Final answer:
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)