CASE STUDY FOR DEMAND FORECASTING

# The research department of the Mohan Corn Flakes Corporation (MCFC) estimated the following regression for the demand of the corn flakes it sells:

Q_x = 1.0 – 2.0 P_x + 1.5 I + 0.8 P_y – 3.0P_M + 1.0A

Where,

Q_x = Sales of MCFC corn flakes, in millions of 10-ounce boxes per year

P_x = The price of MCFC corn flakes, in dollars per 10-ounce box

I = Personal disposable income, in trillions of dollars per year

P_y =price of competitive brand of cornflakes, in dollars per 10-ounce box

P_M = price of milk, in dollars per quart

A = Advertising expenditures of MCFC cornflakes, in hundreds of thousands of dollar per year

This year, P_x = $ 2    I = $4    P_y = $ 2.50   P_M = $ 1 and A = $2

a ) Calculate the sales of MCFC cornflakes this year.

b ) Calculate the elasticity of sales with respect to each variables in the demand function.

c ) Estimate the level of sales next year if MCFC reduces P_x by 10 percent, increases advertising by 20 percent, I rise by 5 percent, P_y is reduced by 10 percent and P_M remains unchanged.

d) By how much should MCFC change its advertising if it wants its sales to be 30 percent higher than this year?

a ) Calculation of the sales of MCFC cornflakes this year:

We have been given the following estimated equation for sales:

Q_x = 1.0 – 2.0 P_x + 1.5 I + 0.8 P_y – 3.0P_M + 1.0A

Where,

• Q_x = Sales of MCFC corn flakes, in millions of 10-ounce boxes per year
• P_x = The price of MCFC corn flakes, in dollars per 10-ounce box
• I = Personal disposable income, in trillions of dollars per year
• P_y =price of competitive brand of cornflakes, in dollars per 10-ounce box
• P_M = price of milk, in dollars per quart
• A = Advertising expenditures of MCFC cornflakes, in hundreds of thousands of dollar per year

Substituting the given values in the above equation as:

• P_x = $ 2  
• I = $4   
• P_y = $ 2.50   
• P_M = $ 1 and 
• A = $2 

We get,

Q_x = 1.0 – 2.0 x 2 + 1.5 x 4 + 0.82 X 2.50 – 3.0 x 1 + 1.0 x 2 = 4

Thus, the MCFC would sell 4 million boxes of its corn flakes this year.

b ) Computation of the elasticity of sales with respect to each variables in the demand function:

To solve this, follow the following steps :

• First calculate the first order derivative of following equation Q_x = 1.0 – 2.0 P_x + 1.5 I + 0.8 P_y – 3.0P_M + 1.0A  with respect to particular elasticity . For example, If price elasticity (E_p ) is to be found than find out the first order derivative with respect to P_x  by treating other variables as constant. 

• Then, compute elasticity accordingly.

The elasticity of demand for MCFC corn flakes with respect to its price, personal disposal income, the price of competitive corn flakes, the price of milk and advertising are:

E_p = (dq_x /dp_x) x (p_x / q_x ) =  - 2 x (2 / 4) = -1 

E_I = (dq_x /dI) x (I / q_x ) = 1.5 x (4 /4) = 1.5

E_XY = (dq_x /dp_y) x (p_y / q_x ) = 0.8 x (2.5 / 4 ) = 0.5

E_XM = (dq_x /dp_M) x (p_M / q_x ) = - 3.0 x (1 / 4) = - 0.75

E_A = (dq_x /dA) x (A / q_x ) = 1.0 x (2 / 4 ) = 0.5 

c ) Estimation of the level of sales next year if MCFC reduces P_x by 10 percent, increases advertising by 20 percent, I rise by 5 percent, P_y is reduced by 10 percent and P_M remains unchanged:

If next year the MCFC reduces P_x by 10 percent, increases advertising by 20 percent, I rise by 5 percent, P_y is reduced by 10 percent and P_M remains unchanged then,

the sales of MCFC corn flakes in the next year ( Q_x ^I ) would be :

Q_x ^I = Q_X + Q_X (∆ P_X / P_X ) X E_p  + Q_X (∆ I / I) X E_I + Q_X (∆ P_Y / P_Y ) X E_XY + Q_X (∆ P_M / P_M ) X E_XM  + Q_X (∆ A / A ) X E_A     

=  4 + 4 (-10% ) X (-1) + 4 (5%) X 1.5 + 4 (-10 %) X 0.5 + 4 ( 0 % ) X (– 0.75)  + 4 (20%) X 0.5

On solving this we get,

Q_x ^I = 4.9

Therefore, the MCFC would sell 4.9 million boxes of its corn flakes in next year.

d ) Computation of changes in advertising that MCFC should change if it wants its sales to be 30 percent higher than this year:

To know that - by how much should MCFC change its advertising if it wants its sales to be 30 percent higher than this year, It must sell 5.2 ( i.e  4 + 30 % x 4 ) million  boxes of corn flakes. This is 0.3 (i. e 5.2 - 4.9 ) million greater than forecast. 

To determine the additional increase in advertisement expenditure, we set up following equation:

Q_x X (Z) X ( E_A)  =  0.3

where, 

• Q_x = 4 

• Z = Additional percentage increase in advertising

• E_A = Elasticity of Advertisement

So, we get 

4 X ( Z) x (0.5) = 0.3 

or, Z x 2 = 0.3

or, Z = 0.15

The additional percentage increase in advertising is Z i.e 0.15

Therefore, 0.15 percent additional increase in advertisement expenditures over this year’s level of $ 200,000 is $ 30,000 ( i.e  $ 200,000 x 0.15 % ).

Note : 

• The above case study was asked to the MBS post graduates by Faculty of Management, Tribhuvan University.
• The problem is taken out from the book (Managerial Economics ) written by Dominick Salvatore.

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