Consider the market for trucks. Assume that the demand for trucks is given by
60 2 5 D Q P Y where P is price per truck and Y is the income of the buyers. The
supply of trucks is given by 30 5 3 S Q P W where W is the price of all the materials
needed to produce a truck. Solve for the equilibrium price P* and equilibrium quantity
Q* of trucks bought and sold.
I have seen this problem in a previous tutoring session, so I am going to assume that your word problem should read something like this:
In a market for trucks the demand for trucks and the quantity supplied are given by the following equations (in the block quote):
Quantity Demanded = 60 - 2p + 5y where p is price and y is income of the buyers.
Quantity Supplied = 30 + 5p -3w where w is raw materials required to make the truck
Compute the equilibrium price and equilibrium quantity of trucks bought & sold.
If this is the wording of your problem (or even if it is not) continue to read my answer because it will work you through the proper steps in solving an equation like this one.
- In order to go about solving this problem, you should first set your QD (quantity demanded) equaled to your QS (quantity supplied). Thus meaning you should have 60-2p+5y=30+5p-3w
- After examing the equation, it is easy to see that the common variable shared between both sides of your newly normed equation is p. Using this knowledge you should solve the equation for the variable p.
- Your newly formed equation, which is also the equilibrium price, will be p=(30+5y+3w)/7
After this point things will seem tricky, but it is actually quite simple.
- Go back to your original functions and substitute your equation for p in both.
- You will find that both equations work out to being (360+25y-6w)/7
- This equation is your equilibrium quantity of trucks bought and sold.
So remember your equilibrium price is (30+5y+3w)/7 and your equilibrium quantity is (260+25y-6w)/7.
Have a nice day!