Questions: The demand function for a given product is D(p)=600-p. What is the elasticity at the price p=100?

To find the elasticity of demand at a given price, we use the formula for the price elasticity of demand, which is:

\[ E(p) = \frac{dD/dp \cdot p}{D(p)} \]

where \( D(p) \) is the demand function, \( dD/dp \) is the derivative of the demand function with respect to price, and \( p \) is the price at which we want to calculate the elasticity.

Given the demand function \( D(p) = 600 - p \), we first find the derivative:

\[ \frac{dD}{dp} = -1 \]

Now, we substitute \( p = 100 \) into the elasticity formula:

\[ E(100) = \frac{-1 \cdot 100}{600 - 100} \]

\[ E(100) = \frac{-100}{500} \]

\[ E(100) = -0.2 \]

The elasticity of demand at the price \( p = 100 \) is \(-0.2\).

Explanation:

• The elasticity of \(-0.2\) indicates that the demand is inelastic at this price point. This means that a 1% increase in price would result in a 0.2% decrease in quantity demanded, which is less than proportional.