Question

Suppose the Demand and supply curve for a particular product is as follows:

D(p)=60-5p

S(p)=5p+20

Suppose city council considers implementing a small lump sum tax of $T per unit traded (i.e. if the consumer pays p then the producer receives p-T).

Question: What is the tax incidence on consumers?

Hint 2: The derivative of demand and supply with respect to price is just the slope of the curves, in this case -5, and 5 respectively.

Answer 1

If per unit tax is imposed then tax incidence depend on the demand and supply elasticities.

The intial equilibrium will take place when demand = supply.

D(p) = S(p)

Or, 60 - 5p = 20 + 5p

Or, 10p = 40

Or, p = 40/10 = 4

Equilibrium price is = $4 and quantity is 60 - 5*4 = 40.

Now, if $T per unit of tax is imposed then consumers pay p and producers receive (p - T).

Now, tax borne by the consumer is Es/(Es + Ed)

Elasticity of supply at Equilibrium is = (∆Qs/∆P)*(P/Q)

∆Qs/∆P = 5 (Already given the derivative value of supply function in the question). Equilibrium price and quantity is 4 and 40.

Es = 5*(4/40) = 20/40 = 1/2.

Ed = (∆Qd/∆P)*(P/Q)

Ed = (-5)*(4/40) = -20/40 = -1/2

So, absolute value of elasticity of supply and elasticity of demand both is 1/2.

Incidence of tax on consumer is = Es/(Es + Ed)

= (1/2)/(1/2 + 1/2)

= (1/2)/1 = 1/2 = 50%.

So, if $T tax is imposed on then incidence on consumer is $T*(1/2) = $T/2.

Tax incidence on consumer is half of the lump sum per unit tax.