Questions: A supply function is QS=20+P, and a demand function is QD=100-2P. If the government imposes a 10 per unit tax on consumers, calculate the new equilibrium price and quantity.

To find the new equilibrium price and quantity after a $10 per unit tax on consumers, we need to follow these steps:

1. Understand the original supply and demand functions:

   • Supply function: \( Q_S = 20 + P \)
   • Demand function: \( Q_D = 100 - 2P \)

2. Determine the effect of the tax on the demand function:

   • A $10 tax on consumers means that the price consumers pay is $10 more than the price producers receive. Let \( P_c \) be the price consumers pay and \( P_p \) be the price producers receive.
   • The relationship between \( P_c \) and \( P_p \) is: \( P_c = P_p + 10 \)

3. Adjust the demand function to reflect the tax:

   • The original demand function is \( Q_D = 100 - 2P_c \)
   • Substitute \( P_c = P_p + 10 \) into the demand function: \[ Q_D = 100 - 2(P_p + 10) \] \[ Q_D = 100 - 2P_p - 20 \] \[ Q_D = 80 - 2P_p \]

4. Set the new demand function equal to the supply function to find the new equilibrium:

   • The new demand function is \( Q_D = 80 - 2P_p \)
   • The supply function remains \( Q_S = 20 + P_p \)
   • Set \( Q_D = Q_S \): \[ 80 - 2P_p = 20 + P_p \]

5. Solve for \( P_p \): \[ 80 - 20 = 2P_p + P_p \] \[ 60 = 3P_p \] \[ P_p = 20 \]

6. Find the equilibrium quantity:

   • Substitute \( P_p = 20 \) back into the supply function: \[ Q_S = 20 + 20 = 40 \]

7. Determine the price consumers pay (\( P_c \)):

   • \( P_c = P_p + 10 \)
   • \( P_c = 20 + 10 = 30 \)

Summary:

• The new equilibrium price producers receive (\( P_p \)) is $20.
• The new equilibrium price consumers pay (\( P_c \)) is $30.
• The new equilibrium quantity is 40 units.