Question

In a market demand and supply equations are:

The demand curve is given as: P = 50 - 3Q

The supply curve is given as: P = 10 + 2Q

Assuming a perfectly competitive market: What is the total wealth?  

Answer 1

In a market demand and supply equations are:

The demand curve is given as: P = 50 - 3Q

The supply curve is given as: P = 10 + 2Q

Assuming a perfectly competitive market, equilibrium is achieved when demand and supply curve intersect each other.

If demand and supply curve intersect each other at equilibrium, then,

50 - 3Q = 10 + 2Q

or, 40 = 5Q

or, Q* = 8.

Therefore, equilibrium quantity = 8.

Equilibrium price (P*) = 50 – 3*8 = 50 – 24 = 26.

Economic welfare is the total benefit of the economy from an economic transaction. It is the sum of producer surplus and consumer surplus.

The producer surplus is the area below the equilibrium market price and above the market supply curve.

Therefore, Producer Surplus (PS) = ½ * (26 – 10) * 8 = ½ * 16 * 8 = 64.

On the other hand, consumer surplus is the area above the equilibrium market price and below the market demand curve.

Therefore, Consumer Surplus (CS) = ½ * (50 - 26) * 8 = ½ * 24 * 8 = 96.

Thus, the total welfare = PS + CS = 64 + 96 = 160.