Refer to Section 6.7 . The demand function for Apex women's...

Refer to Section $6.7 .$ The demand function for Apex women's boots is
$$p=\frac{250}{\sqrt{16+x^{2}}}$$
where $p$ is the unit price in dollars and $x$ is the quantity demanded daily, in units of a hundred. Find the consumers' surplus if the price is set at 50 dollar pair.

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Key Concepts

Consumer Surplus

Consumer surplus represents the extra benefit or value that consumers receive when they pay a market price that is lower than what they are willing to pay. It is calculated as the area under the demand curve and above the market price line over the range of quantities purchased. This concept is fundamental in welfare economics to measure the net gain in utility to consumers from market transactions.

Demand Function

A demand function expresses the relationship between the price of a good or service and the quantity demanded, usually showing that as price decreases, quantity demanded increases. It encapsulates consumer behavior and preferences, and it is vital in economic analysis for both microeconomic theory and market equilibrium studies.

Definite Integration in Economics

Definite integration is the mathematical process used to compute the area under a curve within specified bounds. In economic contexts, it is used to quantify consumer surplus by integrating the demand function over the range of quantities purchased, effectively summing the individual differences between the maximum price consumers are willing to pay and the prevailing market price.

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