Question

Derivative Applications

Please show any necessary work on the following problem:

In February 2017 the price of a daily pass to drive on a Volusia County beach was $10, and at that price 26,467 passes were sold.  In February 2018 the price of a daily pass rose to $20, and the number of passes sold dropped to 17,994.  What is the elasticity of demand for the parking pass?  Is the demand elastic, inelastic, or unit elastic?  Explain the meaning of your answer in the context of this problem.  Is revenue increasing or decreasing?  Next year the County Council may consider raising the price of a daily pass to $30. Based on elasticity of demand, should the Council consider another increase?

Answer 1

Using the mid point elasticiy rule we are given that P1 = 10 and Q1 = 26,467. At P2 = 20, Q2 = 17,994. The formula is given by

Ed = (Q2 – Q1) / [(Q2 + Q1)/2] / (P2 – P1) / [(P2 + P1)/2]

Q1	Q2	P1	P2	Q2-Q1	(Q2+Q1)/2	%Q	P2-P1	(P1+P2)/2	%P	Ed
26467.00	17994.00	10.00	20.00	-8473.00	22230.50	-38.11	10.00	15.00	66.67	-0.57

The elasticity of demand for the parking pass is -0.57. Since |ed| < 1, the demand is inelastic, This is expected as a higher price would not reduce the consumption because there are very few substitutes available for transport system in the given beach.

The revenue is increasing because price is increased and demand is inelastic.

Revenue before price increase = 10*26467 = 264,670

Revenue after price increase = 20*17994 = 359,880

Next year the County Council may consider raising the price of a daily pass to $30. Based on elasticity of demand, the Council can increase the price because the demand is inelastic and so it is expected that it will raise revenue.