Question #42146

The production function for a product is given by Q=100KL. If the price of labor is $30 per day and the price of capital is $20 per day, what is the minimum cost of producing 1000 units of output? Use alternatively three methods (substitution, equal slopes, and lagrange) to solve the problem.

Expert's answer

If production function for a product is given by Q=100KL and Q = 1000 units, so 100KL = 1000, KL = 10

As the price of labor is $30 per day and the price of capital is $20 per day, the cost will be minimal, if we use less labor and more capital, so K = 10, L = 1

So, the minimum cost will be TCmin = 30*1+ 20*10 = $230.

As the price of labor is $30 per day and the price of capital is $20 per day, the cost will be minimal, if we use less labor and more capital, so K = 10, L = 1

So, the minimum cost will be TCmin = 30*1+ 20*10 = $230.

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