Equilibrium price = 34, equilibrium quantity = 8.
In order to get this answer, you need to do some very simple algebra.
When you look at Question 2, please note that both the equation for supply and the equation for demand start with “P =”. That means that both equations are equal to P and are therefore equal to one another. Because of this, all you have to do is set the equations equal to one another and solve for Q. Here is how:
50 – 2Q = 30 + .5Q (now subtract 30 from both sides and add 2Q to both sides)
20 = 2.5Q (now divide both sides by 2.5)
Q = 8.
Since Q is the quantity, we know that the equilibrium quantity will be 8. Now we have to plug this value of Q back into the equations above (either one will do) to find a value for P, which is the equilibrium price.
P = 50 – 2Q
P = 50 – 2(8)
P = 50 – 16 = 34
You can get the same result (P = 34) if you plug 8 in for Q in the equation for supply.
Thus, we can see that the equilibrium price will be 34 and the equilibrium quantity will be 8.