Equilibrium Price Calculation:
To calculate the equilibrium price, we need to set the quantity demanded equal to the quantity supplied and solve for the price.
So, equating the demand and supply functions:
Qd = Qs
a - ßP = -YP
a = ßP - YP
a = P(ß - Y)
P = a / (ß - Y)

Diagrammatic Illustration:
When the market price (P) is equal to the equilibrium price (P*), the market is in a state of equilibrium where the quantity demanded equals the quantity supplied. Let's illustrate this using a supply and demand diagram.

Key Points:
1. Vertical Axis: Quantity (Q)
2. Horizontal Axis: Price (P)
3. Supply Curve (S): It represents the relationship between the price and the quantity supplied. It slopes upward from left to right, indicating that as the price increases, the quantity supplied also increases.
4. Demand Curve (D): It represents the relationship between the price and the quantity demanded. It slopes downward from left to right, indicating that as the price increases, the quantity demanded decreases.
5. Equilibrium Point (E): It is the point where the supply and demand curves intersect. At this point, the quantity demanded equals the quantity supplied.
6. Equilibrium Price (P*): It is the price at which the quantity demanded equals the quantity supplied. It is determined by the intersection of the supply and demand curves.

Explanation:
When the market price (P) is equal to the equilibrium price (P*), the following scenario occurs:
1. Quantity Demanded (Qd) = Quantity Supplied (Qs): At the equilibrium price, the quantity demanded equals the quantity supplied. There is no shortage or surplus in the market.
2. No Incentive to Change: Both buyers and sellers are satisfied with the equilibrium price. Buyers are willing to buy exactly what sellers are willing to sell at that price.
3. Market Stability: The market is in a stable state, as there is no pressure for the price to change. The forces of demand and supply are balanced.
4. Market Efficiency: At the equilibrium price, resources are allocated efficiently. There is no wastage or shortage of the commodity.
5. Market Clearing: The market clears at the equilibrium price, meaning that all the goods produced are sold, and there is no excess supply or excess demand.

In summary, when the market price is equal to the equilibrium price, the market is in a state of balance, with no shortage or surplus. Buyers and sellers are satisfied, and the market operates efficiently and clears at the equilibrium price.