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Calculating Quantity Demanded and Determining Demand Curve

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Gurgling Springs, Inc., is a bottler of natural spring, Inc. is a bottler of natural springs water distributed throughout the New England states. Five-gallon containers of GSI spring water are regionally promoted and distributed through grocery chains. Operating experience during the past year suggests the following demand function for its spring water.

Q = 250 - 100P + 0.0001Pop + 0.0031 + 0.003A

Where Q is quantity in thousands of five-gallon containers, P is price (\$), Popis population, I is disposable income per capita (\$), and A is advertising expenditures (\$).

A. Determine the demand curve faced by CPI in a typical market where P=\$4, Pop=4,000,000 persons, I=\$50,000 and A=\$400,000. Show the demand curve with quantity expressed as a function of price, and price expressed as function of quantity.

B. Calculate the quantity demanded at prices of \$5, \$4 and \$3.
C. Calculate the prices necessary to sell 1,250, 1,500 and 1,750 thousands of five gallon containers.

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Solution Preview

Q = 250 - 100P + 0.0001Pop + 0.003I + 0.003A

If you plug the known factors into the equation, you can find the quantity demanded in the typical market.

Q = 250 - 100(4) + 0.0001(4,000,000) + 0.003(50,000) + 0.003(400,000) = 1600

Q = 1600 thousand five-gallon containers.

To simplify this equation for varying price, we can simply combine all the factors except ...

Solution Summary

Quantity demanded is assessed and the calculation process is explained in an excel attachment with graphs.

\$2.49