1. **Problem statement:** Determine the exchange table for the economy with three sectors: Agriculture, Mining, and Manufacturing, given the percentages of output traded among them. 2. For Agriculture: It sells 5% to Mining, 30% to Manufacturing, and retains the rest. So, Agriculture retains $100\%-5\%-30\% = 65\%$ of its output. 3. For Mining: It sells 20% to Agriculture, 70% to Manufacturing, and retains $100\%-20\%-70\% = 10\%$ of its output. 4. For Manufacturing: It sells 20% to Agriculture, 30% to Mining, and retains $100\%-20\%-30\% = 50\%$ of its output. 5. The exchange table columns represent sectors' outputs and rows represent how these outputs are distributed: $$\begin{bmatrix} \text{Agriculture to Agriculture} & \text{Mining to Agriculture} & \text{Manufacturing to Agriculture} \\ \text{Agriculture to Mining} & \text{Mining to Mining} & \text{Manufacturing to Mining} \\ \text{Agriculture to Manufacturing} & \text{Mining to Manufacturing} & \text{Manufacturing to Manufacturing} \end{bmatrix} = \begin{bmatrix} 0.65 & 0.20 & 0.20 \\ 0.05 & 0.10 & 0.30 \\ 0.30 & 0.70 & 0.50 \end{bmatrix}$$ 6. Each element $a_{ij}$ is the fraction of output sector $j$ sells to sector $i$. **Final answer:** $$\begin{bmatrix} 0.65 & 0.20 & 0.20 \\ 0.05 & 0.10 & 0.30 \\ 0.30 & 0.70 & 0.50 \end{bmatrix}$$