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Pure Monopolist's Marginal Revenue
Market demand is the firm's demand in a case of pure monopoly market structure. Hence, demand curve for a monopoly is downward sloping.
Assume, x - pure monopolist output, P(x) - demand curve formula, therefore P'(x) < 0 (because demand curve is negatively sloped).
TR(x) = P(x) * x - total revenue
Let's differentiate both sides of this equation:
TR'(x) = P(x) + P'(x)*x
MR(x) = P(x) + P'(x)*x, hence
MR(x) < P(x) (because P'(x) < 0,
x > 0)
Where, MR (x) - marginal revenue of pure monopolist.
So, we derived the simple fact that in monopolistic market marginal revenue curve lies below demand curve i.e. marginal revenue is less than price.
Posted by mazoo at May 23, 2005 5:24 PM