Question

APPMaster produced and test marketed a digital product that is particularly appealing to millennials. The variable cost per unit is $5.40. Test markets research predicts that global monthly sales will be 17,000 downloads (sales) at $10 and 9,160 at $14. The elasticity of demand was found to be constant( i.e. curvilinear rather than linear). Suppose APP Master launches a new promotional campaign that reduces target customers sensitivity to price and the elasticity of demand falls by 20% from what you calculated above.

What then will be a. new price elasticity of demand? b. optimal gross margin? c. optimal selling price?

Answer 1

According to the mid-point formula, the price elasticity of demand for a product is given by:

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

PED is found to be -1.8 as computed below

Q1	Q2	P1	P2	Q2-Q1	(Q2+Q1)/2	%Q	P2-P1	(P1+P2)/2	%P	Ed
17000.00	9160.00	10.00	14.00	-7840.00	13080.00	-59.94	4.00	12.00	33.33	-1.8

Now the new campaign reduces target customers sensitivity to price and the elasticity of demand falls by 20%.

Hence new elasticity is -1.44

Optimal selling price P = MC x (PED/PED + 1) = 5.40*(-1.44/-1.44 + 1) = $17.67

Optimal gross margin = (P - MC)/MC = (17.67 - 5.40)/5.40 = 2.72