A monopolist has a constant marginal and average cost of $10 and faces a demand curve of QD = 100 - 10P. Marginal revenue is given by MR=100-.20P.
a. Calculate the monopolist's profit maximizing quantity, price, and profit.
b. Now suppose that the monopolist fears entry, but thinks that other firms could produce the product at a cost of $15 per unit (constant marginal in average cost) and that many firms could potentially enter. How could the monopolist attempt to deter entry, and what would the monopolist quantity and profit be now?
c. Should the monopolist try to deter entry by setting a limit price?
I know the answer for a.
Profit maximizing quantity: 450
Profit maximizing price: $55
Profit: $20,250
Calculate the monopolist’s profit-maximizing quantity, price, and profit.
Q=450, P=55, Profit=
c. Now suppose that the monopolist fears entry, but thinks that other firms could produce the product at a cost of $15 per unit [constant marginal and average cost] and that many firms could potentially enter. How could the monopolist attempt to deter entry, and what would be the monopolist’s quantity and profit be now?.
One way to limit entry would be to lower the price of the product since the average cost is $10 to make and the fear is that a firm can make it on a average cost of $15. Then make the product sell for less than what it takes on average for the other firm to make it.
c. Should the monopolist try to deter entry by setting a limit price?
Yes, by setting a limit price you can deter other firms form coming in on the market. This is done by lowering the price so that others do not want to enter into the market.
a. To calculate the monopolist's profit maximizing quantity, price, and profit, we need to find the point where marginal cost (MC) equals marginal revenue (MR).
Given:
MC = $10
MR = 100 - 0.20P
Setting MC equal to MR:
10 = 100 - 0.20P
Rearranging the equation:
0.20P = 100 - 10
0.20P = 90
P = 90 / 0.20
P = 450
Substituting the price back into the demand equation to find the quantity (QD):
QD = 100 - 10P
QD = 100 - 10(450)
QD = 100 - 4500
QD = -4400
Negative quantity doesn't make sense in this context, so we set QD = 0.
Therefore, the monopolist's profit maximizing quantity is 0, the price is $450, and the profit is 0 since no units are sold.
b. To deter entry, the monopolist can potentially engage in predatory pricing, setting a price lower than the potential entrants' cost of production ($15) to discourage them from entering. This strategy could be to temporarily lower the price to a level that the potential entrants cannot compete with.
Assuming the monopolist successfully deters entry, the monopolist's quantity and profit would depend on the price the monopolist sets. Without further information, it is not possible to determine the exact quantity and profit.
c. Setting a limit price means the monopolist sets a price at or below the competitive price level to discourage new entrants. This may be an effective strategy to deter potential entrants, as they would not find it profitable to enter the market.
Whether or not the monopolist should try to deter entry by setting a limit price depends on several factors, including the monopolist's market power, the potential impact of entry on their profits, and the costs associated with implementing and enforcing a limit price strategy. It would require more information and analysis to make a definitive recommendation.
a. To calculate the monopolist's profit-maximizing quantity, price, and profit, we need to determine the point where marginal revenue equals marginal cost.
Given that marginal revenue (MR) is MR = 100 - 0.20P, and marginal cost (MC) is $10, we can set them equal to each other:
100 - 0.20P = 10
Solving for P, we find:
0.20P = 90
P = 450
Now, we can substitute this value of P into the demand equation to find the quantity:
QD = 100 - 10P
QD = 100 - 10(450)
QD = 100 - 4500
QD = -4400
Since the quantity cannot be negative, this implies that the monopolist should produce 0 units in order to maximize profit.
To find the monopolist's profit, we need to calculate the total revenue (TR) and total cost (TC):
TR = P * QD
TR = $450 * 0
TR = $0
TC = MC * QD
TC = $10 * 0
TC = $0
Profit = TR - TC
Profit = $0 - $0
Profit = $0
Therefore, the monopolist's profit-maximizing quantity is 0 units, the price is $450, and the profit is $0.
b. To deter entry by other firms, the monopolist could engage in anti-competitive practices such as predatory pricing or strategic barriers to entry. For example, the monopolist could lower the price below the cost of production ($15 per unit) to make it unprofitable for new firms to enter the market.
Assuming the monopolist successfully deters entry and continues as the sole producer, the monopolist's profit-maximizing quantity and profit would be the same as in part a (0 units and $0 profit), since there would be no competition.
c. Setting a limit price, which is a price below the monopoly price but above the competitive price, could potentially deter entry by making it less attractive for new firms to enter the market. However, setting a limit price is not always an effective long-term strategy.
If the limit price is set too high, it may still attract new entrants. On the other hand, if the limit price is set too low, it could lead to a loss of potential profits for the monopolist.
In this case, if the monopolist sets a limit price above the competitive price of $15, it may deter entry to some extent, but it would not affect the monopolist's profit-maximizing quantity and profit, which remain at 0 units and $0 profit.