# Price elasticity of demand

The South Beach Cafe recently reduced appetizer prices from $12 to $10 for afternoon "early bird" customers and enjoyed a resulting increase in sales from 90 to 150 orders per day. Beverage sales also increased from 300 to 600 units per day.

A. Calculate the arc price elasticity of demand for appetizers.

B. Calculate the arc cross-price elasticity of demand between beverage sales and appetizer prices.

C. Holding all else equal, would you expect an additional appetizer price decrease to $8 to cause both appetizer and beverage revenues to rise? Explain.

© BrainMass Inc. brainmass.com October 25, 2018, 1:44 am ad1c9bdddfhttps://brainmass.com/economics/elasticity/273070

#### Solution Preview

Price elasticity of demand is defined to be

Price Elasticity = (% Change in Quantity) / (% Change in Price)

In this case the price changed from $12 to $10. So the change is $2. Depending on how you define percentage change the numbers we get will be different. I will use the following formula:

% Change = (New Value - Old Value) / (Average of ...

#### Solution Summary

Price elasticity of demand is examined.

Economics

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