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Calculating price, income & cross price elasticity of demand

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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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Solution Preview

A. What is the estimated demand for the firm's product?

Q=40000-200P+500I+100Px
P=$100
I=$50 (in '000)
Px=$95
Q=40000-200*100+500*50+100*95=54500
Estimated demand=54500

B. Determine the point price elasticity.

Point Price Elasticity of demand =(dQ/dP)*(P/Q)
dQ/dP=-200
We have calculated in part (a), Q=54500 at ...

Solution Summary

Solution depicts the methodology to calculate price, income & cross price elasticity of demand.

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Elasticity of demand

Using the "arc formula" and the data from the table below, compute where possible the own- price and income elasticities of demand. (remember that these elasticities are computed holding all other variables constant).

Price quantity price of related goods income
$10 600 $20 $ 16,000
$10 600 $30 $22,000
$12 500 $30 $22,000
$10 500 $20 $22,000

A. Compute owner price elasticity of demand?

B. Demand is -------- (elastic, inelastic, Unitary elastic)?

C. The cross price elasticity of demand= ------- ?

d. The related good is a------- ?

E. The income elasticity =------- /

F. The good is a ...... good?

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