Asked by Canon Graef on May 02, 2024
Verified
A monopolist faces the inverse demand curve p 120 6q.At what level of output is his total revenue maximized?
A) 20
B) 5
C) 20.
D) 15
E) 10
Inverse Demand Curve
Another term for the inverse demand function, it graphically represents how price depends on the quantity demanded, illustrating the relationship inverse to the demand curve.
Total Revenue
The total amount of money received by a company from selling goods or services before any expenses are deducted.
- Ascertain the ideal pricing and output for a monopolistic entity across a range of cost and demand situations.
Verified Answer
ZK
Zybrea KnightMay 05, 2024
Final Answer :
E
Explanation :
Total revenue (TR) is maximized where marginal revenue (MR) equals zero. The inverse demand curve is given by p=120−6qp = 120 - 6qp=120−6q . Total revenue is TR=p×q=(120−6q)q=120q−6q2TR = p \times q = (120 - 6q)q = 120q - 6q^2TR=p×q=(120−6q)q=120q−6q2 . To find MR, differentiate TR with respect to q: MR=d(TR)dq=120−12qMR = \frac{d(TR)}{dq} = 120 - 12qMR=dqd(TR)=120−12q . Setting MR = 0 to maximize TR, we get 0=120−12q0 = 120 - 12q0=120−12q , which simplifies to q=10q = 10q=10 .
Learning Objectives
- Ascertain the ideal pricing and output for a monopolistic entity across a range of cost and demand situations.
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