Chapter 2.6, Problem 11E

The Leontief production equation, x = Cx + d, is usually accompanied by a dual price equation.

p = C^T p + v

where p is a price vector whose entries list tire price per unit for each sector’s output, and v is a value added vector whose entries list the value added per unit of output. (Value added includes wages, profit, depreciation, etc.) An important fact in economics is that the gross domestic product (GDP) can be expressed in two ways:

{gross domestic product} = p^Td = v^Tx

Verify the second equality. [Hint: Compute p^Tx in two ways.]