Question

6. In the market for millet, the demand curve is Q=50-3P and the supply curve is Q=2P. The government decides to raise revenue by taxing consumers $5/3 for every bag of millet purchased. The price is measured in cedi per bag; and, quantity is in 'number of bags'. Use this information to answer questions 6(a) to 6(d).

a) Graph the supply and demand curves and indicate the deadweight loss, tax revenue, consumer and producer surplus while the tax policy is in place. 

b) How much tax revenue is this policy going to generate for government?

c) What proportion of the tax is paid by consumers?

d) Calculate the deadweight loss due to the tax policy.

Answer 1

a)

$Qd=Qs\\50-3p=2p\\5p=50\\p=10\\Q=2(10)=20\\$

after tax

$p=\frac{50}{3}-\frac{Q}{3}-\frac{5}{3}\\=15-\frac{Q}{3}$

$Qd=Qs\\15-\frac{Q}{3}=0.5Q\\Q=18\\P=9$

deadweight loss will be area BCD

$\frac{1}{2}\times 2\times \frac{32}{3}=\frac{5}{3}$

tax revenue will be area EDBA

$18\times (\frac{32}{3}-9)=30$

consumer surplus  will be area DEG

$\frac{1}{2}\times(\frac{50}{3}-\frac{32}{3})\times 18=54$

producer surplus  will be area FAB

$\frac{1}{2}\times 18\times9=81$

b)

tax revenue will be area EDBA

$18\times (\frac{32}{3}-9)=30$

c)

proportion of tax paid by consumers

$\frac{32}{3}-10=\frac{6}{10}$

d)

deadweight loss will be area BCD

$\frac{1}{2}\times 2\times \frac{32}{3}=\frac{5}{3}$