Consider that the production function Q= F(K,L) = 3K + 9L
Determine the mix of output that minimizes costs when the wage is $20 and the price of capital is $30.
We have the production function Q= F(K,L) = 3K + 9L This is a Leontief production function and so inputs are used in place of each other also. The MRTS is given by - MUL/MUK which is -9/3 = -3. From the prices we see that wage rental ratio is w/r or 20/30 = 2/3. Now we observe that |MRTS| is 3 and wage rental ratio is 2/3. This indicates that labor is more productive as MUL/MUK > w/r or MUL/w > MUK/r. Hence firm will use only labor and no capital. The optimum production is Q = 9L.
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