In a perfectly competitive market with the supply function P=20+0.3Q and demand function P=80-0.1Q, what is the equilibrium price?

To find the equilibrium price in a perfectly competitive market, it's essential to set the supply price equal to the demand price and solve for the quantity (Q). The equilibrium occurs where the quantity supplied equals the quantity demanded.

Given the supply function ( P = 20 + 0.3Q ) and the demand function ( P = 80 - 0.1Q ), we can set these two equations equal to each other:

[ 20 + 0.3Q = 80 - 0.1Q ]

Next, we will isolate ( Q ). First, combine the terms containing ( Q ):

[ 0.3Q + 0.1Q = 80 - 20 ]

This simplifies to:

[ 0.4Q = 60 ]

Now, divide both sides by 0.4:

[ Q = \frac{60}{0.4} = 150 ]

Now that we have the equilibrium quantity, we can substitute ( Q = 150 ) back into either the supply or demand function to find the equilibrium price. Using the supply function:

[ P = 20 + 0.3(150) ] [