Final answer:
The Elasticity of Demand for the given demand function D(p) = 325/p at a price of $68 is calculated using the formula for price elasticity of demand and results in an elasticity of -1, indicating a unitary elastic demand.
Step-by-step explanation:
To find the Elasticity of Demand at a price of $68 for the demand function D(p) = 325/p, we first need to understand that the price elasticity of demand measures how much the quantity demanded of a good responds to a change in the price of that good. It's calculated as the percentage change in quantity demanded divided by the percentage change in price.
The formula for the price elasticity of demand (Ed) is:
Ed = (dQ/dP) · (P/Q)
Where:
For the given demand function:
The derivative of Q with respect to P (dQ/dP) is:
dQ/dP = -325/P2
Now, to find the elasticity at P = $68:
Q at P = $68 is 325/68.
Plug these values into the elasticity formula:
Ed = (-325/682) · (68/(325/68))
Simplify the expression to calculate Ed:
Ed = (-325/4624) · (68 · 68/325)
This simplifies further to:
Ed = -1
Thus, the elasticity of demand at a price of $68 is -1, indicating a unitary elastic demand where the percentage change in quantity demanded is equal to the percentage change in price.