Final answer:
To find the elasticity of demand at a given price, we need to determine the percentage change in quantity demanded when the price changes by a small amount. In this case, the demand function is q = 400 - 5x, where x is the price. We are given x = 42. To find the quantity demanded at this price, substitute x = 42 into the demand function: q = 400 - 5(42) = 400 - 210 = 190. To find the percentage change in quantity demanded, we can use the formula: % change in quantity demanded = [(new quantity - old quantity) / old quantity] x 100%
Step-by-step explanation:
To find the elasticity of demand at a given price, we need to determine the percentage change in quantity demanded when the price changes by a small amount. The formula for elasticity of demand is:
Elasticity of Demand = (% change in quantity demanded) / (% change in price)
In this case, the demand function is q = 400 - 5x, where x is the price. We are given x = 42. To find the quantity demanded at this price, substitute x = 42 into the demand function: q = 400 - 5(42) = 400 - 210 = 190.
To find the percentage change in quantity demanded, we can use the formula:
% change in quantity demanded = [(new quantity - old quantity) / old quantity] x 100%
Substituting the values, we get: % change in quantity demanded = [(190 - 240) / 240] x 100% = -20.83%.
Now, we need to find the percentage change in price. Since x = 42, we can calculate the price by substituting x = 42 into the demand function: P = 42.
% change in price = [(new price - old price) / old price] x 100%
Substituting the values, we get: % change in price = [(42 - 42) / 42] x 100% = 0%.
Using the formula for elasticity of demand, we can now calculate the elasticity:
Elasticity of Demand = (% change in quantity demanded) / (% change in price) = (-20.83%) / (0%)
Since the denominator is 0, the elasticity is undefined.
Therefore, we cannot determine whether the demand is elastic, inelastic, or unit elastic at this given price.