Question

Suppose the total surplus as a function of q could be written as ts(q) = 1000q-5q2. if the equilibrium quantity is 100 units, find the absolute value of the deadweight loss when the quantity traded equals 50 units.

Answer 1

The deadweight loss when the quantity traded equals 50 units is 12500.

Step-by-step explanation:

Deadweight loss occurs when an economy produces at an inefficient quantity, resulting in a reduction in social surplus. In this case, the deadweight loss is the area U + W. The total surplus as a function of quantity is given by ts(q) = 1000q - 5q^2. To find the deadweight loss when the quantity traded equals 50 units, we need to calculate the difference between the total surplus at the equilibrium quantity (100) and the total surplus at 50 units.

At the equilibrium quantity of 100 units, the total surplus is:


ts(100) = 1000(100) - 5(100^2) = 100000 - 50000 = 50000

At 50 units, the total surplus is:


ts(50) = 1000(50) - 5(50^2) = 50000 - 12500 = 37500

Therefore, the absolute value of the deadweight loss when the quantity traded is 50 units is |50000 - 37500| = 12500.