Find the consumer and producer surplus for an item

Question

Supply: p =5q²   Demand: p = 4800 - q²/3

 

I figured out price is p= 4500 and q = 30 (at equilibrium) now how do you solve for the surplus of both.

I know it's a type of interval question but I'm stuck. 

Answer 1

When you graph using x-axis as q, and y-axis as p (price)

  Supply, p=5q², (you may use a graphic calculator) 

  the graph is, from the left to right, going down to hit the origin,  and up.

Again, when you graph Demand, p = 4800 - q²/3,

  the graph is, from the left to right, going up to hit the 4800 point on the y-axis (which is p), and coming down.

 

When the two graphs plotted together, they will meet at the point p=4500, q= 30 (crossing point).

(For the real world, we don't use negative quantity q value which located on the left side of y-axis, so disregard it, and only take the right side of y-axis.)

And, you will see that Supply curve is located under the Demand curve before the cross point, that means more demand, short for the item.  After the crossing point, the Supply curve is located on the top of Demand curve, that means more supply, surplus for the item.