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Suppose the price p and the demand D(p) for a product are related by the price-demand equation D(p) + 600p = 12000. Calculate the point elasticity of demand when p = 4.

User Fizampou
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Final answer:

The question involves the calculation of the point elasticity of demand when p = 4. To do this, we insert p into the price-demand equation to find D(p), calculate D'(p)(the rate of change of quantity), and then use the elasticity formula E = (D'(p) * p) / D(p).

Step-by-step explanation:

The question asks for calculating the point elasticity of demand for a product when the price p is 4, given the price-demand equation D(p) + 600p = 12000.

Point elasticity of demand measures how much the quantity demanded changes with a change in price at a particular point on the demand curve. The general formula for point elasticity is:

Elasticity (E) = (% change in quantity demanded) / (% change in price)

To find point elasticity, we first need to determine the quantity demanded at p = 4 by inserting the value into the given equation, then finding D(p), then computing the derivative of D with respect to p (D'(p)) at that point to find the rate of change of quantity demanded with respect to price.

Finally, we use the formula:

E = (D'(p) * p) / D(p)

The detailed steps of solving for D(p), finding D'(p), and calculating the elasticity at p = 4 will provide the student with the point elasticity of demand at that price.