question archive Suppose that a monopolist faces linear demand given by Q(p)=100−2pQ(p)=100−2p
Suppose that a monopolist faces linear demand given by Q(p)=100−2pQ(p)=100−2p
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Suppose that a monopolist faces linear demand given by Q(p)=100−2pQ(p)=100−2p. The monopolist also pays a marginal cost of $1 for each unit produced.
1. What is the optimal quantity that the monopolist will charge to maximize its profits?
A. 99
B. 49
C. 100
D. 50
2. What is the price that the monopolist will set to maximize its profits?
A. 24.5
B. 51
C. 25.5
D. 50.5
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The answer is B).
The monopolist will charge a price such that the marginal revenue is equal to marginal cost. Given the demand function, the inverse demand function is:
- P = (100 - Q) / 2
- P = 50 - 0.5Q
The marginal revenue function is:
- P = 50 - Q
Given marginal cost of $1, the optimal quantity is:
- 50 - Q = 1
- Q = 49
