Question

The ECON3305 company was considering a price increase and wished to determine the price elasticity of demand (arc elasticity of demand). An economist and a market researcher, Sandy and you, were hired to study demand. In a controlled experiment, it was determined that at 8 cents, 100 pencils were sold while at 10 cents, 60 pencils were sold, yielding an elasticity of 2.25. However, Sandy and you were industrial spies, employed by the EF Pencil Co. and sent to ECON3305 to cause as much trouble as possible. So Sandy and you decided to change the base for their elasticity figure, measuring price in terms of dollars instead of pennies (ie., $0.08 for 8 cents and $0.10 for 10 cents).  How will this sabotage affect the results? You must show all your work and explain your answer in detail to get credit. Make sure you show formula used in your answer. If you do not show the formulas used, you will receive only partial credit.
your answers in detail by covering the inelastic and elastic demand curves. Make sure you define the meaning of the elastic and inelastic demands.

Answer 1

The company was considering a price increase and wished to determine the price elasticity of demand. We have an information that when the price is set at 8 cents, the sales are equal to 100 pencils and when the price is increased to 10 cents, only 60 pencils were sold. This has resulted in an elasticity value of 2.25. Going by this value, we see that demand is highly elastic, which happens when the price elasticity is greater than 1. In that case we should not raise the price because doing so will result in a decline in sales by a greater percentage so that overall the revenue will fall.

However, before making such conclusion, it was decided to change the base for their elasticity figure, measuring price in terms of dollars instead of pennies. Now under the changed scenario, when the price is set at $0.08, the sales are equal to 100 pencils and when the price is increased to $0.10, only 60 pencils were sold.

Using Arc elasticity, we have

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

= (60 - 100)/((100 + 60)/2)/(0.10 - 0.08)/((0.10 + 0.08)/2)

= -2.25

Hence, it really does not matter if the scale is changed. The price elasticity of demand for pencils is still unchanged at 2.25 so the sabotage is prevented. We therefore recommend that, since the demand is elastic, the price should actually decrease and not increase because if increased further, it would reduce the revenue.