Question

Case 1 (12 marks) It becomes important for managers to accurately forecast the demand of their product and also understand as how the demand of other products might affect their own product's demand. In a rapidly growing market like energy drinks, firms need to capture the market scenario quick enough. Firms that fail to keep up the changing pace with the market can lose out to their competitors. Red bull is one of the brands in the energy drink industry. Red bull has estimated the demand of its product by the following function: Q= 12.5 P.-1.1 A2.ly1.3p-1.8 Where, Q = Number of energy drink bottles sold of Red bull Po = Price of red bull energy drink bottle (in $) A = Promotional expenditure yearly in $100 Y = Average income of the consumers per month in $100 P = Number of people using the gyms per month The current price for one bottle of Red Bull energy drink $3, promotional expenditure is $600, Average income of consumers is $500 and on an average 100 people are going to gym every month. You are a quantitative analyst and your role is to analyze the below situations in the given scenario. Explain the reason of your analysis done in each below case supporting by calculations. a) Will the revenue of Red Bull decrease, if they increase the price of their bottles? b) How the price of Red Bull energy drink, promotional expenditure and income of the consumers will affect the sales of Red Bull bottles? c) If number of people going to gym increases, does it affect the sales of energy drink bottles? d) How much will be the demand for bottles sold increases, if the income of the consumers increases by x % (x = the last digit of your student id)? e) Will the profit of Red Bull reduce, if they increase the price of their energy drink bottle? f) Do you think Gym subscription can complement the sale of Red Bull energy drink?

Answer 1

The equation in the question can we re-written as follows:

Q =	12.5 *	1	* (A ^2.1) *	(Y^ 1.3) *	1
		(P0)^1.1			(p) ^1.3

where

Q - number of red bull bottles sold

P₀ - price of red bull per bottle

A - promotional expenditure in $100

Y - income of consumer per month in $100

p - number of people using gym per month

The base case scenario is P₀ - $3, A - 6 [its value in $100], Y - 5 [its value in $100], p - 100

Q = 12.5 * 1/ (3)^1.1 * 6^2.1 * 5 ^ 1.3 * 1/(100)^1.8

= 12.5 * 0.299 * 43.06 * 8.10 * 0.00025

= 0.33

a) when price of bottles are increased, P₀ will increase in the equation. As this is in denominator of the equation, with the increase, the total quantity of bottle sold will be reduced and hence revenue of red bull will decrease.

Assume if the price increase from $3 to $5 then the equation will be as

Q = 12.5 * 1/ (5)^1.1 * 6^2.1 * 5 ^ 1.3 * 1/(100)^1.8

= 12.5 * 0.17 * 43.06 * 8.10 * 0.00025

= 0.19

b) From the equation, we can understand that while the price of the red bull is indirectly proportional to the quantity of red bulls sales, the promotional expenditure and income of consumer are directly proportional to the quantity of red bull sales

In the above example [answer for question (a) we showed the impact of price increase on the sales volume.

Assume if the promotional expenditure is increased from the base case of $600 to $1000, then the equation becomes like:

Q = 12.5 * 1/ (3)^1.1 * 10^2.1 * 5 ^ 1.3 * 1/(100)^1.8

= 12.5 * 0.299 * 125.98 * 8.10 * 0.00025

= 0.96

Hence it is evident that increase in promotional expenditure will increase number of bottles sold

Now, we will assume the consumer income increase from base case of $500 to $700, now the equation become:

Q = 12.5 * 1/ (3)^1.1 * 6^2.1 * 7 ^ 1.3 * 1/(100)^1.8

  = 12.5 * 0.299 * 125.98 * 12.55 * 0.00025

= 0.51

Hence it is evident that increase in income of consumers will increase number of bottles sold

c) If number of people going to gym increases, it will decrease the number of bottles sold as the gym users are inversely proportional to the quantity of bottles sold as per the equation.

Assume if the number of people going to gym increase from 100 to 200, then the equation becomes

Q = 12.5 * 1/ (3)^1.1 * 6^2.1 * 5 ^ 1.3 * 1/(200)^1.8

= 0.09

It is clear that when number of people going to gym increases the quantity of bottle sold is reducing.

d) Assume my role number ends with 5, then as per question, the income of consumers increase by 5%. So from $500, the consumer income increased to $525, then the equation becomes

Q = 12.5 * 1/ (3)^1.1 * 6^2.1 * 5.25 ^ 1.3 * 1/(100)^1.8

= 12.5 * 0.299 * 43.06 * 8.63 * 0.00025

= 0.35

Hence there is increase of 0.02 in quantity of bottles sold

e) repeat of question (a) hence same answer as for question (a)

f) repeat of question (c) hence same answer as for question (c)