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Question: 2. (MRTS, Marginal Products, Returns to Scale) (50 points)For each of the production functions b...

2. (MRTS, Marginal Products, Returns to Scale) (50 points)

For each of the production functions below, solve for the
marginal rate of technical sub- stitution. Does the production
function exhibit diminishing marginal product of labor? What
returns to scale does it exhibit? (you must discuss how your
answers depend on the value of the relevant parameters)

(a) Q = AK^αL^β for some constants A, α, β > 0,

(b) Q = (K^-θ + L^-θ) for θ > -1,

(c) Q = K + L + √KL.

Show transcribed image text 2. (MRTS, Marginal Products, Returns to Scale) (50 points) For each of the production functions below, solve for the marginal rate of technical sub- stitution. Does the production function exhibit diminishing marginal product of labor? What returns to scale does it exhibit? (you must discuss how your answers depend on the value of the relevant parameters) (a) Q B for some constants A, a, B 0, (b) Q (K-0 L-0) 3 for -1,

2. (MRTS, Marginal Products, Returns to Scale) (50 points) For each of the production functions below, solve for the marginal rate of technical sub- stitution. Does the production function exhibit diminishing marginal product of labor? What returns to scale does it exhibit? (you must discuss how your answers depend on the value of the relevant parameters) (a) Q B for some constants A, a, B 0, (b) Q (K-0 L-0) 3 for -1,