Question

Exercise #2 At the present level of consumption, 4,000 movie tickets, and at the current price $5 per ticket, the price elasticity of demand for movie ticket is 1. Using the midpoint method, calculate the percentage by which the owners of movie theaters must reduce the price in order to sell 5,000 tickets.

Answer 1

The price elasticity of demand is defined as the sensitivity of quantity demanded due to the change in price of the good. Mathematically it is expressed as

ΔΟ E = AP

Applying the mid point method

Q2-Q1 x 1 02+04 x 100 BFR x 100

Simplifying the above equation we get

E - (Q2 – Qı)(P2 + Pi) (Q2 +Qi)(P2 - P1)

Given, Q1 = 4,000, P1 = $ 5

Q2 = 5,000 and

elasticity = 1 (remember it is always a negative number)

Plug in the given values in the elasticity equation we get

-1= (5,000 – 4,000) P2+5) (5,000+ 4,000) (P2-5)

= -1 = 1,000(P2 + 5) 9,000(P2 - 5)

= -1= P2 +5 9P2 – 45

P2+5= -1 x (9P2 – 45)

P +5= -9P, + 45

P + 9P, = 45 – 5

10P, = 40

SP2 =

P, = $ 4

Thus, in order to increase sales to 5,000 tickets the owner must charge a price of $ 4 per ticket.

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