Suppose demand for apples is given by the equation D(Q) = 63 – 5Q and supply is given by S(Q) = 4Q. Demand is for retailers (i.e. grocery stores), not final customers and the prices and quantities in question refer to standard 40-lb boxes, in millions). What is the equilibrium price and quantity of 40-lb apple boxes? (Hint, once you have Q, you can plug this into either equation to find price). Suppose supply shifts in (less supply) to S(Q) = 5Q . What is the equilibrium price and quantity now?
First of all, I am certain that your equations are not quite right. You have the equation for demand, for example, as Q = 63 - 5Q. Supply and demand equations are typically given with both price (P) and quantity (Q) as variables. Therefore, your demand equation ought to be P = 63 – 5Q. Your supply equation ought to be P = 4Q. This also does away with the problem of having Q = 4Q as an equation. That equation only works if Q = 0, which would be impossible because you could not use that value for Q in the demand equation.
When you have a supply equation and a demand equation, it is relatively easy to find the equilibrium price and quantity. Equilibrium is the point where the price and quantity are equal for both the supply and the demand. This means that we can find equilibrium by setting the supply and demand equations equal to one another. In this case, the process works like this:
P = 63 – 5Q (demand)
P = 4Q (supply)
4Q = 63 – 5Q from here, we add 5Q to both sides
9Q = 63 now we divide both sides by 9
Q = 7
This tells us that the equilibrium quantity is 7 million boxes of apples.
Now that we have the equilibrium quantity, we plug it in to either the supply or the demand equation to find the equilibrium price.
P = 4Q
P = 4(7) = 28
This tells us that the equilibrium price is 28.
Now what if the supply drops to P = 5Q?
5Q = 63 – 5Q now we add 5Q to both sides
10Q = 63 now we divide both sides by 10
Q = 6.3
This means that the new equilibrium quantity is 6.3 million boxes of apples.
We now plug that quantity in to find the equilibrium price:
P = 5Q
P = 5(6.3) = 31.5
This means that the new equilibrium price is 31.5.