The popular ride-sharing app Lyber has determined that the general form of rider response to its price multiplier p is given by the logit formula d p e

e

( )=

( – )

( – ) D a bp a bp 1

.

Here, D is the total number of people in an area who have opened the Lyber app, p is the multiplier and base price, d(p) is the number of people in the area who will order a Lyber if the multiplier is p, and a and b are parameters.

a. Let S be the number of available drivers in the area, and assume that S < D.
What is the formula for the multiplier that would exactly balance supply and demand in terms of

a, b, S, and D?

b. Let D = 1000, S = 500, a = 10, and b = 5. What value of p would balance supply and demand?