1. **State the problem:** We have the Cobb-Douglas production function $$Q=10L^{0.7}K^{0.3}$$ where $Q$ is output, $L$ is labor, and $K$ is capital. We want to find the approximate percentage change in $Q$ when $L$ increases by 4% and $K$ decreases by 1% using partial differentiation. 2. **Recall the formula:** The total differential of $Q$ is given by $$dQ = \frac{\partial Q}{\partial L} dL + \frac{\partial Q}{\partial K} dK$$ The approximate percentage change in $Q$ is $$\frac{dQ}{Q} \times 100\%$$ 3. **Calculate partial derivatives:** $$\frac{\partial Q}{\partial L} = 10 \times 0.7 L^{0.7-1} K^{0.3} = 7 L^{-0.3} K^{0.3}$$ $$\frac{\partial Q}{\partial K} = 10 \times 0.3 L^{0.7} K^{0.3-1} = 3 L^{0.7} K^{-0.7}$$ 4. **Express $dQ/Q$ in terms of $dL/L$ and $dK/K$:** Using the property of Cobb-Douglas functions, $$\frac{dQ}{Q} = 0.7 \frac{dL}{L} + 0.3 \frac{dK}{K}$$ 5. **Substitute percentage changes:** Given $L$ increases by 4%, so $\frac{dL}{L} = 0.04$ and $K$ decreases by 1%, so $\frac{dK}{K} = -0.01$. Calculate: $$\frac{dQ}{Q} = 0.7 \times 0.04 + 0.3 \times (-0.01) = 0.028 - 0.003 = 0.025$$ 6. **Convert to percentage:** $$0.025 \times 100\% = 2.5\%$$ **Final answer:** The approximate percentage change in $Q$ is an increase of 2.5%.