# Find the equilibrium point given the demand function D(x) = -4x+8 and the supply function ...

## Question:

Find the equilibrium point given the demand function {eq}D(x) = -4x+8 {/eq} and the supply function {eq}S(x) = 4x+2 {/eq}

## Supply-Demand curve

This problem involves use of concept of equilibrium point in the demand and supply curve. If the definition of equilibrium point is known, the problem becomes fairly straightforward.

Equilibrium point is defined as the point where the Supply curve and the demand curve cross each other.

Thus, if {eq}D(x_0) = S(x_0) {/eq} , then, {eq}x_0 {/eq} is the equilibrium point.

Hence, simply equating D(x) and S(x),

{eq}\displaystyle D(x_0) = S(x_0) \rightarrow -4x+8 = 4x +2 \rightarrow x = \frac{6}{8} = 0.75 {/eq}

Hence, equilibrium point is {eq}\displaystyle (0.75,5) {/eq}