Non decreasing and concave.......homogeneous of degree k

fourwindschill

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Let m(?,y) be defined as the minimum value of ?x subject to g(x)>=y, where ?, X ? Rn++,y ? R+, and g(x) is strictly monotonic increasing and quasi-concave. Prove that m (?,y) is (i) non decreasing in ? and y and (ii) concave in ?. Then, given that g(x) is homogeneous of degree k, derive the corresponding form of m(?,y).
 
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