1. **State the problem:** We have the demand function $$Q_{dx} = 10000 - 2p_x + 2m - 5p_y + 2.5t_f - 1t + 3a$$ where $Q_{dx}$ is quantity demanded of good x. Given values: $p_x=10$, $m=50$, $p_y=5$, $t_f=6$, $t=4$, $a=50$. We need to find: 1. Quantity of x bought. 2. Relationship between good x and y. 3. Type of good x. 4. Effect on demand if tax $t$ increases by 10. 2. **Calculate quantity demanded with given values:** Substitute 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: $$= 10000 - 20 + 100 - 25 + 15 - 4 + 150$$ $$= 10000 + ( -20 + 100 - 25 + 15 - 4 + 150 )$$ $$= 10000 + 216 = 10216$$ So, quantity demanded $Q_{dx} = 10216$ units. 3. **Relationship between good x and y:** Coefficient of $p_y$ is $-5$ (negative). Since demand decreases when price of y increases, goods x and y are **complements**. 4. **Type of good x:** Coefficient of income $m$ is $+2$ (positive). Since demand increases as income increases, good x is a **normal good**. 5. **Effect of increasing tax $t$ by 10:** Original tax $t=4$, new tax $t=14$. Change in tax $= 14 - 4 = 10$. Effect on demand due to tax change: $$ ext{Change in } Q_{dx} = -1 imes 10 = -10$$ Demand decreases by 10 units. New quantity demanded: $$Q_{dx,new} = 10216 - 10 = 10206$$ **Final answers:** 1. Quantity demanded = $10216$ units. 2. Goods x and y are complements. 3. Good x is a normal good. 4. Increasing tax by 10 decreases demand by 10 units, new demand is $10206$ units.