JNU SSS 2019 - Question 30 (Solution)

Suppose a tax of $ \$5$ per unit is imposed on a good, and the tax causes the equilibrium quantity of good to decrease from 200 units to 100 units. Th tax decreases consumer surplus by $ \$450$ and decreases producer surplus by $ \$300$. The dead-weight loss from the tax is:
Given,
Tax per unit of good $= \$5$ per unit
Pre-tax Equilibrium quantity $=200$ units
Post-tax Equilibrium quantity $=100$ units

Dead-Weight Loss (DWL)

Dead-weight Loss is given by the area of the triangle $ABC$, 
$$DWL=\frac{1}{2} \times Base \times Height \\ = \frac{1}{2} \times (200-100) \times (5) \\ =250$$

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