Consider a market where the demand is pD = 200 – 2Q while the supply is pS = 50 + Q (same as in the previous question). Calculate the deadweight-loss (DWL) if the government introduces a price cap at p = 80.

To calculate the deadweight loss (DWL) due to a price cap, we first need to find the quantity demanded and supplied at the price cap, and the quantity at equilibrium without the price cap.

1. Set the price cap (p) equal to the demand equation (pD) and solve for Q (quantity demanded at the price cap):

   80 = 200 - 2Q 2Q = 200 - 80 2Q = 120 Q = 120 / 2 Q = 60

2. Set the price cap (p) equal to the supply equation (pS) and solve for Q (quantity supplied at the price cap):

   80 = 50 + Q Q = 80 - 50 Q = 30

3. Set the demand equation equal to the supply equation and solve for Q (quantity at equilibrium without the price cap):

   200 - 2Q = 50 + Q 3Q = 200 - 50 3Q = 150 Q = 150 / 3 Q = 50

4. The deadweight loss (DWL) is the area of the triangle formed by the quantity at equilibrium, the quantity demanded at the price cap, and the quantity supplied at the price cap. The formula for the area of a triangle is 1/2 * base * height.

   Base = Quantity demanded at the price cap - Quantity supplied at the price cap = 60 - 30 = 30 Height = Price cap - Price at equilibrium = 80 - 50 = 30

   DWL = 1/2 * 30 * 30 = 450

So, the deadweight loss due to the price cap is 450.

To calculate the deadweight loss (DWL) due to a price cap, we first need to find the quantity demanded and supplied at the price cap, and the quantity at equilibrium without the price cap.

1. Set the price cap (p) equal to the demand equation (pD) and solve for Q (quantity demanded):

   80 = 200 - 2Q 2Q = 200 - 80 2Q = 120 Qd (quantity demanded at price cap) = 120 / 2 = 60

2. Set the price cap (p) equal to the supply equation (pS) and solve for Q (quantity supplied):

   80 = 50 + Q Q = 80 - 50 Qs (quantity supplied at price cap) = 30

3. Set the demand equation equal to the supply equation to find the equilibrium quantity (Qe) and price (Pe) without the price cap:

   200 - 2Q = 50 + Q 3Q = 200 - 50 Qe = 150 / 3 = 50 Pe = 200 - 2*50 = 100

4. The deadweight loss (DWL) is the area of the triangle formed by the quantity demanded at the price cap (Qd), the quantity supplied at the price cap (Qs), and the equilibrium quantity (Qe). It represents the loss in total surplus due to the price cap. It can be calculated as:

   DWL = 0.5 * (Qd - Qs) * (Pe - p) DWL = 0.5 * (60 - 30) * (100 - 80) DWL = 0.5 * 30 * 20 DWL = 300

So, the deadweight loss due to the price cap is 300.