Question

The number of cinema tickets in Karachi and the ticket fares are regulated. The fare currently charged is Rs.500 a ticket. The Cinema Association want to obtain government's permission to raise the fare to increase their revenues
Price (Rupees per ticket)
300,400,500,600,700
Quantity demanded (tickets per month)
160,120,80,40,0
a) Calculate the price elasticity of demand for cinema tickets as the fare rises from Rs.500 to Rs.600. Is the demand price elastic or inelastic for this fare rise? b) What happens to the cinemas’ total revenue if the fare rises from Rs.500 to Rs.600? Should the ticket sellers try to obtain permission to raise the fare? c) Calculate the price elasticity of demand for cinema tickets as the fare falls from Rs.500 to Rs.400. Is the demand price elastic or inelastic for this fare decrease? Should the Cinema Association willingly accept this new price?

Answer 1

a) Price elasticity of demand $=\frac{\Delta Q}{\Delta P}\times \frac{P_{1}}{P_{2}} = \frac{40-80}{600-500}\times \frac{500}{80}= -2.5$

price elasticity $=|-2.5|=2.5 \text{\textgreater}1$

hence the demand is price elastic for this fare rise.

b) Price $=R_{s}500,$ $quantity = R_{s}80$

total revenues = $500\times 80 = R_{s}40,000$

when price $=R_{s}600, q= R_{s}40, total$ $revenue = 600\times 40 =R_{s}24000$

$40,000\text{\textgreater}24000,$ the total revenue declines due to rise in fare, so the seller should not try to obtain permission to raise the fare.

c) price elasticity of demand $=\frac{\Delta Q}{\Delta P}\times\frac{P_{1}}{P_{2}}= \frac{120-80}{400-500}\times \frac{500}{80}=-2.5$

$|-2.5|=2.5\text{\textgreater}1$ hence the demand is elastic

total revenue, $TR_{1} = P_{1}\times Q_{1}=500\times80 = Rs40,000$

$TR_{2}=P_{2}\times Q_{2}= 400\times 120 = Rs48,000, TR_{2} \text{\textgreater}TR_{1}$

The cinema association should willingly accept this new price.