Question

Please show all work to receive credit for the calculation question.

Godfrey is an artist that paints live portraits for people. If he changed the price of a portrait from $30 to $36 and quantity demanded by customers changed from 300/month to 270/month,

1. What is the price elasticity of demand (e) for his product?
2. Is demand for his product price elastic or price inelastic? Give the criteria used for your conclusion.
3. At what new price (from the original price of $30) would the price elasticity of the product be unitary demand?
4. If Godfrey tested a price increase of 30% from the original price of $30, by how much percentage would quantity demanded change from the original quantity of 300/month to retain the same price elasticity as in (a) above?

Answer 1

Existing price of a portrait (P0) = $30

New price of a portrait (P1) = $36

Existing demand (D0) = 300/month

New demand after price increase (D1) = 270/month

1. Price elasticity of demand = % change in quantity demanded / % change in price

Where,

% change in quantity demanded = [(D1 - D0) / D0] x 100 = [(270 - 300) / 300] x 100 = -10%

% change in price = [(P1 - P0) / P0] x 100 = [(36 - 30) / 30] x 100 = 20%

Putting values in the formula :

Price elasticity of demand = -10% / 20% = -0.5

2. The demand for Godfrey's product is relatively price inelastic because percentage decrease in quantity demanded (10%) is less than percentage increase in price (20%) and total revenues increased as price increased, as shown below:

Revenue before price increase = P0 x D0 = $30 x 300 =$9,000

Revenue after price increase = P1 x D1 = $36 x 270 =$9,720

3. Unitary Demand: occurs when the price elasticity of demand is equal to negative one (-1)

: -1 = % change in quantity demanded / % change in price

: -1 = -10% / {[(P1 - 30) / 30] x 100}

By solving above equation, we get P1 = $33

Hence, at $33, the price elasticity of the product will be unitary demand.

4. New price (P1) = 30 x 130% = $39 or 30% increase

Elasticity in (a) = -0.5

: -0.5 = % change in quantity demanded / % change in price

: -0.5 = {[(D1 - 300) / 300] x 100} / 30%

By solving above equation, we get D1 = 255

% change in quantity = [(255 - 300) / 300] x 100 = -15%

Hence, quantity demanded need to change by -15% from the original quantity of 300/month to retain the same price elasticity as in (a)