The Leontief production equation xIC1d is usually accomanied

The Leontief production equation, x=(I-C)^-1d, is usually accomanied by a dual price equation, p=C^tp+v, where p is the price vecctor and v is the value added vector.

a Show that (I-C^t)=I-C^t. Hint D=C^t and (A+B)^t=A^t+B^t

bUse the Leontief equation, the dual price equation, and (a) to show that p^td=v^tx

Solution

The Leontief production equation, x=(I-C)-1d, is usually accomanied by a dual price equation, p=Ctp+v, where p is the price vecctor and v is the value added vector.

a Show that (I-Ct)=I-Ct. Hint D=Ct and (A+B)t=At+Bt