supply (p = q^2 + 30q) and demand (= -2q^2 + 10q + 8500)

[booklover67]

I'm struggling with the concept of supply and demand and need a little homework help before I need to know this for the final in a couple of weeks.

The question I'm struggling with is:

Find the equilibrium quantity and price for the commodity whose supply and demand functions are given: supply p=q^2+30q demand=-2q^2+10q+8500

Do I need to do the math in a particular order? Is that not important to find this particular answer?

Thanks for the help!

 

[HallsofIvy]

I'm not sure what you mean by "do the math in a particular order"! What "math"? What "order"?

The "supply" equation tells you how many, q, of a particular item producers can supply to a market at a particular price, p. The "demand" equation tells you how many, q, lf a particular item buyers will purchase at a particular price, p. The ideal, the "equilibrium", is to be able to sell all that are produced. You want to have those two "q"s the same for the same "p".

For supply equation p=q^2+30q and demand equation p= =-2q^2+10q+8500, "equilibrium" is when p= q^2+ 30q= -2q^2+ 10q+ 8500. Adding 2q^2 to both sides and subtracting 10q+ 8500 to both sides, 3q^2+ 20q- 8500= 0. That is a "quadratic equation". You can solve it for q by "completing the square" or using the "quadratic formula". After finding q, put it into either of the original equations to find p.