1. **State the problem:** We are given the demand function $$Q_{dx} = 10000 - 2p_x + 2m - 5p_y + 2.5t_f - 1t + 3a$$ with values $$p_x=10, m=50, p_y=5, t_f=6, t=4, a=50$$. We need to find the quantity demanded of good x, analyze the relationship between goods x and y, classify good x, and determine the effect of a tax increase by 10 on demand. 2. **Calculate the quantity demanded of x:** Substitute the given values into the demand function: $$Q_{dx} = 10000 - 2(10) + 2(50) - 5(5) + 2.5(6) - 1(4) + 3(50)$$ Calculate step-by-step: $$= 10000 - 20 + 100 - 25 + 15 - 4 + 150$$ $$= 10000 + ( -20 + 100 - 25 + 15 - 4 + 150 )$$ $$= 10000 + 216 = 10216$$ 3. **Relationship between good x and y:** The coefficient of $$p_y$$ is $$-5$$, which is negative. This means as the price of good y increases, the demand for good x decreases. Therefore, goods x and y are **complements**. 4. **Type of good x:** The coefficient of income $$m$$ is $$+2$$, which is positive. This means as income increases, demand for x increases, so good x is a **normal good**. 5. **Effect of tax increase by 10:** The tax $$t$$ coefficient is $$-1$$, so increasing tax by 10 decreases demand by $$1 \times 10 = 10$$ units. New demand after tax increase: $$Q_{dx,new} = 10216 - 10 = 10206$$ **Final answers:** - Quantity demanded: $$10216$$ - Goods x and y are complements - Good x is a normal good - Demand decreases by 10 units if tax increases by 10