Answer to Question #201742 in Microeconomics for Mavis

Question

Suppose the demand and supply are given by Q=500 - 2P and Q =100 - 3P

A. Which function is demand function and why.

B. Computer the equilibrium price and quantity.

C. Compute the consumer surplus and producer surplus.

D. Suppose a 1 Ghana cedis 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 equation is

$Q =500-2P$

This is because the slope is negative

B.

$Qs=Qd\\500-2P=100+3P\\500-100=3P+2P\\400=5P\\P=80$

$Qd=500-2(80)=340\\Qs=100+3(80)=340$

Therefore, P=80 and Q=340

C.

Consumer surplus

$0=500-2P\\2P=500\\P=250\\\frac{1}{2}\times340\times (250-80)\\=28,900$

Producer surplus

$0=100+3P$

$P=\frac{-100}{3}=-33.33$

$\frac{1}{2}\times340\times(80+33.33)\\=19,266.1$

D.

he imposition of the exercise tax would result in the imposition of the tax on the sale of the good or the service. The exercise tax would result in the reducing the price for the producers and increasing the price for the consumers.

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

After imposition of tax

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

Thus,

$500-2(P+1)=100+3(P-1)\\ 500-2P-2=100+3P-3\\ 400=5P-1\\ 401=5P\\ P=401/5=80.2\\ Q=500-2(80.2+1)\\ Q=500-2(81.2)\\ Q=500-162.4\\ Q=337.6$

E.

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

Revenue$= \$1\times337.6=\$337.6$

F.

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

$Deadweight\space Loss=0.5*(81.2-80)*(340-337.6)\\ Deadweight\space Loss=0.5*(1.2)*(2.4)\\ Deadweight\space Loss=0.5*(2.88)\\ Deadweight \space Loss=1.44$