To solve this problem, let's proceed by analyzing the demand and supply functions and determining the tax revenue.

Given Information

1. Demand Function: $2P + 2Q = 30$
2. Supply Function: $P - 3 = \frac{1}{2}Q$
3. Tax: The government imposes a tax of Rp 3 per unit.

Steps to Solve

1. Simplify the Demand and Supply Functions

• Rewrite the demand function to express $Q$ in terms of $P$: $2P + 2Q = 30 \Rightarrow P + Q = 15 \Rightarrow Q = 15 - P$
• Rewrite the supply function to express $Q$ in terms of $P$: $P - 3 = \frac{1}{2}Q \Rightarrow Q = 2(P - 3) \Rightarrow Q = 2P - 6$

2. Determine Equilibrium Without Tax

• Set the demand and supply equations equal to each other to find the equilibrium price and quantity: $15 - P = 2P - 6$ $21 = 3P \Rightarrow P = 7$ Substitute $P = 7$ back into one of the equations to find $Q$: $Q = 15 - 7 = 8$
• Therefore, the equilibrium price without tax is $P = 7$ and equilibrium quantity is $Q = 8$.

3. Determine New Equilibrium with Tax

• When a tax of Rp 3 is imposed, the supply function shifts vertically upwards by 3 units. The new supply price becomes $P + 3$.
• The adjusted supply equation is: $P + 3 - 3 = \frac{1}{2}Q \Rightarrow P + 3 = \frac{1}{2}Q$ Rewrite this