# Imagine that the basketball team at USC charges $12 per seat for each home match. When the price stay at $12, 12,000 supporters show up on average. An analyst estimated that raising the price by $3 would imply a reduction of ticket sold to 11,053. Determine the price elasticity of demand at $12? Given a linear demand, determine its functional form (e.g. use the elasticity and its relation with the parameters of the demand curve, Q = a – b p, to write quantity as a function of price).

Imagine that the basketball team at USC charges $12 per seat for each home match. When the price stay at $12, 12,000 supporters show up on average. An analyst estimated that raising the price by $3 would imply a reduction of ticket sold to 11,053. Determine the price elasticity of demand at $12? Given a linear demand, determine its functional form (e.g. use the elasticity and its relation with the parameters of the demand curve, Q = a – b p, to write quantity as a function of price).

Answer:

**Price elasticity of demand** measures the responsiveness of demand after a change in a product’s own price.

Price elasticity of demand (PED) shows the relationship between price and quantity demanded and provides a precise calculation of the effect of a change in price on quantity demanded.

P**ED = % change in quantity demand / % change in price**

In this example we find % change in Qunatity demand and % change in price

% change in quantity demand = P1 – P2 / P1 * 100

P1 = price without changes = 12$

P2= Price with changes = 15$

=12-15/12 *100 = -25%

% change in quantity demand = Q1-Q2/Q1 *100

Q1= quantity without changes= 12000

Q2= quantity with changes = 11053.

= 12000-11053/12000*100= 7.89

PED = -25 / 7.89 = – 3.168

A **demand equation** or **demand function** expresses demand q (the number of items demanded) as a function of the unit price p (the price per item). A **linear demand function** has the form

Demand might be represented by a linear demand function such as

Q(d) = a – bP

Q(d) represents the demand for a good

P represents the price of that good.

a represent vertical intercept

b represent slop

Economists might consider how sensitive demand is to a change in price.

This is a typical downward sloping demand curve which says that demand declines as price rises. |

This is a special case of a horizontal demand curve which says at any price above P* demand drops to zero. An example might be a competitor’s product which is considered just as good. |

This is a special case of a vertical demand curve which says that regardless of the price quantity demanded is the same. An example might be medicine as long as the price does not exceed what the consumer can afford. |

We can actually summarize where a linear demand will

be…

(1) Elastic, when |ε|>1

(2) Unit Elastic, when |ε|=1

(3) Inelastic, when |ε|<1

Qd= a -bp

a is coefficient when price = 0

slope = -b elasiticity slope of the curve

if slope -b is increase elasticity also increase.

b = Q2 – Q1 / P2 – P1 = 11053-12000 / 15 – 12 = -315.67

Q = a – Q P

12000 = a – 12000(3) = 12000 = a – 36000

a = 48000

Qd = 48000 – 315.67(3)

= 48000 – 944.01 = 47055.99