Question

The demand and supply function are given by 2P + 3QD = 66 5P – 2QS = 13 Find the equilibrium price and quantity using inverse matrix method.

Answer 1

The equilibrium quantity will be where the Quantity Demanded=Quantity Supplied. So, QD=QS. Lets just represent it with Q in that case. So the equations become

2P+2Q=66
5P-2Q=13

So, the coefficient matrix becomes

A=

The variable matrix is

X=

The constant matrix is

B=

Setting AX=B, we get

=

Now we need to calculate the inverse of the matrix. We know that the inverse is given by

Using this, we get the inverse. First lets calculate 1/(ad-bc). Putting values in from the coefficent matrix, we get

1/(-4-10)=-1/14. Now getting the inverse matrix.

=-1/14

=

Now we multiply both sides of the equation with A^-1

Since the left side is getting multiplied by its own inverse, they will cancel out. Multiplying the two matrices on the right side, we get

Hence,

Equilibrium Price=79/7=11.286

Equiibrium Quantity=152/7=21.714