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# Price Elasticity of demand and revenue maximization

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Problems:

1)For each of the following cases, calculate the arc price elasticity of demand and state whether demand is elastic, inelastic or unit elastic

a) when the price of milk increases from \$2.25 to \$2.50 per gallon, the quantity demanded falls from 100 gallons to 90 gallons
b) when price of paper book falls from \$7.00 to \$6.50, quantity demanded rises from 100 to 150
c) when the rent on apartments rises from \$500 to \$550, the quantity demanded decreases from 1000 to 950 2)

2. For each of the following cases, calculate the point price elasticity of demand and state whether demand is elastic, inelastic or unit elastic. The demand curve is given by
Qd=5000-50Px

a) The price of product is \$50
b) The price of product is \$75
c) The price of product is \$25

3. For each of the following cases, what is the expected impact on the total revenue of the firm. Explain your answer
a) Price elasticity of the demand is known to be -0.5, and the firm raises the price by 10%
b) Price elasticity of the demand is known to be -2.5, and the firm lowers the prices by 5%
c) Price elasticity of the demand is known to be 1, and the firm raises the prices by 1%
d) Price elasticity of the demand is known to be 0, and the firm raises the prices by 50%

4.The demand curve is given by
Qd=500-2Px
a) What is the total revenue function
b) The marginal revenue function is MR=250-Q
Graph the total revenue function, Demand curve and marginal revenue function c) c) At what price is revenue is maximised, What is the revnue at that point
d) Identify the elastic and inelastic portions of demand curve

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#### Solution Preview

Please refer attached file for complete solutions. Work done with the help of equation writer, and graphs may not print here.

Solutions:

1)
For each of the following cases, calculate the arc price elasticity of demand and state whether demand is elastic, inelastic or unit elastic

a) when the price of milk increases from \$2.25 to \$2.50 per gallon, the quantity demanded falls from 100 gallons to 90 gallons
Q1=100 Q2=90
P1=2.25 P2=2.5

Ep =

Where Ep = Coefficient of price elasticity
Q1 = original quantity demanded
Q2 = new quantity demanded
P1 = Original Price
P2 = New Price
Plug in the values in formula above and get
Ep=-1.00
Absolute value of elasticity is 1, arc price elasticity of demand is unit elastic

b) when price of paper book falls from \$7.00 to \$6.50, quantity demanded rises from 100 to 150
Q1=100 Q2=150
P1=7 P2=6.5

Ep =

Where Ep = Coefficient of price elasticity
Q1 = original quantity demanded
Q2 = new quantity demanded
P1 = Original Price
P2 = New Price
Plug in the values in formula above and get
Ep=-5.40
Absolute value of elasticity is more than 1, arc price elasticity of ...

#### Solution Summary

Solution describes the steps for calculting arc and pint elasticities of demand. It also expains the relation between total revenue and elasticity of demand. Steps for calculating revenue maximizing quantity are also demonstrated.

\$2.19