Consider the following specific CES production function defined on x₁ > 0, x₂ > 0: y = f(x₁.x₂) = [0.3x₁² +0.7x₂²]-¹/² (a) Find an expression for the MRTS, and show that isoquants are strictly convex to the origin. (b) Use the determinant condition in theorem 11.12 to show that f is quasiconcave. (e) Show that f is concave.
Consider the following specific CES production function defined on x₁ > 0, x₂ > 0: y = f(x₁.x₂) = [0.3x₁² +0.7x₂²]-¹/² (a) Find an expression for the MRTS, and show that isoquants are strictly convex to the origin. (b) Use the determinant condition in theorem 11.12 to show that f is quasiconcave. (e) Show that f is concave.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![9. Consider the following specific CES production function defined on x > 0,
x₂ > 0:
y = f(x₁.x₂) = [0.3x₁² +0.7x₂²]-1/2
(a) Find an expression for the MRTS, and show that isoquants are strictly
convex to the origin.
(b) Use the determinant condition in theorem 11.12 to show that f is
quasiconcave.
Show that f is concave.
(e)
(d)
(e)
Show that f is homogeneous, and find its degree of homogeneity..
Show that the following result (from Euler's theorem) applies to f
f₁x₁ + f2x₂ = kf (x₁, x₂)
where k is the degree of homogeneity of f.
(f) Use the formula given in definition 11.9 to find the elasticity of sub-
stitution between the inputs for this function.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F122f4fbe-aced-454d-b5ff-0f989b154deb%2F4698332f-1275-439f-91b7-42bc82c09afd%2Fowx9x2b_processed.jpeg&w=3840&q=75)
Transcribed Image Text:9. Consider the following specific CES production function defined on x > 0,
x₂ > 0:
y = f(x₁.x₂) = [0.3x₁² +0.7x₂²]-1/2
(a) Find an expression for the MRTS, and show that isoquants are strictly
convex to the origin.
(b) Use the determinant condition in theorem 11.12 to show that f is
quasiconcave.
Show that f is concave.
(e)
(d)
(e)
Show that f is homogeneous, and find its degree of homogeneity..
Show that the following result (from Euler's theorem) applies to f
f₁x₁ + f2x₂ = kf (x₁, x₂)
where k is the degree of homogeneity of f.
(f) Use the formula given in definition 11.9 to find the elasticity of sub-
stitution between the inputs for this function.
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