In a perfectly competitive market where demand is P=60-0.3Q and supply is P=10+0.2Q, what are the equilibrium price and quantity?

To find the equilibrium price and quantity in a perfectly competitive market, you need to determine where the quantity demanded equals the quantity supplied. This is done by setting the demand equation equal to the supply equation.

You have the demand equation given by P = 60 - 0.3Q, which represents how the price (P) adjusts according to the quantity demanded (Q). Similarly, the supply equation is P = 10 + 0.2Q, indicating how the price corresponds to the quantity supplied.

Setting these two equations equal to each other allows us to solve for the equilibrium quantity (Q):

60 - 0.3Q = 10 + 0.2Q

To solve for Q, first, rearrange the equation:

60 - 10 = 0.3Q + 0.2Q 50 = 0.5Q

Next, divide both sides by 0.5:

Q = 100

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

P = 60 - 0.3(100) P = 60 - 30 P = 30

Thus