Answer to Question #212840 in Economics of Enterprise for promzydecutetoy

Question

Given this equation Q - 30pa = 100 and Q + 20px + 100 = 0 calculate equilibrium price, equilibrium quantity demanded and equilibrium quantity supplied

Answer 1

Solution:

At equilibrium Quantity demanded = Quantity supplied

Q_D = Q_S

30pa = price of quantity demanded

20px = price of quantity supplied

Derive quantity demanded equation from inverse demand function given:

Inverse demand function: Q – 30p = 100

Quantity demanded function: Q_D = 100 + 30P

Derive quantity supplied equation from inverse supply function given:

Inverse supply function: Q + 20p + 100 = 0

Quantity supplied function: Q_S = -100 – 20P

At equilibrium: Q_D = Q_S

100 + 30P = -100 – 20P

100 + 100 = -20P – 30P

200 = -50P

P = -4

Equilibrium price = -4

Substitute in the quantity demanded function to derive the equilibrium quantity demanded:

Q_D = 100 + 30P

Q_D = 100 + 30(-4)

Q_D = 100 – 120

Q_D = -20

Equilibrium quantity demanded = -20

Substitute in the quantity supplied function to derive the equilibrium quantity supplied:

Q_S = -100 – 20P

Q_S = -100 – 20(-4)

Q_S = -100 + 80

Q_S = -20

Equilibrium quantity supplied = -20