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Calculating own price, income and cross-price elasticities

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A book publisher has the following demand function for the firm's novels (Qx):
Qx = 12,000-5,000Px + 5I + 500Pc
where Px is the price charged for the firm's novels, I is income per Capita, and Pc is the price of books from competing publishers.
Assume that the initial values of Px, I, and Pc are $5, $10,000, and $6, respectively

(A) Calculate the price elasticity and determine what effect a marginal (small) price increase from the initial price would have on total revenues?

(B) Calculate the income elasticity and evaluate how sale of the novels would change during a period of rising incomes?

(C) Calculate the cross elasticity and assess the probable impact if competing publishes raise.

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Solution Preview

(A) Calculate the price elasticity and determine what effect a marginal (small) price increase from the initial price would have on total revenues

Qx = 12,000-5,000Px + 5I + 500Pc

Put Px=$5, I=$10000 and Pc=$6
Qx =12000-5000*5+5*10000+500*6 =40000
Now dQx/dPx=-5000
Price elasticity of demand=Ed=(dQx/dPx)*(Px/Qx)=-5000*(5/40000)=-0.625

So, we find that demand is inelastic at the initial level.

We know that ...

Solution Summary

Solution describes the steps to calculate own price, income and cross-price elasticities of demand.

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Elasticity of demand

A company has the following demand function for its product.

Q=40,000-200P+500I+100Px
Where P is the price of the firm's product, I is household disposable income in thousands of $, and Px is the price of a competitor's product.

The firm charges a price of $ 100 per unit.
Estimated household income = $ 50. (in thousands of $)
The competitor's price = $ 95 per unit.

A. What is the estimated demand for the firm's product?
B. Determine the point price elasticity.
C. Determine the point income elasticity.
D. Determine the point cross price elasticity.

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