Question

1. (20 total points) Suppose the demand for a product is given by QD = 50 – (1/2)P.a) (10 points) Calculate the Price Elasticity of Demand when the price is $40.b) (5 points) What price should the firm charge if it wants to maximize its revenue?c) (5 points) Over what price range is demand elastic?

Answer 1

Answer:

a) PED = 0.5

b) Total revenue is maximized at $50

c) PED is elastic beyond price $50

Explanation:

a) QD = 50 - (1/2)P

Price = $40

When substituted,

QD = 50 - (0.5 x 40)

QD = 30 units

Price elasticity of demand is the responsiveness of quantity demanded to a change in price. It is calculated by dividing the % change in quantity demanded by a % change in price. For this we require the quantity demanded for two different prices.

As an example, at price $30

QD = 50 - 0.5 x 30 = 35 units

Assume that price reduced from $40 to $30

% change in QD = Change in Qd / original Qd x 100

= (30-35)/30 x 100 = - 16.67%

% change in price = Change in price / original price x 100

= (40-30) / 40 x 100 = 33.33%

PED = 16.67 / 33.33 = 0.5

b) A PED that is less than 1 suggests that it is inelastic. This means that the percentage change in quantity demanded is lower than the percentage change in price. When PED is inelastic, firms can maximize its revenue by charging higher prices because a % change in quantity demanded is less than a % change in price.

For example, at price $30 sales would be = $30 x 35 = $1050

At price $40, sales would be = $40 x 30 = $1200

At price $50, sales would be = $50 x 25 = $1250

At price $60, sales would be = $60 x 20 = $1200

The price charged should be $50, since after this, TR starts to gradually decrease.For example, at price $51, sales is $51 x 24.5 = $1249.5

c) PED is price elastic if it is higher than 1. This means that the percentage change in quantity demanded is higher than the percentage change in price. This is common for products that are non-essentials or have a lot of substitutes.

When price changes from $50 to $51, quantity demanded falls from  25 units to 24.5 units.

Hence PED = [(25-24.5)/25] / [(50-51) /50)] = 1

PED is elastic after $50 which also explains why total revenue begins to fall as price increases beyond $50.