Question

Suppose demand and supply are given by

𝑄 = 500-2P and 𝑄 =-100+3P

a) Which function is the demand function andwhy?

b) Compute the equilibrium price and quantity in thismarket?

c) Compute the consumer surplus and producersurplus.

d) Suppose a GHC 1 exercise tax is imposed on the good. Determine the new

equilibrium price and quantity.

e) Compute the tax revenue to the government.

f) Compute the deadweight loss resulting from the tax.

Answer 1

a)

The demand function is 500-2p

This is because it has a negative slope

b)

$Qd=Qs\\500-2p=-100+3p\\500+100=3p+2p\\600=5p\\p=120$

$Qd=500-2(120)=260\\Qs=-100+3(120)=260$

Therefore, pe=120 and Qe=260

c)

Consumer surplus

$0=500-2p\\2p=500\\p=250\\ \frac{1}{2}\times260\times(250-120)\\=16,900$

producer surplus

$0=-100+3p\\p=\frac{100}{3}\\=33.33\\\frac{1}{2}\times260\times(120-33.33)\\=11,267.6$

d)

$Qd=500-2P\\Qs=-100+3P$

After imposition of tax

$Qd=500-2(P+1)\\ Qs=-100+3(P-1)$

Thus,

$500-2(P+1)=-100+3(P-1)\\ 500-2P-2=-100+3P-3\\ 600=5P-1\\ 601=5P\\ P=\frac{601 }{5}=120.2\\ Q=500-2(120.2+1)\\ Q=500-2(121.2)\\ Q=500-242.4\\ Q=257.6$

e)

The revenue is the total amount of exercise tax collected by the government on the sale of the good.

Revenue$= \$1\times257.6=\$257.6$

f.

The deadweight loss would be the lost surplus which would neither be received by the producers nor the consumers.

$Deadweight\space Loss=0.5*(121.2-120)*(260-257.6)\\ Deadweight\space Loss=0.5*(1.2)*(2.4)\\ Deadweight\space Loss=0.5*(2.88)\\ Deadweight \space Loss=1.44$