Determine the equilibrium price and quantity if demand is re

Determine the equilibrium price and quantity if demand is represented by the equation, P = 40 - 2Q_D and supply by the equation P = 10 + 4Q_S Suppose demand changes and is now represented by the equation P = 52 - 2Q_D. Has demand increased or decreased? What is the new equilibrium price and quantity? Suppose instead supply changes and is now represented by the equation P = 16 + 4Q_s. Has supply increased or decreased? What is the new equilibrium price and quantity?

Solution

Equilibrium:

In Equilibrium, a perfect competition market will set a price and quantity such that there is no excess supply and no excess demand, hence demand equals supply.

                                              Q_S = Q_D

a) Determine the equilibrium price and quantity:

Demand Equation is: P = 40 – 2Q_D

                P = 40 – 2Q_D

                Q_D = P – 40/2

Supply Equation is: P = 10 +4Q_S

                  P = 10 + 4Q_S

                Q_S = P -10/4

The Equilibrium of demand and supply is: Q_S = Q_D

                P – 40/2= P -10/4

              4 (P - 40) = 2 (P - 10)

              4P – 160 = 2P -20

                P = 70

Now P = 70 plug it into either the demand or supply Equation for find the Equilibrium Quantity

            P = 10 + 4Q_S

           70 = 10 + 4Q_S

                Q = 15

Therefore the Equilibrium at Price is “70” and Quantity is “15”.

b) Suppose P = 52 – 2Q_D Has demand increased or decreased? What is the new equilibrium price and quantity?

Demand Equation is: P = 52 – 2Q_D

                Q_D = P – 52/2

The Equilibrium of demand and supply is: Q_S = Q_D

                P – 52/2= P -10/4

              4 (P - 52) = 2 (P - 10)

              4P – 208 = 2P -20

                P = 94

Now P = 94 plug it into either the demand or supply Equation for find the Equilibrium Quantity

             P = 10 + 4Q_S

           94 = 10 + 4Q_S

                Q = 21

New Equilibrium at Price is “94” and Quantity is “21”, the price increases from ‘70’ to ‘94’ as well as the quantity also increase from ‘15’ to ‘21’. Therefore the demand is increased.

c) Suppose P = 16 + 4 Q_S Has supply increased or decreased? What is the new equilibrium price and quantity?

Supply Equation is: P = 16 +4Q_S

                 P = 16 + 4Q_S

                Q_S = P -16/4

The Equilibrium of demand and supply is: Q_S = Q_D

                P – 40/2= P -16/4

             4 (P - 40) = 2 (P - 16)

             4P – 160 = 2P -32

                P = 128

Now P = 128 plug it into either the demand or supply Equation for find the Equilibrium Quantity

                P = 16 + 4Q_S

             128 = 16 + 4Q_S

                Q = 28

New Equilibrium at Price is “128” and Quantity is “28”, the price increases from ‘70’ to ‘128’ as well as the quantity also increase from ‘15’ to ‘28’. Therefore the supply is increased.