Final answer:
Equilibrium is found by setting the quantity demanded equal to the quantity supplied and solving for price. Graphically, it's where the demand and supply curves intersect.
Elasticity requires knowing how the quantity supplied changes in percentage terms in response to price changes, which isn't provided here.
Step-by-step explanation:
To solve for the equilibrium using the given demand and supply equations (where Qd is the quantity demanded and Qs is the quantity supplied), you set Qd equal to Qs and solve for the price (P).
With the equations provided, this process would normally involve algebra, but it can also be done using graphs. When the equations are graphed, the point where the demand curve intersects the supply curve will give the equilibrium price and quantity.
The problem seems to mention different demand and supply equations, but does not fully provide them. However, based on the example provided,
if we have demand and supply curves expressed as P = 8 - 0.5Qd and P = -0.4 + 0.2Qs respectively, and they cross each other, the equilibrium price would be $2 and the equilibrium quantity would be 12 units. This is because at the intersection point of the two curves, Qd equals Qs, indicating market equilibrium.
As for the elasticity of the supply curve given by the equation P = 3Q - 8, the price elasticity of supply (PES) can be calculated between two price points.
However, the formula for PES requires additional information such as the percentage change in quantity supplied in response to the percentage change in price, which is not provided here.