Question

Suppose that the market for a product is characterized by a downward-sloping, linear demand curve and an upward-sloping, linear supply curve.
(a) Suppose the price elasticity of supply is 0.6. Will the deadweight loss from a $2 tax per unit be smaller if the absolute value of the price elasticity of demand is 0.3 or if the absolute value of the price elasticity of demand is 1.5? Explain.
(b) If a $2 tax per unit results in a deadweight loss of $100, how large would be the deadweight loss from a $4 tax per unit? Explain.

Answer 1

Answer:

A) The deadweight loss will be greater when the absolute value of price elasticity of demand = 0.3

B) The deadweight loss is bigger when the value of Nd is larger and also

since a $2 tax per unit results in a deadweight loss of $100 the deadweight loss for a $4 tax per unit will be 2 times larger  i.e. $200

Explanation:

A) Given

price elasticity of supply (Ns)= 0.6

absolute value of elasticity (Nd) = 0.3

absolute value of elasticity 2 ( Nd ) = 1.5

we will apply the deadweight rule here

DWL = -0.5*(Ns Nd)/(Ns - Nd ) * (t^2) * Q/P

For;

( Nd = 0.3 ) = -0.5*( 0.6*0.3) / (0.6-0.3 ) * 2^2

                  = - 0.5 * ( 0.18 / 0.3 ) * 4 = -1.2

( Nd = 1.5 ) = -0.5*(0.6*1.5 )/( 0.6 - 1.5 ) * 2^2

                 = -0.5 * ( 0.9 ) / (-0.9) * 4 = 2

The deadweight loss will be greater when the absolute value of price elasticity of demand = 0.3

B) The deadweight loss is bigger when the value of Nd is larger and also

since a $2 tax per unit results in a deadweight loss of $100 the deadweight loss for a $4 tax per unit will be 2 times larger  i.e. $200