Download presentation
Presentation is loading. Please wait.
Published byFiona Raybon Modified over 10 years ago
1
§ 5.3 Applications of the Natural Logarithm Function to Economics
2
Section Outline Relative Rates of Change Elasticity of Demand
3
Relative Rate of Change
Definition Example Relative Rate of Change: The quantity on either side of the equation is often called the relative rate of change of f (t) per unit change of t (a way of comparing rates of change for two different situations). An example will be given immediately hereafter.
4
Relative Rate of Change
EXAMPLE (Percentage Rate of Change) Suppose that the price of wheat per bushel at time t (in months) is approximated by What is the percentage rate of change of f (t) at t = 0? t = 1? t = 2? SOLUTION Since we see that
5
Relative Rate of Change
CONTINUED So at t = 0 months, the price of wheat per bushel contracts at a relative rate of 0.22% per month; 1 month later, the price of wheat per bushel is still contracting, but more so, at a relative rate of 0.65%. One month after that (t = 2), the price of wheat per bushel is contracting, but much less so, at a relative rate of %.
6
Elasticity of Demand
7
Elasticity of Demand EXAMPLE (Elasticity of Demand) A subway charges 65 cents per person and has 10,000 riders each day. The demand function for the subway is (a) Is demand elastic or inelastic at p = 65? (b) Should the price of a ride be raised or lowered in order to increase the amount of money taken in by the subway? SOLUTION (a) We must first determine E(p).
8
Elasticity of Demand CONTINUED Now we will determine for what value of p E(p) = 1. Set E(p) = 1. Multiply by 180 – 2p. Add 2p to both sides. Divide both sides by 3. So, p = 60 is the point at which E(p) changes from elastic to inelastic, or visa versa.
9
Elasticity of Demand CONTINUED Through simple inspection, which we could have done in the first place, we can determine whether the value of the function E(p) is greater than 1 (elastic) or less than 1 (inelastic) at p = 65. So, demand is elastic at p = 65. (b) Since demand is elastic when p = 65, this means that for revenue to increase, price should decrease.
Similar presentations
© 2025 SlidePlayer.com. Inc.
All rights reserved.