Problem 124 - Introductory Chemistry Atoms First

Question

Consider the two curves, one showing supply of tapes, the other showing demand for tapes. At what price per quantity is equilibrium established?

Step-by-Step Solution

Answer

The equilibrium price per quantity is established at \(p = \frac{a - c}{1 + b}\), where a, b, and c are constants in the demand and supply curve equations \(q_D = a - p\) and \(q_S = bp + c\). To find the equilibrium price for tapes, substitute the specific values of a, b, and c from the given demand and supply curves into this formula.

Step 1: Set the demand equal to the supply

To find the equilibrium price, set the demand quantity equal to the supply quantity: \(a - p = bp + c\)

Step 2: Solve for price per quantity

Rearrange the equation to solve for price per quantity (p): \(p = \frac{a - c}{1 + b}\) Now we have the general formula for the equilibrium price. Plug in the specific coefficients a, b, and c from the given demand and supply curves to find the equilibrium price for the tapes.

Key Concepts

Supply and Demand

The foundation of any market economy is the relationship between supply and demand. These are two forces that determine how much of a product is available and how much of it people want to buy.

Supply refers to how much of a product, say tapes in this case, producers are willing and able to produce at a given price. Generally, the higher the price, the more producers are willing to supply.

Demand, on the other hand, shows how much of the product consumers are willing to buy at a particular price. When prices are high, demand often decreases because consumers may not be willing or able to buy as much.

In this exercise, you are considering these opposing forces through two curves: one showing the quantity of tapes supplied and the other showing the quantity demanded. Where these two meet is where both consumers’ desires match the producers’ offerings.

Equilibrium Concept

Equilibrium is a central concept in economics and signifies the point where the supply and demand curves intersect. At this point, the quantity of goods supplied equals the quantity of goods demanded.

This balance ensures that the market can function smoothly without any surplus (extra goods not sold) or shortage (demand that isn't met). Finding the equilibrium point ensures that everyone gets what they want at an agreeable price.

In mathematical terms, we set the equation for demand equal to the equation for supply. The step-by-step solution shows how to do this: by equating the two, you can solve for the equilibrium price.

This price is where both buyers and sellers are satisfied, and transactions can occur without anyone thinking they paid too much or received too little.

Price Determination

Price determination in a market happens at equilibrium. To determine this specific price, you rely on both the demand and supply equations.

Using the formula derived in the step-by-step solution, the equilibrium price can be calculated using:

• a: Represents the intercept of the demand curve, showing maximum willingness to pay.
• b: Represents the slope of the supply curve, indicating how supply reacts to price changes.
• c: Is a constant in the supply equation that impacts producer pricing needs.

To find the equilibrium price of tapes, plug the specific values of a, b, and c into the formula: \[ p = \frac{a - c}{1 + b} \]This formula captures the interaction and pricing balance of real-world demand and supply forces. It shows how prices reach a point where both sides, consumers and producers, agree on."