1. Initial Equilibrium (Before Tax)

Given the demand and cost curves:

• Demand Curve: \( p = 200 - 8q \)
• Cost Curve: \( C = 25 + 10q \)

The monopolist maximizes profit where Marginal Revenue (MR) equals Marginal Cost (MC).

Revenue (R): \( R = p \times q = (200 - 8q)q = 200q - 8q^2 \)

Marginal Revenue (MR): \( MR = \frac{dR}{dq} = 200 - 16q \)

Marginal Cost (MC): \( MC = \frac{dC}{dq} = 10 \)

Equating \( MR = MC \):

\[ 200 - 16q = 10 \]

Solving for \( q \):

\[ 16q = 190 \quad \Rightarrow \quad q = \frac{190}{16} = 11.875 \]

Substitute \( q = 11.875 \) into the demand curve to find \( p \):

\[ p = 200 - 8(11.875) = 200 - 95 = 105 \]

Initial Equilibrium: Quantity = 11.875, Price = 105

2. Effect of Per-Unit Tax of 10

When a per-unit tax of 10 is imposed, the new Marginal Cost becomes:

New MC: \( MC = 10 + 10 = 20 \)

Equating \( MR = MC \) with the new MC:

\[ 200 - 16q = 20 \]

Solving for \( q \):

\[ 16q = 180 \quad \Rightarrow \quad q = \frac{180}{16} = 11.25 \]

Substitute \( q = 11.25 \) into the demand curve to find the new price \( p \):

\[ p = 200 - 8(11.25) = 200 - 90 = 110 \]

New Equilibrium with Per-Unit Tax: Quantity = 11.25, Price = 110

3. Effect of 18% Specific Sales Tax

A specific sales tax of 18% implies the price consumers pay increases by 18% of the price charged by the monopolist. Thus, the price paid by the consumer is \( p_t = p(1 + 0.18) = 1.18p \).

The new demand curve becomes:

\[ 1.18p = 200 - 8q \]

The monopolist will adjust the price to reflect the tax. The equilibrium will be similar to the per-unit tax, where the price consumers pay will be higher due to the sales tax.

Conclusion

For the Per-Unit Tax of 10: The equilibrium quantity decreases to 11.25, and the equilibrium price increases to 110.

For the 18% Sales Tax: The price paid by consumers increases by 18% over the monopolist's price, leading to a similar effect on equilibrium price and quantity.