A monopoly produces widgets at a marginal cost of $8 per unit and zero fixed costs. It faces an inverse demand function given by P = 38 - Q.
Suppose fixed costs rise to $200. What will happen in the market?
A.The firm will decrease its output and lower its price.
B. The firm will increase the price.
C. The firm will shut down immediately.
D. The firm continues to produce the same output and charge the same price.
To determine what will happen in the market when fixed costs rise to $200, we need to analyze the impact on the monopolist's profit-maximizing behavior.
First, let's recall the profit-maximization rule for a monopolist:
The monopolist maximizes profit by producing the quantity of output where marginal cost (MC) equals marginal revenue (MR), and setting the corresponding price.
Given the inverse demand function P = 38 - Q, where P represents the price and Q represents the quantity, we can rewrite it as Q = 38 - P.
Since the marginal revenue (MR) is the derivative of the inverse demand function with respect to quantity, we have MR = 38 - 2Q.
Considering that the monopolist's marginal cost (MC) is a constant $8 per unit, we can set MC equal to MR to find the profit-maximizing quantity.
8 = 38 - 2Q
Rearranging the equation, we have 2Q = 30, which gives us Q = 15.
Now, let's evaluate the different options:
A. The firm will decrease its output and lower its price.
If the monopolist decreases its output from 15 units, it would mean producing less than the profit-maximizing quantity. Since the fixed costs have increased to $200, lowering the price would further reduce the monopolist's profit. Therefore, this option seems unlikely.
B. The firm will increase the price.
Increasing the price would lead to a decrease in quantity demanded, which may reduce the monopolist's revenue. Since the fixed costs have increased to $200, raising the price might be necessary to maintain profitability. Hence, this option has the potential to happen.
C. The firm will shut down immediately.
Given that there are zero fixed costs initially and the cost per unit is only $8, it is highly unlikely for the firm to shut down completely when fixed costs rise to $200. This option can be ruled out.
D. The firm continues to produce the same output and charge the same price.
This option does not take into account the change in fixed costs and neglects the profit-maximization principle. By not adjusting its behavior in response to the increase in fixed costs, the firm would not be optimizing its profit. Therefore, this option is unlikely.
Considering the analysis, the most reasonable option would be:
B. The firm will increase the price.
By increasing the price, the monopolist aims to offset the increase in fixed costs and maintain profitability.