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Managerial decisions based on price and demand elasticity.

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Estimation of sales from multiple regression models – figuring out the own price elasticity of demand and cross price elasticity of demand – the relevant business decision to increase the total revenue.
Your technical staff estimates the model of sales (units, not revenue) for your product presented in Lecture 2:
Sales = 28.0-4.29.price + 0.85.pop in region + 0.25.per cap income + 1.09.% pop<18+0.85.ad
The current values of the variables are:

  units Current value
price $ 12
rival’s price $ 12.25
population in region 1000 10
per capita income $1,000 22.6
% of population <18 years # 15
advertising $1,000 20

a. What is the formula for the demand curve, taking into account the values of the variables? The inverse demand curve?
b. What is your price elasticity of demand? If you raise your price, will your total revenue rise of fall?
c. If your rival lowers their price to match yours, how does this affect your demand curve? How does it shift graphically?
d. What is your product’s cross-price elasticity of demand? Does its magnitude make sense, compared to your own price elasticity? What is your product’s elasticity of demand with respect to advertising expenditures?
e. What is consumer surplus from your product? Might this represent a business opportunity for your firm? Explain intuitively.
f. What kinds of business decisions could be usefully aided by the kind of information contained in the estimated demand curve and data above?

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