Question

Suppose demand and supply are given by 𝑄 = 14 − ଵ ଶ 𝑃 and 𝑄 = ଵ ସ 𝑃 − 1 a) Which function is the demand function and why? b) Compute the equilibrium price and quantity in this market? c) Compute the consumer surplus and producer surplus. d) Compute the elasticity of demand and elasticity of supply at the equilibrium. Assuming an excise tax is imposed, would you expect consumers or producers to bear a greater percentage of the tax? Explain. e) Suppose a GHC 12 exercise tax is imposed on the good. Determine the new equilibrium price and quantity. f) Compute the tax revenue, the shares of the tax paid by the consumer and the producer. g) Compute the consumer surplus, producer surplus and the deadweight loss resulting from the tax.

Answer 1

a)

Given

$Q=14-10p\\ Q=10p-1$

Q=14-10p is the demand function because it has a negative slope .

Q=10p-1 is the demand function because it has a positive slope .

b)

$Qd=Qs\\14-10p=10p-1\\14+1=10p+10p\\15=20p\\p=7.5\\Q=10(7.5)-1 \\Q=74$

C)

Consumer surplus

$0=14-10p\\14=10p\\p=1.4\\\frac{1}{2}×(1.4-7.5)×74=-225.7\\deficit=225.7$

Producer surplus

$0=10p-1\\1=10p\\p=0.1\\\frac{1}{2}×(7.5-0.1)×74\\=273.8$

d)

Elasticity of demand

$=\frac{\Delta Q}{\Delta P}×\frac{P}{Q}\\-10×\frac{7.5}{74}=-1.012$

Elasticity of supply

$=\frac{\Delta Q}{\Delta P}×\frac{P}{Q}\\10×\frac{7.5}{74}=1.012$

Tax will increase price paid by consumers.

e)

Price of consumers will be $=7.5+12=19.5\\so\\Q=10(19.5)-1=194$

f)

$Tax revenue=price ×quantity\\=19.5×194=3783$

g)

Consumer surplus

$\frac{1}{2}×19.5×194=1891.5$

Producer surplus

$\frac{1}{2}×7.5×194=727.5$

Dead weight loss

$1891.5-727.5=1164$