Chapter B, Problem 1PA

To determine

To derive: the Demand equation from the given demand curve.

Answer to Problem 1PA

The demand equation for the given demand curve is:

  $Q=40-\frac{1}{3}P$

Explanation of Solution

Demand refers to the consumer's desire to purchase goods and services and willingness to pay a price for a specific good or service.

Assuming all the other factors constant, an increase in the price of the commodity decreases the quantity demanded of a commodity and vice versa.

General demand equation is as follows:

  $Q=a+\frac{1}{m}P$

Here,

Q= Quantity.

m= slope.

p= price.

a= quantity intercept (constant)

Calculation of the slope is as follows:

  $\begin{array}{l}Slope=\frac{Pric{e}_2-Pric{e}_1}{Quantit{y}_2-Quantit{y}_1}\\ Slope=\frac{45-90}{25-10}\\ Slope=\frac{-45}{15}\\ Slope=-3\end{array}$

Calculation of Quantity intercepts is as follows:

  $\begin{array}{l}\begin{array}{cc}Quantity& intercept=\end{array}Pric{e}_1\times \left(\frac{1}{-Slope}\right)+Quantit{y}_1\\ \begin{array}{cc}Quantity& intercept=\end{array}90\times \left(\frac{1}{-3}\right)+10\\ \begin{array}{cc}Quantity& intercept=\end{array}40\end{array}$

Demand Equation is as follows:

  $\begin{array}{l}Q=a+\frac{1}{m}p\\ Q=40+\frac{1}{-3}p\\ Q=40-\frac{1}{3}p\end{array}$