Chapter 7.2, Problem 70E

To determine

To find : the point of equilibrium of the demand and supply

Answer to Problem 70E

The equilibrium point is 500 unit and price $p$ is 75.

Explanation of Solution

Given information :

Demand - $p=100-0.05x$

Supply- $100-0.05x$

Calculation :

Because $p$ is written in terms of $x$ ,begin by substituting the value of $p$ given in the supply equation into the demand equation.

  $\begin{array}{l}p=100-0.05x\\ 25+0.1x=100-0.05x\\ 0.1x+0.05x=100-25\\ 0.15x=75\\ x=\frac{75}{0.15}\\ x=500\end{array}$

So, the equilibrium point occurs when the demand and supply are each 500 unit.

Therefore, the price $p$ is:

  $\begin{array}{l}p=100-0.05x\\ p=100-0.05\left(500\right)\left[\text{substitute }x\right]\\ p=100-25\\ p=75\end{array}$

Hence, the equilibrium point is 500 unit and price $p$ is 75.