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

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(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 provided by:
Lokesh Jain, MSc
Education
  • BEng (Hons) , Birla Institute of Technology and Science, India
  • MSc (Hons) , Birla Institute of Technology and Science, India
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