Question

Joe is a manager in a drug store and he is responsible for setting prices of batteries. He knows the price elasticities of the top 2 brands – Energizer and Duracell – from previous research. They are shown in the table below, in which the column represents the brand with price change. For instance, the number on the top right is the cross price elasticity of the demand for Energizer with respect to the price of Duracell.

	Price change
	Energizer	Duracell
Energizer	-2	1.3
Duracell	1.5	-1.8

The current price and sales are shown in the table

	Price	Cost	Units (packs)	Profits
Energizer	$5.5	$4.5	700
Duracell	$6	$5	500
Total

Interpret the cross-price elasticity of 1.3. (2 points)

If Joe wants to increase price of one of the product by 10%, which brand should he increase price in order to achieve greater total profits? Show your work. (6 points)

Answers:

Answer 1

Answer (a) -

Here, we need to interpret the cross-price elasticity of 1.3

Price Change

	Energizer	Duracell
Energizer	-2	1.3
Duracell	1.5	-1.8

Cross-price elasticity is a way to measure how closely the two products are related and how the change of one product's price will impact the demand of the other product. It is measured as follows:

% Change in Qty = (New Quantity Demanded of Energizer – Old Quantity Demanded of Energizer)/(Old Quantity Demanded of Energizer) /

% Change in Price = (New Price of Duracell – Old Price of Duracell)/(Old Price of Duracell)

If XED is positive, it means that the two products are substitutes

If XED is zero, then the two products are unrelated

If XED is negative, then the two products complement each other.

Since the cross-price elasticity is positive in this case (1.3), so we can interpret that these two products are substitutes of each other (closely related). So if we increase the price for Duracell, the qty for Energizer will increase and other way round is also true.

Answer (b)

	Price	Cost	Units (Packs)	Profit
Energizer	$5.5	$4.5	700	$700
Duracell	$6	$5	500	$500
Total	11.5	9.5	1200	$1200

Profit is calculated as, Profit = (Price - Cost) x Units (Packs)

Now consider the following two cases of price increase.

Case 1: let us assume that the price of Duracell will be increased by 10%.

So new price of Duracell = $6+ (10% of $6) = $6.6

Since Price Elasticity of Duracell is -1.8, it means that the demand for Duracell will decrease if the price of Duracell is increased. Let us find the new demand based on this price elasticity of Duracell w.r.t its own price.

(%Change in Duracell demand qty) / (%Change in Duracell Price) = -1.8

%Change in Duracell Demand Qty = -1.8 X 10% (since % change for price is 10%)

Solving the above, we will get New Qty of Duracell = 410 units

Now since there is a cross price elasticity between the two brands, an increase in the price of Duracell will also increase the demand qty of Energizer (XED is 1.3).

(%Change in Energizer demand qty) / (%Change in Duracell Price) = 1.3

New Qty for Energizer = (0.13 x 700) + 700 = 791.

Updating all these values in the given table, we can find the total profit as following:

	Price	Cost	Units (Packs)	Profit
Energizer	$5.5	$4.5	791	$791
Duracell	$6.6	$5	410	$656
Total	$12.10	$9.5	1201	$1447

Case 1: let us assume that the price of Energizer will be increased by 10%.

Applying the above logic (as in case 1), we will arrive at the following table:

New Demand for Energizer = 560 units

New Demand for Duracell = 575 units

Updating all these values in the given table, we can find the total profit as following:

	Price	Cost	Units (Packs)	Profit
Energizer	$6.05	$4.5	560	$868
Duracell	$6	$5	575	$575
Total	$12.05	$9.5	1135	$1443

So we see that the total profit in Case 1 ($1447) was more than the total profit in Case 2 ($1443). Hence, it is advisable to increase the price for Duracell by 10% to maximize the profits.