Question

A market can be described by the equations Qd = 50 - 3P and Qs = 2P. What are the equilibrium price and quantity in this market?

A) Equilibrium price = $10, Equilibrium quantity = 20 units
B) Equilibrium price = $15, Equilibrium quantity = 10 units
C) Equilibrium price = $5, Equilibrium quantity = 30 units
D) Equilibrium price = $20, Equilibrium quantity = 5 units

Answer 1

The equilibrium price is $10, and the equilibrium quantity is 20 units, determined by setting the demand and supply equations equal to each other and solving for P and Q.

Step-by-step explanation:

To determine the equilibrium price and quantity in a market, we need to solve for where the quantity demanded (Qd) equals quantity supplied (Qs). Given the demand equation Qd = 50 - 3P and the supply equation Qs = 2P, setting these two equations equal to each other gives us 50 - 3P = 2P. Adding 3P to both sides and subtracting 2P from both sides, we get 50 = 5P, and dividing both sides by 5, we find P = 10. This is the equilibrium price. To find the equilibrium quantity, we replace P in either the demand or supply equation with 10. Using the supply equation, Qs = 2P gives us Qs = 2(10) = 20. Therefore, the equilibrium price is $10, and the equilibrium quantity is 20 units.