# Calculating Quantity Demanded and Determining Demand Curve

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.

https://brainmass.com/economics/macroeconomics/calculating-quantity-demanded-and-determining-demand-curve-134168

#### 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.

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.