Inverse demand function: Difference between revisions

Revision as of 16:39, 27 September 2009

Revision as of 06:12, 28 September 2009

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To compute the inverse demand function simply solve for P in the [[demand curve|demand function]]. For example, if the demand function has the form Q = 240 - 2P then the inverse demand function would be P = 120 - .5Q<ref> Samuelson $ Marks, Managerial Economics 4th ed. (Wiley 2003) </ref>

The inverse demand function can be used to derive the total and marginal revenue functions. Total revenue equals price, P, times quantity, Q, or TR = PQ. Multiply the inverse demand function by Q to derive the total revenue function: TR = (120 - .5Q) x Q = 120Q - 0.5Q². The marginal revenue function is the first derivative of the total revenue function or MR = 120 - Q. Note that the MR function has the same y-intercept as the inverse demand function, the x-intercept of the MR function is one-half the value of the inverse demand function and the slope of the MR function is twice that of the inverse demand function. This relationship holds true for all linear demand equations. The importance of being ablie to quickly calculate MR is that the profit maximizing conditions for firms regardless of market structure is to produce where marginal revenue equals marginal cost. To derive MC you take the first derivative of the total cost function.

For example assume cost, C, equals 420 +60Q + Q2 ²+q³. then MC = 60 + 2Q<small>2</small><ref>Perloff, Microeconomics, Theory & Applications with Calculus (Pearon 2008) 240.ISBN 0-321-27794-5</ref> Equating MR to MC and solving for Q gives Q = 20. So 20 is the profit maximizing quantity - to find the profit maximizing price simply plug the value of Q into the inverse demand equation and solve for P.