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- How would you determine that a two-input Cobb-Douglas production function has decreasing returns to scale (DRS), increasing returns to scale (IRS) or constant returns to scale (CRS) depending on whether α1 + α2 is larger than, smaller than, or equal to one?How would you determine that a two-input Cobb-Douglas production function has decreasing returns to scale (DRS), increasing returns to scale (IRS) or constant returns to scale (CRS) depending on whether β is larger than, smaller than, or equal to one?Suppose the US total output is represented by the standard Cobb-Douglas production function with capital and labor inputs. If all inputs are tripled (and TFP is unchanged), then output per worker Exactly triples B. Increases but not exactly triples C. Is unchanged D. Decreases E. None of the other options
- Consider the simple (one period) production model. The production function is Cobb Douglas, exhibits constant returns to scale, and the exponent on capital equal to 0.25.Show that the two-input Cobb-Douglas production function (attached) has decreasing return in scale (DRS), constant return of scale (CRS) or increasing return of scale (ITS) depending on if alpha1 + alpha2 is smaller than, equal, or larger than 1.The Cobb-Douglas production function can be shown to be a special case of a larger class of linear homogeneous production functions having the following mathematical form: Q=γ[δK−ρ+(1 - δ)L−ρ]−ν/ρ�=�[δK−ρ+(1 - δ)�−ρ]−ν/ρ where γ is an efficiency parameter that shows the output resulting from given quantities of inputs; δ is a distribution parameter (0 ≤ δ ≤ 1) that indicates the division of factor income between capital and labor; ρ is a substitution parameter that is a measure of substitutability of capital for labor (or vice versa) in the production process; and ν is a scale parameter (ν > 0) that indicates the type of returns to scale (increasing, constant, or decreasing). Complete the following derivation to show that when ν = 1, this function exhibits constant returns to scale. First of all, if ν = 1: Q� = = γ[δK−ρ+(1 - δ)L−ρ]−1/ρ�[δK−ρ+(1 - δ)�−ρ]−1/ρ = = γ[δK−ρ(−1/ρ)+(1 - δ)L−ρ(−1/ρ)]�[δK−ρ(−1/ρ)+(1 - δ)�−ρ(−1/ρ)] = = Then, increase the…
- Which of the following equations does not represent a plausible production function? a.F(K,L) = 2KL b.F(K,L) = 2K-2L c.F(K,L) = 2(KL)0.5 d.F(K,L) = KLA19 Subject - economics Consider a constant returns-to-scale production function f(k, l). Show that f(k, l) = k ∂f/ ∂k + l ∂f /∂lThe aggregate production function is Y = 5KL. If there are 18 units of capital and 50 units of labor, the capital productivity is ___________.