Question

UD creamery is selling 500 cones a day for an average of $5 a cone. The elasticity of the demand is -10. How can the creamery make more money? Suggest a new price and calculate the quantity sold for that price, and show that revenues go up. What will happen if elasticity is -1?

Answer 1

Price elasticity of demand is the ratio of percentage change in quantity demanded to the percentage change in price.
PED = % Change in Quantity / % Change in Price

PED is given as -10 in the question. So if the price is decreased by $1 or by 20% then the quantity demanded will rise by 200%.
-10 * (-20%) = 200%
Quantity Demanded = 500+ ((500 * 200) / 100) = 1500
Revenue = 4 * 1500 = 6000

This is more than the earlier revenue of $2500
We will further lower the price to $3 which is a 40% decrease
-10 * (-40%) = 400%
Quantity Demanded = 500+((500 * 400) / 100) = 2500
Revenue = 2500 * 3 = 7500

We will create a table for different price and revenue

Price	% Change in Q	Quantity	Revenue
5		500.00	2500
4	200.00	1500	6000
3	400.00	2500	7500
2.5	500.00	3000	7500
2	600.00	3500	7000
1	800.00	4500	4500

The maximum revenue is generated at the price of $2.5 and $3 which is $7500

Any further cut in the price would not increase the revenue.

Now if the PED has a value of -1then it is not advisable to decrease or increase the price.

Price	% Change in Q	Quantity	Revenue
6	-20.00	400	2400
5		500	2500
4	20.00	600	2400
3	40.00	700	2100
2.5	50.00	750	1875
2	60.00	800	1600
1	80.00	900	900