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4. [2.5 marks] A firm produces two outputs, which it sells into perfectly competitive markets. It uses one input, which is available in fixed supply.

4. [2.5 marks] A firm produces two outputs, which it sells into perfectly competitive markets. It uses one input, which is available in fixed supply. Each output is produced according to a strictly concave production function. a. Formulate and solve the problem of the optimal allocation of the input between the two outputs. Find an expression or value for the increase in profit that would result from a small increase in the amount of the fixed input the firm has available.

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