Final answer:
The profit-maximizing price for Market A is $30, and for Market B, it is approximately $23.33, calculated using the marginal revenue equals marginal cost principle and the provided demand elasticities and marginal cost.
Step-by-step explanation:
To determine the profit-maximizing prices for a firm that faces different demand elasticities in two markets, we can use the formula derived from MR = MC. MR (Marginal Revenue) can be found using the inverse of the demand elasticity. The profit-maximizing price in each market is the price at which the generated marginal revenue equals the marginal cost (MC). Since the MC is given as $20, we can calculate the prices for Market A and Market B by using the demand elasticity for each market and the formula MR = P (1 + 1/e), where P represents the price and e represents the demand elasticity.
For Market A where demand elasticity is -3: MR = P (1 + 1/e) = $20, P = $20 / (1 - 1/3) = $20 / (2/3) = $30, For Market B where demand elasticity is -7: MR = P (1 + 1/e) = $20, P = $20 / (1 - 1/7) = $20 / (6/7) = $23.33. Therefore, the profit-maximizing price in Market A is $30, and in Market B, it's approximately $23.33.