Production Function Consider a production technology that uses two categories of factor inputs in production. Define K as the amount of capital input, L as the amount of labor input, x as the amount of output. The production function is x = F (K, L) =3K^1/3L^1/3 1. Calculate the marginal product of capital and labor respectively. Confirm that the law of diminishing marginal returns is satisfied. 2. Calculate the marginal rate of technical substitution (MRTS) of labor for capital. Draw an iso quant curve with output to be x0. Confirm that there exists a decreasing marginal marginal rate of technical substitution as L increases. 3.Confirm that this production function exhibits decreasing returns to scale.