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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.

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A tutorial that explains how to calculate the Equilibrium price of a product, cross price elasticity of demand, Income elasticity of Demand and Elasticity of Demand.

The tutorial also explains how to determine the exogenous and endogenous variables in a function.

1. Suppose the market demand curve for a Product is given by Q = 250 - 5P and the market supply curve is given by Q = -50 + 25P.
1. What are the equilibrium price and quantity in this market?
2. At the market equilibrium, what is the price elasticity of demand?
3. Suppose the price in this market is $8. What is the amount of excess demand?

2. Suppose the market demand curve for a product is given by Q = 500 - 156P + 20I and the market supply curve is given by Q = -25 + 10P - 10K. Assume initially that I= 10 and K = 5.
1. What are the equilibrium price and quantity in this market?
2. What are the endogenous and exogenous variables in the equilibrium model?
3. Suppose K suddenly increases to 20. How will this affect the market equilibrium calculated in part 1?

3. Suppose demand for good A is given by Q = 500 - 10Pa + 2Pb + 0.70I where Pa is the price of Good A, Pb is the price of some other good B, and I is income. Assume that Pa is currently $10, Pb is currently $5, and I is currently $100.
1. What is the elasticity of demand for good A with respect to the price of good A at the current situation.
2. What is the cross price elasticity of the demand for good A with repect to the price of good B at the current situation?
3. What is the income elasticity of demand for good A at the current situation.

4. Suppose the market demand curve for a product is given by Q = 500 - 5P and the market supply curve is given by Q = 20P
1. What are the equilibrium price and quantity in this market?
2. Now suppose that the new demand curve for the same product is given by Q = 1000 - 5P and the market supply curve remains unchanged. What are the new equilibrium price and quantity in this market.

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