A utility company faces demand given by q = 40

Question

A utility company faces demand given by q = 40 - 0.1p, where p is the price per unit.
If the company adopts a two-tier pricing structure, the price per unit for the lower price that maximizes revenue is $____.
A) 266.67
B) 233.33
C) 166.67
D) 133.33

Quizplus · Accepted Answer

To maximize revenue under a two-tier pricing structure, we first need to find the price that maximizes revenue with the given demand function, q = 40 - 0.1p. Revenue (R) is price (p) times quantity (q), so R = p*q = p(40 - 0.1p). To maximize revenue, we differentiate R with respect to p and set the derivative equal to zero. The derivative of R with respect to p is 40 - 0.2p. Setting this equal to zero gives 40 = 0.2p, or p = 200. Since this is the price that maximizes revenue for a single price system, the lower price in a two-tier system would be lower than this. The options given are all lower than 200, so we need to determine which would be part of a strategy to maximize revenue. In a two-tier system, the lower price would typically be set to encourage higher volume, and the higher price would capture additional revenue from less price-sensitive customers. Without specific details on the two-tier structure (e.g., quantity limits for the lower tier), we choose the option that represents a significant discount from the single price maximizing revenue to encourage volume, which is $133.33, option D. This approach assumes a significant discount is necessary to stimulate the desired volume increase, given the lack of specific two-tier structure details.