Marginal Revenue Example

Business Calculus · Axiom Academy

EXAMPLE Marginal Revenue Example Working with demand functions to find marginal revenue Problem: Concert Ticket Pricing A concert venue has found that the demand for tickets follows the equation: where p is the price in dollars and x is thousands of tickets Find the marginal revenue function Determine where revenue is maximized Revenue equals price times quantity: Substitute the demand function for price: Revenue function (in thousands of dollars) Take the derivative of the revenue function: For a linear demand function p = a - bx , the marginal revenue is always MR = a - 2bx . The coefficient of x doubles! Let's see how MR changes as ticket sales increase: When MR decreases total revenue. The price has been cut too much! Revenue is maximized when MR = 0: Sell 15,000 tickets at a price of p = 90 - 3(15) = \ 45 each. Maximum Revenue = R(15) = 90(15) - 3(15)^2 = 1350 - 675 = \ 675,000 MR starts at the same value as demand (when x = 0) MR decreases faster than price (double the slope) MR = 0 at the revenue-maximizing quantity When MR < 0, total revenue decreases This analysis helps venues find the sweet spot between ticket price and attendance. Selling too many cheap tickets can actually generate less total revenue than fewer higher-priced tickets! You've mastered finding and interpreting marginal revenue. Based on the example above, which approach is correct?

This is the written version of the interactive lesson above. See the full Business Calculus course.