Chapter 8 - Part III - Application: The Costs of Taxation - Problems and Applications - Page 170: 10

a) 100 dollars, 200 units demanded and supplied b) The quantity sold is $200-\frac{2}{3}*T$, and the price is $100-\frac{1}{3}*T$. c) $R = T*200-\frac{2}{3}*T$; Please see the first graph for the relationship. d) The deadweight loss is $\frac{T^2}{3}$. e) A tax of 200 dollars is bad since there are better tax levels that would collect more tax and have a lower deadweight loss. At a tax of 150 dollars, tax revenue increases to 15,000 dollars, and the deadweight loss decreases to 7,500 dollars.

a) $Q^{S}=2*P$ $Q^{D}=300-P$ $2*P=300-P$ $2P=300-P$ $2P+P=300-P+P$ $3P=300$ $3P/3=300/3$ $P=100$ $2*P$ $2*100$ $200 = Q^{S} = Q^{P}$ b) $Q^{S}=2*P$ $Q^{D}=300-(P+T)$ $2P=300-P-T$ $2P+P=300-P-T+P$ $3P = 300-T$ $3P/3 = (300-T)/3$ $P = 100-\frac{1}{3}*T$ (price received by sellers) Buyers pay the amount sellers receive and the amount of the tax $P+T = 100-\frac{1}{3}*T+T$ $P+T = 100+\frac{2}{3}*T$ $Q^{S}=2*P$ $Q^{S}=2*P = 2*(100-\frac{1}{3}*T)$ $Q^{S}=200-\frac{2}{3}*T$ c) $Q^{S}=200-\frac{2}{3}*T$ revenue is the tax * quantity $Q^{S}=200-\frac{2}{3}*T$ $R = T*200-\frac{2}{3}*T$ d) The orange line on the first graph is the height of the triangle, $\frac{2T}{3}$. The green line on the first graph is the base of the triangle, $T$. $2/3*T*T*1/2$ $T^2*2/3*1/2$ $1/3*T^2$ The second graph shows the deadweight loss relationship for $T$ between $0$ and $300$. e) tax revenue = tax per item * quantity sold $R = 200 * 200-(2/3)(200)$ $R=200*200-(400/3)$ $R=200*(600/3-400/3)$ $R=200*200/3$ $R=40000/3$ $R=13,333.33$ deadweight loss = $T^2/3$ $DWL = T^2/3$ $DWL = 200^2/3$ $DWL = 40000/3$ $DWL = 13,333.33$ If we reduced the tax to 150 dollars, the tax revenue would be as follows: $150*(200-2/3*T)$ $150*(200-2/3*150)$ $150*(200-100)$ $150*100$ $15000$ Deadweight loss = $T^2/3$ $DWL = 150*150/3$ $DWL = 22500/3$ $DWL =7500$