Question

Suppose the weekly demand function for a product is given by

rho = 100e⁻⁰;²⁵ᑫ
where rho is the price in dollars and q is the number of tons demanded.
(a) What is the elasticity of demand when the price is $36.79 and the quantity demanded is 42 (Round your answer to two decimal places.) 6.25 X

Answer 1

To calculate the elasticity of demand, we can use the formula: Elasticity of Demand = (% change in quantity demanded) / (% change in price). In this case, we have the price (rho) and the demand function (q) given. To find the elasticity of demand when the price is $36.79 and the quantity demanded is 42, we need to calculate the percentage change in quantity demanded and the percentage change in price.

Step-by-step explanation:

The elasticity of demand measures the responsiveness of the quantity demanded to changes in price. To calculate the elasticity of demand, we can use the formula:

Elasticity of Demand = (% change in quantity demanded) / (% change in price)

In this case, we have the price (rho) and the demand function (q) given. To find the elasticity of demand when the price is $36.79 and the quantity demanded is 42, we need to calculate the percentage change in quantity demanded and the percentage change in price.

Let's calculate the percentage change in quantity demanded:

% change in quantity demanded = [(new quantity demanded - old quantity demanded) / old quantity demanded] * 100

new quantity demanded = 42

old quantity demanded = 42 - 1

% change in quantity demanded = [(42 - (42 - 1)) / (42 - 1)] * 100

Now, let's calculate the percentage change in price:

% change in price = [(new price - old price) / old price] * 100

new price = 36.79

old price = 36.79 - 1

% change in price = [(36.79 - (36.79 - 1)) / (36.79 - 1)] * 100

Finally, we can calculate the elasticity of demand:

Elasticity of Demand = (% change in quantity demanded) / (% change in price)