The ECON3305 company was considering a price increase and wished to determine th

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.

Explanation / Answer

We are given that the the company is planning a price increase and it finds the price elasticity of demand using the mid point or arc elasticity of demand method. Now when the price is 8 cents, a total of 100 pencils were sold and when the price is increased to 10 cents, there is a reduction and now only 60 pencils were sold, This has resulted in a price elasticity of 2.25.

Using the mid point method we see that Ed = (Q2 – Q1) / [(Q2 + Q1)/2] / (P2 – P1) / [(P2 + P1)/2]

Here P1 = 8 and P2 = 10. Similarly Q1 = 100 and Q2 = 60. Use this information and find ed

ed = (60 - 100)/((100 + 60)/2) divided by (10 - 8)/((10 + 8)/2)

= -2.25

Hence the results are correct . Now if we change the base for their elasticity figure from dollars instead of pennies we can check that this will not cause any damage to the elasticity computation.

Using the mid point method we see that Ed = (Q2 – Q1) / [(Q2 + Q1)/2] / (P2 – P1) / [(P2 + P1)/2]

Here P1 = 0.08 and P2 = 0.10. Similarly Q1 = 100 and Q2 = 60. Use this information and find ed

ed = (60 - 100)/((100 + 60)/2) divided by (0.10 -0.08)/((0.10 + 0.08)/2)

= -2.25

Hence this sabotage does not affect the result. Note that the aim of the company was to see if the price increase can increase the revenue. We have found on the price elasticity of demand is greater than 1 in absolute terms.

This implies that the demand for the company's product is relatively elastic. The theory of elasticity suggests that when the demand is elastic, prices should be reduced in order to increase the revenue. This is because an elastic demand experiences a greater percentage reduction in quantity demanded when there is a given percentage increase in the price. This causes the revenue to decline. Therefore an appropriate strategy for the firm is to reduce the price and not increase it. Only then the company can increase its revenue.

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