In an economy,

There are 600 consumers of type a, with utility function: U^A(x₁,x₂) = 0.5log(x₁) + 0.5log(x₂)

Each type a consumer has income m_A.

There are 300 consumers of Type B, with utility function: U^B(x₁,x₂) = 1/3log(x₁) + 2/3log(x₂)

Each Type B consumer has income m_B.

The prices of the two goods are p1,p2 > 0

Part A) Find the market demand curve, denoted by X₁(p1, m_A, m_B)

Part B) Does the distribution of income does/does not affect the market demand in this economy? If not, show a counterexample.