One of the most commonly used mathematical models for a demand function in micro-economics is x = Mp-k where p is the price of a commodity and x is the quantity of the commodity that can be sold. Suppose that M = 4, k = ½ p is the price per ride on a New York City subway, and x is the number of riders per day (in millions).
(a) Find the ridership when the price is two dollars.
(b) Find the drop in ridership if the price is raised to $2.25.
(c) Find the equation of the tangent line to the demand curve at p = 2.
(d) Use the value of x on the straight line to find the approximate drop in ridership if the price is raised to $2.25. This is called the marginal demand.
(e) Find the ratio of the value found in (d) to the change in price.