A firm uses two inputs, labor and capital, to produce a good. To keep up with...

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 z^1/5 ℓ z^3/5 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?

Expert Solution

Rahul Sunny answered 2 years ago

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A firm uses two inputs, labor and capital, to produce a good. To keep up with...

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