Final answer:
To find the equilibrium price and quantity in a perfect competition market, set the demand equation equal to the supply equation and solve for P. An alternate method is to graph the demand and supply curves and find where they intersect.
Step-by-step explanation:
When analyzing problems in perfect competition and seeking to determine the equilibrium price and quantity, we first need to set the demand equation (Qd) equal to the supply equation (Qs). Given the information Qd = 80 - 4P and Qs = 20 + 6P, we find equilibrium where Qd = Qs by solving these equations simultaneously.
The correct algebraic step after setting the demand and supply equations equal to each other (Qd = Qs) is to use algebra to solve for P, the price. The provided equations seem to contain a typo or error, but generally, you would solve the equation 16 - 2P = 2 + 5P, which simplifies to a single linear equation after combining like terms. Once the equilibrium price P is found, it can be substituted back into either the demand or supply equation to find the equilibrium quantity Q.
Alternatively, if algebra is challenging, these equations can also be graphed to find the equilibrium price and quantity. The demand curve equation P = 8 - 0.5Qd and the supply curve equation P = -0.4 + 0.2Qs can be plotted, where the point they intersect indicates the equilibrium price and quantity.