Suppose there is a firm producing two commodities with labour (L) and capital (K). The production...

  

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Suppose there is a firm producing two commodities with labour (L) and capital (K). The production functions for the two commodities are given respectively by 1 Q₁ (K₁,L₁) = 2 ln K₁ 1 +In L₁, +=" 1 ln K₂ +3 In L₂. Q2 (K₂, L₂) = Assume that the prices of the two commodities are both equal to one. The firm owns the total amount of labour Lo and total amount of capital Ko. (a) Write down the total revenue function of the firm. (5 marks) (b) Prove that the total revenue function is concave. (8 marks) (c) Find (K₁, L₁, K₂, L₂) which maximizes the total revenue function. (10 marks) (d) If Lo increases by one unit, how much of it will be used to produce commodity one and how much will be used to produce commodity two? (5 marks) Suppose there is a firm producing two commodities with labour (L) and capital (K). The production functions for the two commodities are given respectively by 1 Q₁ (K₁,L₁) = 2 ln K₁ 1 +In L₁, +=" 1 ln K₂ +3 In L₂. Q2 (K₂, L₂) = Assume that the prices of the two commodities are both equal to one. The firm owns the total amount of labour Lo and total amount of capital Ko. (a) Write down the total revenue function of the firm. (5 marks) (b) Prove that the total revenue function is concave. (8 marks) (c) Find (K₁, L₁, K₂, L₂) which maximizes the total revenue function. (10 marks) (d) If Lo increases by one unit, how much of it will be used to produce commodity one and how much will be used to produce commodity two? (5 marks)

Answer rating: 100% (QA)

a The total revenue function of the firm is given by TRKL P1Q1KL P2Q2KL TRKL Q1KL Q2KL TRKL InK 5 In ... View the full answer