# Market Equilibrium & Calculus

I am a math nerd, but I'm working on my majorly lacking derivative analysis calculus. Trying to break into better understanding market equilibrium. I found some example questions that I am working through.

DEMAND: 344 - 2x

SUPPLY: 80 + 4x

The questions:

1. What are the value of the equilibrium price and quantity? I already devised 44 as the value of x, is this the answer to both price and quantity, or just one of them?

2. How exactly would graph these two functions by hand? Kind of a vague question, but I'm unsure how a function like this actually graphed.

3. The value of surplus at equilibrium quantity is $___? Based on this question I am assuming that the 256 I devised for x is the quantity, not the price/value? 4. At what price would there be a surplus of 50? Completely lost here, but I am assuming you use the original formulas in some manner. Not for school or any sort of homework, just for personal knowledge. Thanks! • For getting a rough sketch of the graphs by hand, read this article. – Prasun Biswas Jun 24 '15 at 18:38 • You'll need to have a starting graph to use that technique. The graph$y=x$is pretty simple to draw. Use that as a starting point to sketch the two graphs. – Prasun Biswas Jun 24 '15 at 18:41 • If you don't tell us whether$x$is price or quantity, we cannot know whether$x$is price or quantity. As a general rule, demand and supply are written as functions of price, which suggests that$x$is price. But as another general rule, price tends to be denoted$P$while quantity tends to be denoted$Q$or$x$, which suggests that$x\$ is quantity. Only the poser of the question (i.e. you) can reconcile this. – WillO Jun 24 '15 at 18:42
• @WillO, you are saying that if the formulas were written as Q = 344 - 2p we would be calculating the price, since P were used? Therefore in this case, the quantity would be 256 and the price would be 44? – user3223880 Jun 24 '15 at 18:52
• @PrasunBiswas, I will look through that article. Graphing as a whole isn't too complicated in my eyes, I guess I'm just unsure of the first steps in determining the starting point. – user3223880 Jun 24 '15 at 18:53