Question

Hi how do i find the equilibrium point? The supply and demand equations for the production of widgets are given below: Supply: p = 0.80x + 58 Demand: p = −0.50x + 162. Find the equilibrium point.

Answer 1

122

Explanation:

We calculate the equilibrium pointt by equating both functions, we solve for x, and for that value of x we replace in each function and that value is the equilibrium point.

Just like that:

`0.80x\: +\: 58=\: -0.50x\: +\: 162`

We solve for x:

`\begin{gathered} 0.80x+0.50x=162-58 \\ 1.3x=104 \\ x=(104)/(1.3) \\ x=80 \end{gathered}`

Therefore, the equilibrium point would be:

`\begin{gathered} p=0.80\cdot80\: +\: 58=64+58=122 \\ \: p=-0.50\cdot80+\: 162=-40+162=122 \end{gathered}`

The equilibrium point is 122