Answered: Consider the following specific CES… | bartleby

Linear Algebra: A Modern Introduction

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 70EQ

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Question

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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