We are given the market demand and supply functions:

Demand function: \( Q_d = -500P + 5000 \)

Supply function: \( Q_s = 400P - 400 \)

Step 1: Find the initial equilibrium (without tax)

At equilibrium, quantity demanded \( Q_d \) equals quantity supplied \( Q_s \):

\( -500P + 5000 = 400P - 400 \)

Solving for \( P \):

\( 5000 + 400 = 400P + 500P \)

\( 5400 = 900P \)

\( P = \frac{5400}{900} = 6 \)

Now, substitute \( P = 6 \) into either the demand or supply equation to find the equilibrium quantity. Using the demand function:

\( Q_d = -500(6) + 5000 = -3000 + 5000 = 2000 \)

Thus, the initial equilibrium price is \( P = 6 \) and the equilibrium quantity is \( Q = 2000 \).

Step 2: Effect of specific sales tax of 18%

A specific sales tax of 18% means that the price paid by consumers increases by 18% of the price. Let the price received by producers be \( P_s \) and the price paid by consumers be \( P_c \), where:

\( P_c = 1.18P_s \)

Substitute \( P_c = 1.18P_s \) into the demand function and supply function to find the new equilibrium.

Demand function becomes: \( Q_d = -500(1.18P_s) + 5000 \)

Supply function becomes: \( Q_s = 400P_s - 400 \)

At equilibrium, \( Q_d = Q_s \), so:

\( -500(1.18P_s) + 5000 = 400P_s - 400 \)

Simplify and solve for \( P_s \):

\( -590P_s + 5000 = 400P_s - 400 \)

\( 5000 + 400 = 400P_s + 590P_s \)

\( 5400 = 990P_s \)

\( P_s = \frac{5400}{990} = 5.45 \)

Thus, the price received by producers is \( P_s = 5.45 \).

Now, calculate the price paid by consumers \( P_c \):

\( P_c = 1.18 \times 5.45 = 6.43 \)

Step 3: Find the new equilibrium quantity

Substitute \( P_s = 5.45 \) into the supply function:

\( Q_s = 400(5.45) - 400 = 2180 - 400 = 1780 \)

Thus, the new equilibrium quantity is \( Q = 1780 \).

Step 4: Conclusion

- The equilibrium price paid by consumers rises from \( P = 6 \) to \( P_c = 6.43 \).

- The equilibrium quantity decreases from \( Q = 2000 \) to \( Q = 1780 \).

Thus, the imposition of the specific sales tax leads to an increase in the price paid by consumers and a decrease in the equilibrium quantity.