Calculating Point Price Elasticity at Given Price

What is the point price elasticity when the price is $126?

Final answer: The point price elasticity at P = 126 is given by the formula E = (-1/3) * (126/Q), where Q represents the quantity demanded.

Understanding Point Price Elasticity

Point price elasticity measures the responsiveness of quantity demanded to a change in price at a specific point on the demand curve. It helps determine how sensitive consumers are to price changes for a particular product. The formula to calculate point price elasticity is given by E = (dQ/dP) * (P/Q).

Calculating Point Price Elasticity at P = 126

To calculate the point price elasticity at P = 126, we first need to find the derivative of the demand function with respect to price. The demand function is given as P = 583 - 3Q. By differentiating the equation with respect to P, we get dP/dP = -3(dQ/dP).

Substituting the given price P = 126 into the equation, we have -3(dQ/dP) = 1. Solving for dQ/dP, we get dQ/dP = -1/3.

Now, we can substitute the values into the point price elasticity formula: E = (-1/3) * (126/Q). Since the quantity demanded (Q) is not given, we cannot calculate the exact value of the point price elasticity.

However, we have determined the formula for the point price elasticity at P = 126, which is E = (-1/3) * (126/Q). This formula will give us the price elasticity at the given price point.