Assume that the production function has the following CES (constant elasticity of substitution) form Yt A K t 1 (1 )N 1 1 (a) Prove that this production function features constant returns to scale (b) Compute the first partial derivatives with respect to Kt and Nt Argue that these are positive (c) Compute the own second partial derivatives with respect to Kt and Nt Show that these are both negative (d) As 1, how do the first and second partial derivatives for this pro duction function compare with the Cobb Douglas production discussed in the text (e) Does function satisfy the assumption that labor and capital are essential goods in production process If so, then for what values do so, if at all

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Question: Assume that the production function has the following CES (constant elasticity of substitution) form: Yt = A[K t 1/ + (1 )N 1/ ] /1

Assume that the production function has the following CES (constant elasticity of substitution) form:

Yt = A[K_t^1/ + (1 )N^1/ ]^/1

(a) Prove that this production function features constant returns to scale.

(b) Compute the first partial derivatives with respect to Kt and Nt. Argue that these are positive.

(d) As 1, how do the first and second partial derivatives for this pro-

duction function compare with the Cobb-Douglas production discussed in the text?

(e) Does function satisfy the assumption that labor and capital are essential goods in production process? If so, then for what values do so, if at all?

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