4. Let the following Cobb Douglas production function with constant returns to scale: 𝑌 = 𝐹(𝐾, &

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4. Let the following Cobb Douglas production function with
constant returns to scale: 𝑌 = 𝐹(𝐾, 𝐿) = 𝐾 𝛼𝐿 1−𝛼 , where 𝑌 defines
output, 𝐾 capital, 𝐿 labour, and 𝛼 ∈ (0,1). Prove that the
(partial) elasticity of output with respect to capital is equal to
𝛼 and that the (partial) elasticity of output with respect to
labour is equal to 1 − 𝛼.