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The questions presented are about market equilibrium in economics, specifically dealing with supply and demand functions, as well as government interventions through taxes and subsidies. I’ll break down each question to explain how to approach solving them.

### Solutions Outline

1. **Problem 1**
   - Demand function: \( 2Q = 10 - P \)
   - Supply function: \( 3Q = 2P - 2 \)
   - To find equilibrium without intervention, set the demand equal to supply. 
   - To incorporate a tax of Rp 2 per unit, adjust the supply function by increasing the price by 2.
   - For a subsidy of Rp 1 per unit, adjust the supply by reducing the price by 1.

2. **Problem 2**
   - Demand function: \( P - 12 + 2Q = 0 \)
   - Supply function: \( 3 + Q - P = 0 \)
   - Set the demand equal to the supply to find the equilibrium price and quantity.
   - Then apply a Rp 1 subsidy by adjusting the supply function.

3. **Problem 3**
   - Demand function: \( P_d = 200 - 20Q^2 \)
   - Supply function: \( P_s = 75 + 3Q^2 \)
   - For the subsidy, reduce the supply price by 55 per unit.

4. **Problem 4**
   - Demand function: \( P = 4 - Q^3 \)
   - Supply function: \( P = \sqrt{4 + Q} \)
   - Set the functions equal and solve for equilibrium, then apply a Rp 2 subsidy to the supply.

5. **Problem 5**
   - Demand function: \( P = 15 - Q \)
   - Supply function: \( P = 3 + 0.5Q \)
   - Find equilibrium and apply a 1.5 subsidy per unit to the supply function.

6. **Problem 6**
   - Demand function: \( P_d = 40 - Q^2 \)
   - Supply function: \( P_s = 70 + Q^2 \)
   - Calculate the equilibrium and apply a 15 per unit tax.

7. **Problem 7**
   - Demand function: \( P = 10 - 2Q \)
   - Supply function: \( P = 10Q - 2 \)
   - First find equilibrium, then adjust for a Rp 6 tax and Rp 6 subsidy.

8. **Problem 8**
   - Demand function: \( P = 10 - 4Q \)
   - Supply function: \( 3Q = 24P - 22 \)
   - Solve for equilibrium, adjust for Rp 12 tax and Rp 10 subsidy.

Let me know if you would like a detailed solution for any specific question! 

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### Further Questions
1. How does adding a tax affect the supply function in each scenario?
2. What is the effect of a subsidy on the equilibrium quantity and price?
3. How would you graph the new supply and demand functions after a tax or subsidy is applied?
4. What is the economic interpretation of shifting the supply function vertically due to subsidies or taxes?
5. How does the shape of nonlinear demand and supply functions, like \( Q^2 \) or \( Q^3 \), impact the equilibrium?

#### Tip:
When adjusting for a tax, increase the supply price by the tax amount. For a subsidy, decrease it by the subsidy amount.

Calculate market equilibrium under different tax and subsidy scenarios for various supply and demand functions.

Explore step-by-step solutions to market equilibrium problems involving taxes and subsidies. Learn to apply supply and demand functions to find equilibrium points under various scenarios. Ideal for undergraduate economics students.

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