Question

Suppose that the demand per ounce of a rare type of chocolate, Qp, is represented by the following equation, where P is the price of chocolate and QD is the quantity of chocolate sold:

QD = 2200 - 18P
The supply of chocolate, Qₛ, is represented by the equation:
Qₛ = -500 + 77P

Answer 1

To find the equilibrium price and quantity for a rare type of chocolate, set the demand equation QD = 2200 - 18P equal to the supply equation Qs = -500 + 77P, and solve for P. Alternatively, graph both curves and find their intersection point.

Step-by-step explanation:

The student's question is about finding the equilibrium price and quantity for a rare type of chocolate given the demand and supply equations. To find the equilibrium, we set the demand equation QD = 2200 - 18P equal to the supply equation Qs = -500 + 77P. By solving this system of equations, we can determine the price at which the quantity demanded equals the quantity supplied. This is the equilibrium price, where the market is in balance, and the corresponding quantity is the equilibrium quantity.

If algebra is challenging, graphs can be used to find the equilibrium. By plotting the demand curve as P = (2200/Qd) - 18 and the supply curve as P = (500/Qs) + 77 on the same set of axes, the intersection point gives the equilibrium price and quantity. This method of solving models with graphs offers a visual approach to understanding market equilibrium.