So I have p with an upper dash equal to 9 and demand is q=15-1/3p. I know my consumer surplus is 216 after calculating p=-3x+45 and q with an upper dash to be 12. I just do not understand how I am supposed to find how much consumers were willing to spend on the first q with upper dash items or how much they actually spent. I thought it would be the 12 and 9 but I know that those values are wrong.
ah yes. I missed that equilibrium price of p=9
so, according to the article at
corporatefinanceinstitute.com/resources/knowledge/economics/consumer-surplus/
p = 45-3q
and so you want the area
∫[0,12] (45-3q) - 9 dq = 216
money spent is quantity * price, right?
the total quantity the bought is ∫ q(p) dp = ∫[0,9] 15 - p/3 dp = 243/2
and the total spent would be ∫[0,9] p(15 - p/3) dp = 1053/2
This is kinda new for me, so I may be wrong, but if so, it may give you a starting place.