At the price of $100, tourists demand 237 airplane tickets.At the same price, business travelers demand 247.At the price $110, tourists demand 127 tickets and business travelers demand 127.Assuming that the demand curves of business travelers and tourists are both linear over this price range, what is the price elasticity of demand at the price $100?
A)-4.75
B)-5.23
C)-23
D)-0.05
E)none of the above.

Question

Quizplus · Accepted Answer

We can calculate the price elasticity of demand at the price $100 using the formula:
$$
E_{p}=\frac{\%	ext{ change in quantity demanded}}{\%	ext{ change in price}}
$$
First, we need to calculate the demand slope for tourists and business travelers separately. We can use the two points given for each group to calculate the slopes:
For tourists:
$$
	ext{slope}=\frac{127-237}{110-100}=-11
$$
For business travelers:
$$
	ext{slope}=\frac{127-247}{110-100}=-12
$$
Next, we can use the midpoint formula to calculate the average quantity and price for each group:
For tourists:
$$
	ext{average price}=\frac{100+110}{2}=105
$$
$$
	ext{average quantity}=\frac{127+237}{2}=182
$$
For business travelers:
$$
	ext{average price}=\frac{100+110}{2}=105
$$
$$
	ext{average quantity}=\frac{127+247}{2}=187
$$
Now, we can use these quantities to calculate the price elasticity of demand for each group at the price $100$:
For tourists:
$$
E_{p}=\frac{\%	ext{ change in quantity demanded}}{\%	ext{ change in price}}=\frac{\frac{237-182}{182}}{\frac{100-105}{105}}=-4.75
$$
For business travelers:
$$
E_{p}=\frac{\%	ext{ change in quantity demanded}}{\%	ext{ change in price}}=\frac{\frac{247-187}{187}}{\frac{100-105}{105}}=-5.23
$$
We take the average of these two elasticities:
$$
	ext{Average }E_{p}=\frac{-4.75-5.23}{2}=-4.99\approx -5
$$
Since the demand curves for both groups are linear, the price elasticity of demand is constant over this price range. Therefore, the price elasticity of demand at the price $100$ is approximately equal to the average price elasticity of demand for both groups at this price. The closest choice to this value is answer choice A, which is $-4.75$.

At the Price of $100, Tourists Demand 237 Airplane Tickets