Suppose that demand is given by the equation Q^D=500-50 P,...

Suppose that demand is given by the equation $Q^{D}=500-50 P,$ where $Q^{D}$ is quantity demanded, and $P$ is the price of the good. Supply is described by the equation $Q^{S}=50+25 P,$ where $Q^{S}$ is quantity supplied. What is the equilibrium price and quantity? (See Appendix.)

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Key Concepts

Demand

Demand represents the quantity of a good or service that consumers are willing and able to buy at various prices. It is typically expressed as a function showing that as the price decreases, consumers are willing to purchase more, reflecting the inverse relationship known as the law of demand.

Supply

Supply refers to the quantity of a good or service that producers are willing and able to offer for sale at different prices. It is generally expressed as a function showing that higher prices motivate producers to supply more, encapsulating the direct relationship illustrated by the law of supply.

Market Equilibrium

Market equilibrium is the point where the quantity demanded equals the quantity supplied, resulting in a stable price and quantity in the market. This concept is fundamental in economics because it indicates a state of balance where there is no inherent force causing a shift in price or quantity.

Solving Equilibrium Equations

Solving equilibrium equations involves setting the demand function equal to the supply function to find the price at which the market clears. Once the equilibrium price is determined, it is substituted back into either the demand or supply equation to calculate the equilibrium quantity. This process of solving simultaneous equations is a key analytical tool in economic analysis.

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