Let p = f(q) be a demand function where p is the price per unit when q units are demanded, p, q> 0. Assume that f'(q) < 0 and f"(q) > 0 for all q> 0. Suppose s > 0 and that demand is: (i) elastic on the open interval (0, s), (ii) unit at s, and (iii) inelastic on the open interval (s, ∞). (a) Use calculus to prove mathematically that the revenue r = pq has a critical value at q=s. (b) Justify why r is maximized at q = s.

Let p = f(q) be a demand function where p is the price per unit when q units are demanded, p, q> 0. Assume that f'(q) < 0 and f"(q) > 0 for all q> 0. Suppose s > 0 and that demand is: (i) elastic on the open interval (0, s), (ii) unit at s, and (iii) inelastic on the open interval (s, ∞). (a) Use calculus to prove mathematically that the revenue r = pq has a critical value at q=s. (b) Justify why r is maximized at q = s.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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