Asked by Abigail Rodriguez on May 14, 2024
Verified
In a market with the inverse demand curve P 10 Q, Brand X is a monopolist with no fixed costs and with a marginal cost of $2.If marginal cost rises to $4, by how much will the price of Brand X rise?
A) $2.
B) $1.
C) $3.
D) $0; the firm is already charging the monopoly price.
E) None of the above.
Marginal Cost
The extra expense linked to generating one more unit of a product or service.
Inverse Demand
A representation of demand that shows how the price of a good or service can vary inversely with changes in the quantity demanded.
- Familiarize yourself with the approach to maximizing profits in monopolies.
- Execute the application of price elasticity of demand in relation to setting prices in a monopoly.
Verified Answer
EL
Esmeralda LopezMay 20, 2024
Final Answer :
B
Explanation :
To find the monopoly price, we need to set marginal revenue equal to marginal cost. The marginal revenue for a monopolist is given by the derivative of the inverse demand curve.
MR = d/dQ (P) = d/dQ (10 - Q) = 10 - 2Q
Setting MR = MC:
10 - 2Q = 2
Q = 4
So, the monopoly price is P = 10 - 4 = $6.
If the marginal cost increases to $4, the monopoly price will increase. The new equilibrium quantity is found by setting the new marginal cost equal to the new marginal revenue:
10 - 2Q = 4
Q = 3
The new monopoly price is P = 10 - 3 = $7. So, the price of Brand X will rise by $1. Thus, the correct answer is (B).
MR = d/dQ (P) = d/dQ (10 - Q) = 10 - 2Q
Setting MR = MC:
10 - 2Q = 2
Q = 4
So, the monopoly price is P = 10 - 4 = $6.
If the marginal cost increases to $4, the monopoly price will increase. The new equilibrium quantity is found by setting the new marginal cost equal to the new marginal revenue:
10 - 2Q = 4
Q = 3
The new monopoly price is P = 10 - 3 = $7. So, the price of Brand X will rise by $1. Thus, the correct answer is (B).
Learning Objectives
- Familiarize yourself with the approach to maximizing profits in monopolies.
- Execute the application of price elasticity of demand in relation to setting prices in a monopoly.
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