Laura runs a nightclub, ‘Two Standard Drinks’. Given the popularity and cache of the club, she has a monopoly position in the market. The market demand curve is given by P = 176–q. Laura has a marginal cost per drink of MC = 4q and a fixed cost FC = $144. If Laura charges the same price to all customers, what is the resulting DWL? [Round your final answer to 2 decimal points when necessary]

To calculate the Deadweight Loss (DWL), we first need to find the quantity and price at the socially optimal point (where Marginal Cost (MC) equals Demand (D)) and the quantity and price at the monopoly point (where Marginal Revenue (MR) equals Marginal Cost (MC)).

1. Set MC = D to find the socially optimal quantity (q) and price (P): MC = D 4q = 176 - q 5q = 176 q = 176 / 5 q = 35.2

   Substitute q into the demand equation to find P: P = 176 - 35.2 P = 140.8

2. To find the monopoly quantity and price, we first need to find the MR. The MR is found by taking the derivative of the total revenue (TR), which is P*q. But since P = 176 - q, TR = (176 - q) * q. The derivative of this is MR = 176 - 2q.

   Set MR = MC to find the monopoly quantity: 176 - 2q = 4q 176 = 6q q = 176 / 6 q = 29.33

   Substitute q into the demand equation to find P: P = 176 - 29.33 P = 146.67

3. The DWL is the area of the triangle formed by the socially optimal and monopoly quantities and prices. The formula for the area of a triangle is 0.5 * base * height.

   The base of the triangle is the difference in quantities: 35.2 - 29.33 = 5.87 The height of the triangle is the difference in prices: 146.67 - 140.8 = 5.87

   DWL = 0.5 * 5.87 * 5.87 DWL = 17.22

So, the resulting Deadweight Loss (DWL) is 17.22.

To calculate the deadweight loss (DWL), we first need to find the monopoly quantity (q) and price (P), and then the socially optimal quantity (q*) and price (P*).

1. Monopoly Quantity and Price: Laura maximizes her profit where Marginal Cost (MC) equals Marginal Revenue (MR). The MR is derived from the demand curve. The demand curve is P = 176 - q, so the total revenue (TR) is P*q = 176q - q^2. The MR is the derivative of TR, which is MR = 176 - 2q.

Setting MC = MR to find the monopoly quantity: 4q = 176 - 2q 6q = 176 q = 176 / 6 q = 29.33

Substitute q into the demand equation to find the monopoly price: P = 176 - 29.33 P = 146.67

2. Socially Optimal Quantity and Price: The socially optimal quantity and price is where the demand curve intersects the MC. Setting P = MC to find the socially optimal quantity: 176 - q = 4q 176 = 5q q* = 176 / 5 q* = 35.2

Substitute q* into the demand equation to find the socially optimal price: P* = 176 - 35.2 P* = 140.8

3. Deadweight Loss: The DWL is the area of the triangle formed by the monopoly quantity, the socially optimal quantity, and the demand curve. The formula for the area of a triangle is 0.5 * base * height.

Base = q* - q = 35.2 - 29.33 = 5.87 Height = P - P* = 146.67 - 140.8 = 5.87

DWL = 0.5 * 5.87 * 5.87 = 17.22

So, the resulting deadweight loss is approximately 17.22.

To calculate the Deadweight Loss (DWL), we first need to find the quantity and price at the socially optimal point (where Marginal Cost equals Demand) and the quantity and price at the monopoly point (where Marginal Revenue equals Marginal Cost).

1. Set up the Demand equation: P = 176 - q
2. Set up the Marginal Cost equation: MC = 4q
3. Set up the Marginal Revenue equation. The Marginal Revenue curve has the same y-intercept as the Demand curve but twice the slope. So, MR = 176 - 2q

Now, find the socially optimal point:

4. Set Demand equal to Marginal Cost: 176 - q = 4q
5. Solve for q: q = 176 / 5 = 35.2
6. Substitute q into the Demand equation to find P: P = 176 - 35.2 = 140.8

Then, find the monopoly point:

7. Set Marginal Revenue equal to Marginal Cost: 176 - 2q = 4q
8. Solve for q: q = 176 / 6 = 29.33
9. Substitute q into the Demand equation to find P: P = 176 - 29.33 = 146.67

Finally, calculate the Deadweight Loss:

10. DWL = 0.5 * (Pm - Ps) * (Qs - Qm)
11. DWL = 0.5 * (146.67 - 140.8) * (35.2 - 29.33) = 1.75

So, the resulting Deadweight Loss is approximately 1.75.