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The demand equation is a formula that reflects the relationship between the price of a product and the quantity demanded by consumers. It is typically expressed in the form of a linear equation, which helps us understand how demand changes with price fluctuations. In the provided exercise, the demand equation is given as: \[ p = 140 - 0.00002x \]

• **Price (\( p \)):** Represents the cost per unit of the product. This is influenced by consumer preferences and market conditions.
• **Quantity demanded (\( x \)):** This is the number of units consumers are willing and able to purchase at a certain price.

The negative coefficient before \( x \) (i.e., \(-0.00002\)) indicates that as the price decreases, the quantity demanded increases, exhibiting the law of demand. This inverse relationship is essential for determining the equilibrium, where consumer demand aligns with producer supply.

The supply equation reflects the behavior of producers concerning the price and the quantity they are willing to bring to market. In this problem, the supply equation is:\[ p = 80 + 0.00001x \]

• **Price (\( p \)):** This represents the selling price per unit at which producers are willing to supply the product.
• **Quantity supplied (\( x \)):** Indicates the number of units producers are ready to sell at a particular price.

Here, the positive coefficient before \( x \) (i.e., \(0.00001\)) represents the law of supply — as the price rises, producers are more willing to increase the quantity supplied. Understanding this positive relationship is crucial for identifying the equilibrium point where supply meets demand, and the market is stable.

The equilibrium point is where the demand and supply equations intersect, suggesting no surplus or shortage in the market. To find this equilibrium, we solve linear equations by setting the demand equal to supply:
\[ 140 - 0.00002x = 80 + 0.00001x \]This process involves eliminating one variable (usually by adding or subtracting terms across the equation) to isolate \( x \):

• Combine terms: \(0.00002x + 0.00001x = 60\)
• Divide by the resulting coefficient: \(x = 60/0.00003 = 2,000,000\)

Next, substitute \( x = 2,000,000 \) back into either the demand or supply equation to find \( p \):

• Using the demand equation: \(p = 140 - 0.00002 \times 2,000,000 = 100\)

This tells us that the equilibrium price \( p \) is 100, and 2,000,000 units are bought or sold. Solving these linear equations is a powerful method for understanding market economics, ensuring efficiency where consumer demand and producer supply meet.