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Calculating price and advertising elasticity values

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General Cereals is using a regression model to estimate the demand for Tweetie Sweeties, a whistle-shaped, sugar-coated breakfast cereal for children. The following (multiplicative exponential) demand function is being used:

QD = 6,280P-2.15A1.05N3.70
where
QP=quantity demanded in 10 oz. boxes
P =price per box in dollars
A =advertising expenditures on daytime television, in dollars
N =proportion of the population under 12 years old

a. Determine the point price elasticity of demand for Tweetie Sweeties.
b. Determine the advertising elasticity of demand.
c. What interpretation would you give to the exponent of N?

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Solution Preview

a. Determine the point price elasticity of demand for Tweetie Sweeties.

QD= 6,280*P^(-2.15)*A^1.05*N^3.70

Differentiate with respect to P, we get
dQD/dP=-2.25*6280*P^(-2.15-1)*A^1.05*N^3.70
=-2.25*6280*P^(-2.15) ...

Solution Summary

Solution depicts the steps to calculate the price elasticity and advertising elasticity of demand in the given case.

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Quantitative analysis

1. The demand curve for a product is given by Qdx =1,000 - 2pPx +.02Pz where Pz = $400.

a. What is the own price elasticity of demand Px = $154? Is demanded elastic or inelastic at this price? What would happen to the firm's revenue if it decided to charge a price below $154?
b. What is the own price elasticity of demand Px = $354? Is demanded elastic or inelastic at this price? What would happen to the firm's revenue if it decided to charge a price below $354?
c. what is the cross-price elasticity of demand between good X and good Z when Px = $154? Are goods X and Z substitutes or compliments?

2. Suppose the demand function for a firm's product is given by
In Qdx =3-0.5 In Px - 2.5 In Py+In M+2 In A
Where
Px = $10
Py = $4
M = $20,000, and
A =$250
a. Determine the own price elasticity of demand, and state whether demand is elastic, inelastic, or unitary elastic.
b. Determine the cross-price elasticity of demand between good X and good Y, and state whether these two are substitutes or complements.
c. Determine the income elasticity of demand, and state whether good X is a normal or inferior good.
d. Determine the own advertising elasticity of demand.

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