(Modeling) Equilibrium Demand and Price The supply and...

(Modeling) Equilibrium Demand and Price The supply and demand equations for
a certain commodity are given.
$$
\text { supply: } p=\sqrt{0.1 q+9}-2 \text { and demand: } p=\sqrt{25-0.1 q}
$$
(a) Find the equilibrium demand.
(b) Find the equilibrium price (in dollars).

Key Concepts

Supply and Demand

Supply and demand are fundamental economic concepts that model the behavior of sellers and buyers in a market. The supply curve represents how much of a good producers are willing to offer at various prices, while the demand curve shows how much consumers are willing to purchase. Understanding these curves helps in analyzing market behavior and predicting changes in prices and quantities, which is essential in economic analysis.

Market Equilibrium

Market equilibrium occurs when the quantity supplied equals the quantity demanded, resulting in a stable price and quantity where there is no inherent tendency for change. Finding the equilibrium involves setting the supply and demand functions equal to each other and solving for the quantity and price at which the market balances.

Solving Equations with Radicals

In certain economic models, especially those involving nonlinear relationships, equations can include radical expressions. Solving these equations requires techniques such as isolating the radical expression and then squaring both sides to eliminate the square root, while keeping in mind the potential introduction of extraneous solutions. This method is an important part of mathematical problem solving in economic modeling.

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