monopoly produces widgets at a marginal cost of $10 per unit and has zero fixed costs. It faces an inverse demand function given by P=50-Q. Suppose fixed costs are rise by $400; what happens in the market

The company will not make a profit anymore, but it is still able to pay its production costs. In the short run it will continue to operate, but in the long run it will exit the market.

Explanation:

first we must determine the marginal revenue function:

total revenue = price x quantity

total revenue = (50 - q) x q = 50q - q²

marginal revenue = total revenue'

marginal revenue = (50q - q²)' = 50 - 2q

in order to maximize profits, marginal revenue = marginal costs

marginal costs = 50 - 2q

10 = 50 - 2q

2q = 40

q = 20

profits will maximize when q = 20

profit per unit = 50 - q - marginal cost = 50 - 20 - 10 = $20

since the total units sold are 20, then total profit = 20 x $20 = $400

if fixed costs increase by $400, then profits = $400 - $400 = $0

if the company tries to increase the selling price by $20 per unit ($400 / 20 = $20), the total number of units sold will be 0 (50 - 20 - 10 - 20 = 0).

The company will not make a profit anymore, but it is still able to pay its variable production costs. In the short run it will continue to operate, but in the long run it will exit the market.

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