Final answer:
The equilibrium price is $2, and the equilibrium output is 12 units. This can be found by setting the quantity demanded equal to quantity supplied algebraically or by graphing the demand and supply curves and finding their intersection.
Step-by-step explanation:
Equilibrium Price and Output
To find the equilibrium price and output, we look at the point where the quantity demanded (Qd) equals the quantity supplied (Qs). The equilibrium for a market occurs where the demand curve intersects the supply curve. The given equations for Qd (P) = P and Qs (P) = 12 - P can be used to find this point algebraically by setting them equal to each other, resulting in P being the equilibrium price while the output is the quantity at that price level.
By setting Qd = Qs, we get 16 - 2P = 2 + 5P. Solving for P, we rearrange terms to isolate P on one side of the equation:
• 16 - 2P = 2 + 5P
• 16 - 2 = 5P + 2P
• 14 = 7P
• P = 2 (Equilibrium Price)
Substituting P back into either the demand or supply equation, we find that Qd = Qs = 12 (Equilibrium Output). Hence, the equilibrium price is $2 and the equilibrium output is 12 units. If you prefer to use graphs instead of algebra, you can plot these equations and find that the demand and supply curves intersect at the same equilibrium price of $2 and equilibrium output of 12 units, confirming our algebraic solution.