a. The price elasticity of demand for tickets -1.50.
b. See the attached pdf file for the demand curve.
Explanation:
a. Calculate price elasticity of demand for tickets
Given;
p = 12
D(p) = D = 200,000 - 10,000p (1)
Substituting p = 12 into equation (1) to find the value of D, we have:
D = 200,000 – (10,000 * 12) = 200,000 - 120,000 = 80,000
Differentiating equation (1) with respect to p, we have:
dD/dp = -10,000
To calculate elasticity of demand, we use the formula for calculating the elasticity of demand as follows:
E = Elasticity of demand = (p / D) * (dD/dp) (2)
Substituting the relevant values into equation (2), we have:
E = (12 / 80,000) * (-10,000) = 0.00015 * (-10,000) = -1.50
Therefore, the price elasticity of demand for tickets -1.50.
Note: Since the absolute value of E i.e. |-1.50| is greater one, it therefore implies that the demand for tickets is elastic.
b. Draw the demand curve.
Note: See the attached pdf file for the demand curve
To draw the demand curve, we need to obtain the new price and the new quantity demanded as follows:
We start by assuming that the price of tickets decreases from 12 birr to 11 birr. Therefore, the percentage change in price is obtained as follows:
Percentage change in price = ((New price – Old price) / Old price) * 100 = ((11 - 12) / 12) * 100 = -8.33%
To calculate the percentage change in demand for tickets, we use the following formula for calculating the elasticity of demand:
E = Percentage change in demand / Percentage change in price (3)
Since from part a above, E = -1.50
And, as calculated here, Percentage change in price = -8.33%, or 0.0833
Substituting the values into equation (3) and solve for Percentage change in demand, we have:
-1.50 = Percentage change in quantity demanded / -0.0833
Percentage change in quantity demanded = (-0.0833) * (-1.50) = 0.12495, or 12.495%
Approximating to 2 decimal places, we have:
Percentage change in quantity demanded = 12.50%
Since the answer is positive, this implies that the demand for tickets D increases by 12.50% when price for tickets decreases by 8.33%. This confirms that the demand for tickets is truly elastic as the percentage change in demand for ticket of 12.50% is greater than the percentage change in price of -8.33%.
The new D can therefore be calculated as follows:
New D = D + (D * Percentage change in demand demanded) = 80,000 + (80,000 * 12.50%) = 90,000
From the calculations above, we have:
Initial price = 12 birr
New price = 11 birr
Initial quantity = D = 80,000
New quantity = New D = 90,000
The values above are then used to draw the demand curve in the attached pdf file.
Since there is a negative relationship between price and quantity demanded in economics, the curve in the attached excel file shows the effect of a decrease in the price of tickets from 12 birr to 11birr (as shown by the arrow) on the quantity demanded for tickets that increases from 80,000 to 90,000 (as shown by the arrow).
Since the demand for tickets is elastic as obtained in part a above, it implies that the percentage change in the quantity demanded for ticket is greater than the percentage change in the price of tickets. This makes the demand curve to be flatter as shown in the attached pdf file
From the demand curve in the attached pdf file; the demand curve for tickets is flatter, and the gap between the initial quantity demanded 80,000 and the new quantity demanded 90,000 is wider than the gap between the initial price 12 birr and the new price 11 birr. This indicated that the percentage change in the quantity demanded of 12.50% which is an increase from 80,000 to 90,000 is higher than the percentage n the price for tickets of 8.33% which is a decrease from 12 birr to 11 birr.
