Discussion
The production function \(Q = A\,[\beta K^{-a} + \alpha L^{-a}]^{-1/a}\) is homogeneous of degree
Answer: B
The function is the constant elasticity of substitution form, and it is homogeneous of degree one. If both inputs are multiplied by a factor \(\lambda\), the bracket becomes \(\lambda^{-a}\) times the original bracket, because each term contains one input raised to the power \(-a\). Raising to the power \(-1/a\) gives \(\lambda\) times the original output. So \[ Q(\lambda K, \lambda L) = \lambda Q(K, L) \] and the degree is one, option B. Zero, infinity and \(a\) do not follow, since the degree of homogeneity is fixed by the outer exponent matching the inner one.
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