Question

The demand functions for the only two goods in the economy are Q1 = 10 - 2p1 + p2 and Q2 = 10 - 2p2 + p1. There are five units of each good. Solve for the equilibrium: p1, p2, Q1, and Q2?

Answer 1

Q₁ = 10 - 2p₁ + p₂

Q₂ = 10 - 2p₂ + p₁

There are five units of each good that means:

Q₁ = 5

Q₂ = 5

Put value of Q₁ in first equation:

5 = 10 - 2p₁ + p₂

2p₁ - p₂ = 5 ----------------(i)

Put value of Q₂ in second equation:

5 = 10 - 2p₂ + p₁

2p₂ - p₁ = 5 ----------------(ii)

then

p₁ = 2p₂ - 5

Put value of p₁ in equation (i)

2(2p₂ - 5) - p₂ = 5

4p₂ - 10 - p₂ = 5

3p₂ = 15

p₂ = 15 / 3 = 5

p₁ = 2*5 - 5 = 5

So, the equilibrium prices and quantities are:

Q₁ = 5

Q₂ = 5

p₁ = 5

p₂ = 5