Supply and Demand Let the supply and demand functions for...

Supply and Demand Let the supply and demand functions for butter pecan ice cream be given by $$ p=S(q)=\frac{2}{5} q \quad \text { and } \quad p=D(q)=100-\frac{2}{5} q $$ where $p$ is the price in dollars and $q$ is the number of 10 -gallon tubs. a. Graph these on the same axes. b. Find the equilibrium quantity and the equilibrium price. (Hint: The way to divide by a fraction is to multiply by its reciprocal.)

Supply and Demand Let the supply and demand functions for butter pecan ice cream be given by
$$ p=S(q)=\frac{2}{5} q \quad \text { and } \quad p=D(q)=100-\frac{2}{5} q $$
where $p$ is the price in dollars and $q$ is the number of 10 -gallon tubs.
a. Graph these on the same axes.
b. Find the equilibrium quantity and the equilibrium price. (Hint: The way to divide by a fraction is to multiply by its reciprocal.)

Key Concepts

Supply and Demand Curves

These curves represent the fundamental relationship in a market where the supply curve indicates the quantity producers are willing to offer at different price levels, and the demand curve shows the quantity consumers are willing to purchase at those prices. They are central to understanding market behavior, illustrating how changes in price affect supply and demand, and are the building blocks for analyzing market dynamics.

Market Equilibrium

Market equilibrium occurs where the supply and demand curves intersect, meaning the quantity supplied equals the quantity demanded. This intersection determines both the equilibrium price and the equilibrium quantity, which reflect the optimal transaction point in a competitive market. Understanding equilibrium is crucial for analyzing how markets allocate resources efficiently.

Graphical Representation of Linear Functions

Graphing linear functions involves plotting equations with constant slopes and intercepts on a coordinate system, usually with price on the vertical axis and quantity on the horizontal axis in economic models. This visual tool helps in understanding the behavior of the functions and in identifying the point of intersection, which is important for interpreting market equilibrium.

Solving Linear Equations

Solving linear equations involves setting two linear expressions equal to each other and finding the variable value that satisfies the equation. In the context of supply and demand, this method is used to determine the equilibrium quantity by equating the supply and demand expressions and solving for the quantity, after which the equilibrium price can be found by substitution.

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