Question

Given that the demand function is pd(q)q and that the supply function is ps(q)q, find the equilibrium quantity and the equilibrium price.

Answer 1

The equilibrium price is determined by setting the demand function equal to the supply function. Solving the equation 16 - 2P = 2 + 5P yields an equilibrium price of $2 and an equilibrium quantity of 12 units.

Step-by-step explanation:

To find the equilibrium quantity and equilibrium price, we set the demand function equal to the supply function. The given demand and supply functions are:

Demand: Qd = 16 - 2P

Supply: Qs = 2 + 5P

Setting Qd equal to Qs, we get:

16 - 2P = 2 + 5P

Combining like terms and solving for P:

16 - 2 = 5P + 2P

14 = 7P

P = 2

Substitute P back into either the demand or supply function to find Q:

Qd = Qs = 16 - 2(2)

Qd = Qs = 16 - 4 = 12

Thus, the equilibrium price is $2, and the equilibrium quantity is 12 units.