Calculating Point Price Elasticity of Demand

What is the point price elasticity of demand when the price is $28 for a good with the demand function P = 327-4Q?

Understanding Point Price Elasticity of Demand

The point price elasticity of demand measures how the quantity demanded of a good changes in response to a change in its price. It is calculated by taking the derivative of the demand equation with respect to price and then multiplying it by the ratio of price to quantity demanded. In this case, the demand function is given as P = 327-4Q, where P is the price and Q is the quantity demanded. When the price is $28, we can calculate the point price elasticity of demand as follows: Substitute P = 28 into the demand function: 28 = 327 - 4Q 4Q = 327 - 28 Q = (327 - 28) / 4 Q = 74.75 Calculate the derivative of the demand function with respect to P: dQ/dP = -4 Substitute P = 28 and Q = 74.75 into the derivative: dQ/dP = -4 Finally, calculate the point price elasticity of demand using the formula: Elasticity = (dQ/dP) * (P/Q) Elasticity = -4 * (28 / 74.75) Elasticity ≈ -1.06 Therefore, the point price elasticity of demand when the price is $28 for the good with the demand function P = 327-4Q is approximately -1.06.

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