Question

A firm produces and sells two commodities. The demand function

for one commodity is x = 24 − 1/4 Px . The demand function for the
other commodity is y = 42 − 1/2py . Note, the quantities

Answer 1

To find the equilibrium price for the two commodities, set the demand and supply curves equal to each other and solve the resulting system of equations.

Step-by-step explanation:

To find the intersection point of the demand and supply curves, we should first set X and Y to be equal to each other. So:

24 - 1/4Px = 42 - 1/2Py

To solve for Px (the price of the first commodity), we can rearrange the equation:

1/4Px = -18 + 1/2Py

Px = -72 + 2Py

Similarly, to solve for Py (the price of the second commodity), we rearrange the equation again:

1/2Py = -18 + 1/4Px

Py = -36 + 1/2Px

Now we have two equations to work with: Px = -72 + 2Py and Py = -36 + 1/2Px. By substituting the second equation into the first equation, we can find Px:

Px = -72 + 2(-36 + 1/2Px)

We can then solve for Px:

Px = -72 - 72 + Px

Px = -144 + Px

144 = 2Px

Px = 72

Finally, substitute the value of Px into the second equation to find Py:

Py = -36 + 1/2(72)

Py = -36 + 36

Py = 0

So, the equilibrium price for the first commodity is $72 and the equilibrium price for the second commodity is $0