Answer to Question #42146 in Microeconomics for adura

Question

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.

Answer 1

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.