Answer:
a. The elasticity of demand for tickets is calculated to be -1.50.
b. Please refer to the attached PDF for the demand curve.
Explanation:
a. To determine the elasticity of demand for tickets
Given;
p = 12
D(p) = D = 200,000 - 10,000p .................................................................... (1)
By substituting p = 12 into equation (1) to solve for D:
D = 200,000 – (10,000 * 12) = 200,000 - 120,000 = 80,000
Taking the derivative of equation (1) with respect to p yields:
dD/dp = -10,000
To compute the elasticity of demand, the following formula is used:
E = Elasticity of demand = (p / D) * (dD/dp) ................... (2)
By substituting the pertinent values into equation (2):
E = (12 / 80,000) * (-10,000) = 0.00015 * (-10,000) = -1.50
Thus, the price elasticity of demand for tickets is -1.50.
Note: Since the absolute value of E, |-1.50|, exceeds one, this indicates that the demand for tickets is elastic.
b. To create the demand curve:
Note: Please reference the attached PDF file for the demand curve.
To illustrate the demand curve, we need the new price and quantity demanded as follows:
Assuming a price decrease from 12 birr to 11 birr. Thus, the percentage change in price becomes:
Percentage change in price = ((New price – Old price) / Old price) * 100 = ((11 - 12) / 12) * 100 = -8.33%
To determine the percentage change in demand for tickets, we apply the following elasticity calculation formula:
E = Percentage change in demand / Percentage change in price ............. (3)
Utilizing the previously calculated E = -1.50 from part a, and the percentage change in price of -8.33%, or 0.0833:
Inserting these figures into equation (3) allows us to solve for the percentage change in demand:
-1.50 = Percentage change in quantity demanded / -0.0833
Thus, the percentage change in quantity demanded is calculated as (-0.0833) * (-1.50) = 0.12495, or 12.495%
Rounding to two decimal places leads to:
Percentage change in quantity demanded = 12.50%
The positive outcome implies that ticket demand increases by 12.50% when the ticket price drops by 8.33%. This reaffirms that ticket demand is elastic, as the demand change of 12.50% surpasses the price change of -8.33%.
To compute the new D:
New D = D + (D * Percentage change in demand) = 80,000 + (80,000 * 12.50%) = 90,000
From the preceding calculations:
Initial price = 12 birr
New price = 11 birr
Initial quantity = D = 80,000
New quantity = New D = 90,000
These values are utilized to illustrate the demand curve in the attached PDF.
Due to the inverse relationship between price and quantity demanded in economics, the curve in the attached excel file demonstrates the outcome of reducing ticket prices from 12 birr to 11 birr (as indicated by the arrow) resulting in an increase in the quantity demanded from 80,000 to 90,000 (as shown by the arrow).
Given that the demand for tickets is elastic as established in part a, this means that the percent change in ticket demand exceeds the percent change in ticket prices. Consequently, this results in a flatter demand curve as depicted in the presented PDF file.
The demand curve from the PDF clearly shows a flatter nature, with a broader gap between the initial demand of 80,000 and the revised demand of 90,000 compared to the gap between the original price of 12 birr and the new price of 11 birr. This clearly indicates that the 12.50% increase in ticket demand from 80,000 to 90,000 is greater than the 8.33% reduction in ticket prices from 12 birr to 11 birr.
