In: Economics
A firm uses two inputs, labor and capital, to produce a good. To keep up with the story, let zℓ ≥ 0 denote the units of labor and zk ≥ 0 the units of capital. The firm’s technology is expressed as a production function f(zℓ, zk) = 20 z1/5 ℓ z3/5 k . Let w > 0 and r > 0 be the cost of hiring a unit of labor and a unit of capital, respectively.
(a) Find the technical rate of substitution between labor and capital.
(b) At which input vector(s) z = (zℓ, zk) will it be equal to 2?