Write down the budget constraint of each consumer

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Reference no: EM132286608

Exercise -

One firm g(y₁, y₂) = y₂ - 10 √(-y₁) (where y₁ 0) uses good 1 as the input to produce good 2.

Two consumers -

Ann: u_A(x₁^A, x₂^A) = (x₁^A)^½ · (x₂^A)^½, ω^A = (160, 0), θ^A = 2/5.

Bob: u_B(x₁^B, x₂^B) = (x₁^B)^½ · (x₂^B), ω^B = (90, 0), θ^B = 3/5.

Assume that p₁ = 1.

1. Derive the profit-maximizing input amount y₁^*(1, p₂) and the maximized profit Π(y₁^*, y₂^*) = y₁^*(1, p₂) + p₂ · y₂^*(1, p₂) as functions of p₂.

2. Write down the budget constraint of each consumer.

3. Derive Ann's demand function of good 1, x₁^*A(1, p₂).

4. Derive Bob's demand function of good 1, x₁^*B(1, p₂).

5. Find the competitive price vector (1, p₂^*).

Recall: f(y) = √(-y) ⇒ df/dy = 1/(2√-y) · (-1) .

Note - Need detailed solution. Step by Step Approach on how reached a solution.

Reference no: EM132286608

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