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Unformatted text preview: minimizing the cost of producing a vector q when input prices are w , i.e. min w z f ( z ) q where w R M ++ , z R M + , and q R L + . Assume that there is a twice continuously dierentiable solution function z * ( w,q ) to the minimization problem. z * ( w,q ) corresponds to the input vector that minimizes the cost of producing at least q when input prices are w , and is referred to as conditional factor demand . (i) Show that the associated cost function C ( w,q ) = w z * ( w,q ) is homogeneous of degree one in w . (ii) Show that if q q (componentwise) then C ( w, q ) C ( w,q ). (iii) Show that C ( w,q ) is concave in w . (iv) Show that 5 w C ( w,q ) = z * ( w,q ), and use this to show that D w z * ( w,q ) is symmetric and negative semidenite. Can D w z * ( w,q ) be negative denite? 1...
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