The demand and supply equations for a new gadget that can calculate your mood at any given point in time are given by

where p is the price in dollars and x represents the number of units. Find the equilibrium point for this market.

Equilibrium point:

x= gadgets (round to nearest whole unit)

p= $ (round to the nearest whole dollar)

The equilibrium point is the price p and number of units x that satisfy both the demand and supply equations.

Substitute the value of p given in the supply equation into the demand equation (p is written already conveniently in terms of x)

480+0.001x=600-0.004x

0.005x=120

x=120/0.005=24000

So, the equilibrium point occurs when the demand and supply are each 24,000 units. The price that corresponds to this x-value can be obtained by back-substituting x=24,000 back into either of the original equations.

p=480+0.001x=480+0.001(24000)=$504