A firm can allocate its labour force between two factories that produce two different goods. The...

   

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A firm can allocate its labour force between two factories that produce two different goods. The production function of the first factory, which produces good A, is QA = √I. The production function of the second factory, which produces good B, is qB = 2√ī. The firm can sell q units of good A at a price of PA 15 - A and they can sell q units of good B at a price of PB = 30 - 2qB. The firm has a total labour force of L 100 available. = = (a) How much revenue does the firm earn if they allocate LA units of labour to the first factory and the remaining LB units to the other factory? 5 marks (b) What constraint is the firm facing? (c) Write down a Lagrangian that represents the firm's constrained optimization their goal is to allocate their labour force to maximize their revenues. 2 marks problem if 2 marks (d) What are the optimal quantities of labour LA and LB for the firm to allocate to their two factories? Show that this is a global maximum. 6 marks A firm can allocate its labour force between two factories that produce two different goods. The production function of the first factory, which produces good A, is QA = √I. The production function of the second factory, which produces good B, is qB = 2√ī. The firm can sell q units of good A at a price of PA 15 - A and they can sell q units of good B at a price of PB = 30 - 2qB. The firm has a total labour force of L 100 available. = = (a) How much revenue does the firm earn if they allocate LA units of labour to the first factory and the remaining LB units to the other factory? 5 marks (b) What constraint is the firm facing? (c) Write down a Lagrangian that represents the firm's constrained optimization their goal is to allocate their labour force to maximize their revenues. 2 marks problem if 2 marks (d) What are the optimal quantities of labour LA and LB for the firm to allocate to their two factories? Show that this is a global maximum. 6 marks

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