group A, which is willing to pay a higher price for the product, and group B, which is only willing to pay a lower price. The demand curve for group A is given by p = 30 - q and the demand curve for group B is given by p = 20 - q. The monopolist can set different prices for each group. What is the monopolist's profit-maximizing output level and prices for each group?

4. How does the monopolist's profit compare to the profit that would be earned by a competitive firm in the same market?

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