Question

A demand function for Lenovo model SL computer is

Q=200-20P+0.04A+0.5Y

Where P = price of Lenovo, A = total advertising expenditure for Lenovo and Y = disposable income of the consumers. Assume that A = RM10,000 and Y=RM40,000.

a) Derive demand equation for Lenovo. Calculate the current quantity demanded for Lenovo if its price is RM650.

b) If the sellers would like to increase their sales revenue, what is your suggestion pertaining to the price? Give your reason.

c) Should Lenovo spend more on advertising expenditure to increase sales quantity? Give your reason.

d) Would you advise Lenovo to target their sales of model SL to high income earners? Support your answer with appropriate calculation and give reason.

e) How many units should Lenovo sell it model SL to gain maximum total revenue. Suggest the price that Lenovo should set for model SL.

Answer 1

A.

Q=200-20P+0.04A+0.5Y

So, demand equation is as follows:

Q=200-20P+0.04*10000+0.5*40000

Q = 20600 - 20P            ( it is a demand equation)

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If P =  RM650

Then,

Q = 20600-20*650

Q = 7600 units         ( it is quantity demanded at the price level of RM650).

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B.

Q=200-20P+0.04A+0.5Y  --------- (1)

The differentiation of above equation with respect to P gives dQ/dP

dQ/dP = -20

At price of RM650 and quantity demanded of 7600 units

Price elasticity of demand = (dQ/dP)*(P/Q)

Price elasticity of demand =  (-20)*(650/7600)

Price elasticity of demand = -1.71

Since there is a relatively elastic demand as value of price elasticity if demand is more than 1 in absolute terms, then  seller will decrease the price to increase the sales revenue. Here, quantity demanded will increase, more than the decrease in price. It will help increase in sales revenue.

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C.

Q=200-20P+0.04A+0.5Y

dQ/dA = .04 by differentiation of above equation,

So,

Advertising elasticity of demand = (dQ/dA)*(A/Q)

Advertising elasticity of demand = (.04)*(10000/7600)

Advertising elasticity of demand = .05

in the given scenario, Advertising elasticity of demand is inelastic as its value is less than 1. Hence, increase in advertising, is not going to help much to the seller. So, seller should not increase spending on advertising to increase sales quantity.

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D.

Q=200-20P+0.04A+0.5Y

Differentiation of above equation with respect to Y,

dQ/dY = .5

So,

Income elasticity of demand = (dQ/dY)*(Y/Q)

Income elasticity of demand = (.5)*(40000/7600)

Income elasticity of demand = 2.63

Here, it can be seen that Income elasticity of demand is 2.63 to be more than 1. It means that this product is more  suitable for the high income earners. Further,Income elasticity of demand  of 2.63 ( greater than 1) , means that this computer model is luxury product. Hence, Lenovo should target high income earners who can buy this computer model.

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E.

Q = 20600 - 20P  

20P = 20600 - Q

P = 20600/20 - Q/20

P = 1030-Q/20          ---- (1)

Multiplying equation (1) by Q and differentiation will give marginal revenue (MR).

P*Q = R =  1030*Q - Q^2/20

MR = 1030 - 2*Q/20

MR = 1030 - Q/10

For revenue maximization,

MR = 0

1030 - Q/10 = 0

Q = 1030*10

Q = 10300 units        ( it is the output to be produced)

Price = 1030 - 10300/20

Price = RM 515           ( it is the price to be charged)