Find the price elasticity of demand for the demand function...

Find the price elasticity of demand for the demand function at the indicated -value. Is the demand elastic, inelastic, or of unit elasticity at the indicated -value? Use a graphing utility to graph the revenue function, and identify the intervals of elasticity and inelasticity. $$ p=5-0.03 x \quad x=100 $$

Key Concepts

Revenue Function

The revenue function is derived from the demand function and represents the total income received by selling a product at a given price and quantity. Typically formulated as revenue equals price times quantity, this function is essential for understanding how changes in demand and pricing affect overall revenue, and it plays a significant role in determining the profit-maximizing output level.

Elastic, Inelastic, and Unit Elastic Demand

These terms describe how sensitive the quantity demanded is to price changes. When demand is elastic, a small price change leads to a larger percentage change in quantity demanded. Inelastic demand indicates that the percentage change in quantity demanded is smaller than the percentage change in price. Unit elastic demand occurs when the percentage change in quantity demanded is exactly equal to the percentage change in price. This classification is fundamental in pricing strategy, as it influences decisions regarding revenue optimization.

Price Elasticity of Demand

Price elasticity of demand measures the responsiveness of the quantity demanded of a good to a change in its price. It is calculated as the percentage change in quantity demanded divided by the percentage change in price. This concept is crucial in economics because it helps determine how consumers will react to price changes, affecting revenue and market strategy decisions.

Linear Demand Function

A linear demand function depicts the relationship between price and quantity demanded using a straight-line equation. The slope of this function indicates the rate at which price changes with respect to changes in quantity. It provides a simplified yet instructive model to analyze consumer behavior and make predictions in response to price shifts.

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