There are two households (B and C) and there are two companies (1 and 2). Company...

 

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There are two households (B and C) and there are two companies (1 and 2). Company 1 produces Good 1 and company 2 produces Good 2. Labor L is the only input to production. Goods prices are p₁ and P2. Wage is w = 1. Their utility functions are as follows: u³ (x₁, x₂) = x²x₂ u²(x₁, x₂) = x₁x₂ Their production functions are as follows: x₁ =√₁₂ x₂ = 3√1₂ Household B provides 3 units of labor while Household C provides 6 units of labor. (LB=3 and LC-6) Household B owns 1/3 and Household C owns 2/3 of both firms. 2 0² = 13,0² = 13,05 = 1²3,0£ 02 02 - P₁ Calculate MRS 2, MRS 2, MRT 12, 2 2 W|N 1.Calculate/derive the labor demand for each firm by solving its profit maximization given p₁ and p₂. 2.Calculate/derive income of each household. 3.Calculate/derive Walrasian equilibrium of the economy, that is, equilibrium prices (p*1 and p 2) and equilibrium resource allocations (x2*,x²*), (x{*, x2*),(x₁, L₁), (x₂, L₂) 4.If allocation is Pareto optimal, that is, MRS2 = MRS2 = MRT₁2 P₁ P2 There are two households (B and C) and there are two companies (1 and 2). Company 1 produces Good 1 and company 2 produces Good 2. Labor L is the only input to production. Goods prices are p₁ and P2. Wage is w = 1. Their utility functions are as follows: u³ (x₁, x₂) = x²x₂ u²(x₁, x₂) = x₁x₂ Their production functions are as follows: x₁ =√₁₂ x₂ = 3√1₂ Household B provides 3 units of labor while Household C provides 6 units of labor. (LB=3 and LC-6) Household B owns 1/3 and Household C owns 2/3 of both firms. 2 0² = 13,0² = 13,05 = 1²3,0£ 02 02 - P₁ Calculate MRS 2, MRS 2, MRT 12, 2 2 W|N 1.Calculate/derive the labor demand for each firm by solving its profit maximization given p₁ and p₂. 2.Calculate/derive income of each household. 3.Calculate/derive Walrasian equilibrium of the economy, that is, equilibrium prices (p*1 and p 2) and equilibrium resource allocations (x2*,x²*), (x{*, x2*),(x₁, L₁), (x₂, L₂) 4.If allocation is Pareto optimal, that is, MRS2 = MRS2 = MRT₁2 P₁ P2

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To solve the given problem lets go step by step Labor Demand for Each Firm To maximize profit each firm will hire labor until the marginal productivity of labor equals the wage rate The production fun... View the full answer