The demand for tickets to an Ethiopian Camparada film is given by D(p)= 200,000-10,000p

The demand for tickets to an Ethiopian Camparada film is given by D(p)= 200,000-10,000p, where p is the price of tickets.If the price of tickets is 12 birr, calculate price elasticity of demand for tickets and draw the demand curve

The correct answer and explanation is :

Solution: Calculating Price Elasticity of Demand

The price elasticity of demand (PED) is given by the formula:

[
E_d = \frac{dD}{dp} \times \frac{p}{D}
]

Step 1: Compute ( dD/dp )

Given the demand function:

[
D(p) = 200,000 – 10,000p
]

Differentiate with respect to ( p ):

[
\frac{dD}{dp} = -10,000
]

Step 2: Compute Demand at ( p = 12 )

Substituting ( p = 12 ):

[
D(12) = 200,000 – 10,000(12) = 200,000 – 120,000 = 80,000
]

Step 3: Compute PED

Now, apply the values to the elasticity formula:

[
E_d = (-10,000) \times \frac{12}{80,000}
]

[
E_d = -1.5
]

Since elasticity is negative (due to the law of demand), we take the absolute value:

[
|E_d| = 1.5
]

Interpretation of Elasticity

The price elasticity of demand for Ethiopian Camparada film tickets is 1.5, which means demand is elastic. A 1% increase in price leads to a 1.5% decrease in demand. Since ( |E_d| > 1 ), revenue will decrease if the price increases.

Graphing the Demand Curve

The demand function is: