Burden of taxation in supply and demand Model

The aim of this post is to analyze what happens to the quantity of goods produced and the market equilibrium price when the government imposes a tax supply. In addition, we will analyse the “burden” that is placed on consumers and suppliers.

The first thing we need to do is determine what the original equilibrium price and quantities.

Let’s consider an example where the demand curve is specified as follows:

QD = 10 – P

The supply curve before the subsidy has been implemented is defined as:

Qs = P

In this case we know that the market equilibrium is here supply equals demand. This is the same as saying that the quantity demanded (QD) and quantity supplied (Qs). This implies:

10 – P = P
10 = 2P
P = 5

We can now find the quantity that is consumed/produced in equilibrium by substituting our equilibrium price back into either the supply or demand function. It can trivially be seen that

Q = 5

By substituting the price back into the Qs (quantity supplied) equation.

Introducing a tax

Now consider the case the tax (t) = 2. In this case suppliers only receive price minus the tax. We should define a new “price” as follows:

Pt = P – T
Pt = P - 2

Therefore, we can now write our quantity supply equation becomes:

Qs = Pt
Qs = P - 2

The market equilibrium in this case can be solved in the similar manner as it was above:

10 – P = P - 2
P = 6
Q = 4

It might be of interest to see the overall size of the tax collected by the government. Recall, that the government pays the subsidy for each unit sold. Therefore, the overall amount paid by the government is:

T * Q

Therefore the total amount paid by the government is $12. There are a few things worth noting

  • The price increases by less than the size of the tax
  • The tax leads to a decrease in quantity being produced

This leads to the next interesting question. How is the burden shared between consumers and firms (suppliers). First we need to define what is “burden”. For a consumer (demand), burden is defined as:

Burden = (Price paid after the introduction of the tax) – (Equilibrium Price before tax)

Applying this definition to calculate burden yields:

Burden = $6 –$5
Burden = $1

For a firm (supply), the burden is slightly different and is defined as:

Burden = (Equilibrium Price before tax) - (Price received after tax)
Price received after tax = Price in equilibrium with tax – tax
Price received after tax = $6 – $2
Price received after tax = $4

Now to calculate burden:

Burden = $5 –$4
Burden = $1

It is worth noting that the overall burden should equal up to the tax since the burden is the measurement of how tax is shared among suppliers and consumers.

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