Consider an economy with three goods. Suppose that a consumer has a continuous utility function satisfying local nonsatiation. Suppose also that the consumer's Walrasian demands for goods 1 and 2 when p₃ = 1 satisfy

x₁(p₁, p₂, 1, W) = a₁ + b₁p₁ + c₁p₂ + d₁p₁p₂

x₂(p₁, p₂, 1, W) = a₂ + b₂p₁ + c₂p₂ + d₂p₁p₂

(a) State Walras' law and use it to find the Walrasian demand for good 3. (It's fine to just give the demand when p₃ = 1.)

(b) State a mathematical result about the homogeneity of Walrasian demands and use it to find the consumer's Walrasian demands at other values of p₃.