Chapter 7.2, Problem 75E

To determine

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

Answer to Problem 75E

The equilibrium point is $2000000$ unit and price $p$ is 100.

Explanation of Solution

Given information :

Demand - $p=140-0.00002x$

Supply- $p=80+0.00001x$

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.

  $\begin{array}{l}p=140-0.00002x\\ 80+0.00001x=140-0.00002x\\ 0.00001x+0.00002x=140-80\\ 0.00003x=60\\ x=\frac{60}{0.00003}\\ x=2000000\end{array}$

So, the equilibrium point occurs when the demand and supply are each $2000000$ unit.

Therefore, the price $p$ is:

  $\begin{array}{l}p=140-0.00002x\\ p=140-0.00002\left(2000000\right)\left[\text{substitute }x\right]\\ p=140-40\\ p=100\end{array}$

Hence, the equilibrium point is $2000000$ unit and price $p$ is 100.