Asked by Mike Tyson Bing Bong on Jun 13, 2024
Verified
A monopolist faces the inverse demand curve p 64 2q.At what level of output is his total revenue maximized?
A) 24
B) 26
C) 8
D) 32
E) 16
Inverse Demand Curve
Describes the relationship between price and quantity demanded, showing price as a function of quantity.
Total Revenue
The total amount of money received by a company for goods sold or services provided during a certain time period.
- Identify the optimum price and quantity of goods for a monopolist in diverse demand and cost environments.
Verified Answer
RK
Reese KlingelJun 18, 2024
Final Answer :
E
Explanation :
To find the level of output where total revenue is maximized, we need to find the quantity at which the marginal revenue equals zero. Using the inverse demand equation, we can find the monopolist's total revenue function:
TR(q) = p*q = (64 - 2q)*q = 64q - 2q^2
The monopolist's marginal revenue function is the derivative of the total revenue function with respect to q:
MR(q) = 64 - 4q
Setting MR(q) equal to zero and solving for q:
64 - 4q = 0
q = 16
Therefore, the monopolist's total revenue is maximized at a quantity of 16.
TR(q) = p*q = (64 - 2q)*q = 64q - 2q^2
The monopolist's marginal revenue function is the derivative of the total revenue function with respect to q:
MR(q) = 64 - 4q
Setting MR(q) equal to zero and solving for q:
64 - 4q = 0
q = 16
Therefore, the monopolist's total revenue is maximized at a quantity of 16.
Learning Objectives
- Identify the optimum price and quantity of goods for a monopolist in diverse demand and cost environments.
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