given the demand and supply equations shown below:\n$q_d = 5121 - 13.81 \\times p$\n$q_s = -1757 + 28.8…

given the demand and supply equations shown below:\n$q_d = 5121 - 13.81 \\times p$\n$q_s = -1757 + 28.8 \\times p$\ncalculate the deadweight loss if the market price is 266.12.\n\nthe deadweight loss is $\\square$ (please keep two decimal places)

given the demand and supply equations shown below:\n$q_d = 5121 - 13.81 \\times p$\n$q_s = -1757 + 28.8 \\times p$\ncalculate the deadweight loss if the market price is 266.12.\n\nthe deadweight loss is $\\square$ (please keep two decimal places)

Answer

Explanation:

Step1: Find equilibrium price/quantity

Set $Q_d = Q_s$: $$5121 - 13.81P = -1757 + 28.8P$$ $$5121 + 1757 = 28.8P + 13.81P$$ $$6878 = 42.61P$$ $$P_e = \frac{6878}{42.61} \approx 161.42$$ $$Q_e = 5121 - 13.81*161.42 \approx 5121 - 2229.21 = 2891.79$$

Step2: Find $Q_d$ at given price

Given $P=266.12$, calculate $Q_d$: $$Q_d = 5121 - 13.81*266.12$$ $$Q_d = 5121 - 3675.12 = 1445.88$$

Step3: Find $P_s$ at $Q_d$ level

Set $Q=1445.88$ in supply equation, solve for $P_s$: $$1445.88 = -1757 + 28.8P_s$$ $$28.8P_s = 1445.88 + 1757$$ $$P_s = \frac{3202.88}{28.8} \approx 111.21$$

Step4: Calculate deadweight loss

Deadweight loss is area of triangle: $\frac{1}{2}(P-P_s)(Q_e-Q_d)$ $$\text{Deadweight Loss} = \frac{1}{2}(266.12-111.21)(2891.79-1445.88)$$ $$= \frac{1}{2}154.911445.91$$ $$= \frac{1}{2}*223987.42 \approx 111993.71$$

Answer:

111993.71