Question

Burger Queen (BQ) conducted research with respect to the price sensitivity of their premiere burger, know widely as The Boss. In the month of July, BQ reduced the price of The Boss from $7.99 to $7.49, and experienced an increase in sales from 86,000 units per month in June to 93,000 units in July. In the past, June and July unit sales have been about the same. No additional promotions or changes were made for the study period. Answer the following questions related to the product, being sure to show work and explain where appropriate: (a) Calculate the PED for The Boss given this info. (b) Is the PED for The Boss elastic or inelastic, and who do you know? (c) Calculate the dollar sales (Total Revenues) for each of the months of June and July, given your answers in a and b. (d) Given this PED, let’s say BQ raises the price of the Boss by $.25 (from $7.99) for the month of August. (e) Calculate the percent change in price this would represent. (f) Now use the PED and this proposed change in price, and calculate the unit and dollar sales for the month of August.

Answer 1

Part - (a).

Burger Queen (BQ) reduced the the price of the premiere burger The Boss from $7.99 to $7.49 and this resulted increase in sales from 86,000 units per month in June to 93,000 units per month in July.

So change in price from $7.99 to $7.49 and change in quantity is from 86,000 units to 93,000 units.

We can Price elasticity of demand (PED) by using mid-point method.

PED = (∆Q/∆P)*[{(P1 + P2)/2}/{(Q1 + Q2)/2}]

PED = [(93,000 - 86,000)/(7.49 - 7.99)]*[{(7.99 + 7.49)/2}/{(86,000 + 93,000)/2}]

PED = (7000/-0.5)*{(15.48/2)/(179,000/2)}

PED = -14,000*(7.74/89,500)

PED = -108,360/89,500 = -1.21.

Therefore Price elasticity of demand for The Boss is -1.21. The negative sign represent the inverse change in price and quantity.

Part - (b):

The value of Price elasticity of demand is -1.21 and absolute value is 1.21 which is greater than 1. As price elasticity of demand is greater than 1, the price elasticity is elastic.

We know, when PED > 1 ---- PED is Elastic

When PED < 1 ----- PED is Inelastic

When PED = 1 ----- PED is unitary elastic.

As, here PED = 1.21 > 1 , It will be elastic.

Part - (c).

Sales in ($) in June = Price*Quantity sales

Sales in ($) in June = $7.99*86,000 = $687,140. (Answer)

Sales in ($) in July = Price*Quantity sales

Sales in ($) in July = $7.49*93,000 = $696,570. (Answer).

This increase in revenue occurs because the elasticity is Elastic which shows change in quantity will be higher due to change in price. As price decreases quantity changes i.e increases more which results more revenue. When elasticity is elasticity is elastic then decrease in price leads to increase in revenue. Price elasticity 1.21 implies if price decrease by 100% quantity will increase by 121% i.e this higher increase in quantity increases the revenue.

Part - (d).

Given the price elasticity of demand (1.21) if BQ raises the price of The Boss by $0.25 from $7.99 in the month of August.

In the August new price will be $7.99 + $0.25 = $8.24.

Part - (e).

As price changes from $7.99 to $8.24 i.e change in price is $0.25.

Percentage change of this price = (0.25/7.99)*100 = 3.128911%. (Answer).

Part - (f).

Given the price elasticity of demand = -1.21 , it means if price change by 3.128911% , quantity will change by 3.128911*-1.21 = -3.78598231%.

It means due to price increase of $0.25 quantity sales will fall by 3.78598231%.

So, in June, when price was $7.99 quantity sales was 86,000 units.

If due to price increase of $0.25 , quantity will fall by

(3.78598231/100)*86,000 = 3,255.94 = 3,256 units (Approx).

So, quantity sales in August will be = (86,000 units - 3,256 units) = 82,744 units.

Sales revenue in ($) in August is = Price*Quantity sales

Sales revenue in ($) in August is = $8.24*82,744 = $681,810.56 = $681,811 (Approx) (Answer).