question archive Suppose that a monopolist faces a linear demand given by [Math Processing Error]Q(p)=100−2p
Suppose that a monopolist faces a linear demand given by [Math Processing Error]Q(p)=100−2p
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Suppose that a monopolist faces a linear demand given by [Math Processing Error]Q(p)=100−2p. The monopolist also pays a marginal cost of $1 for each unit produced. What is the optimal quantity that the monopolist will charge to maximize its profits?
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As given in the question,
Q(p)=100-2p
MC=1
The profit maximizing quantity of the monopoly firm is at the point of intersection of marginal revenue and marginal cost.
The marginal revenue of the monopoly firm in the give case will be:
TR=P*Q
TR=(100-2p)p
MR=100-4p
Putting MR=MC we get:
100-4p=1
p=24.75
By putting the value of p in the equation of demand we get:
Q=100-2(24.75)=50.5
