Question

Can someone give me a rough explanation of how I'm supposed to start? I know how to do the math involved, I'll b offline but will be back :)

The demand function for a certain brand of CD is given by
p = −0.01x2 − 0.2x + 11
where p is the unit price in dollars and x is the quantity demanded each week, measured in units of a thousand. The supply function is given by
p = 0.01x2 + 0.6x + 1
p=unit price $ and x =quantity that will be made available in the market by the supplier, measured in units of a thousand. Determine the producers' surplus if the market price is set at the equilibrium

Answer 1

say you start selling a product, so you calculate a price for it
you dunno how many folks are going to buy it, so you start at a price that's a bit high
thinking that many may not buy it

as more people like it, more buy it, you sell more
so if you decrease the price, even more will buy it

so you start decreasing the price, a few cents off the price, may mean say extra 50 people or 100
so the price is "elastic", meaning just a few cents off, give you a bigger proportional profit

so you keep on doing that, at some point, no matter how low you put it, no more folks buy it anymore
thus you've reached the point at which, you're selling the most, for the price that gives you profits the most

and that's the equillibrium point

that happens when the folks buying it, (DEMAND)
at the price you're asking for it (SUPPLY)
give you the most profit

that is, when those two curves meet so is just a system of equations
and just like any other, just either graph it and solve by getting the intersection point
or
keep in mind that when they meet, p=p
that is \(\bf −0.01x^2 − 0.2x + 11=0.01x^2 + 0.6x + 1\)