Chapter 7, Problem 14QE

(a)

To determine

Determine the percentage of tax borne by a demander and supplier if Es is 1.2 and ED is 0.3.

Explanation of Solution

If the elasticity of demand is 0.3 and elasticity of supply is 1.2, then the percentage of tax borne by a demander and a supplier is as follows:

$\begin{array}{c}\text{Percentage of tax borne by demander}=\left(\frac{{\text{E}}_{\text{S}}}{\left({\text{E}}_{\text{S}}+{\text{E}}_{\text{D}}\right)}\times 100\right)\\ =\left(\frac{\text{1}\text{.2}}{\left(1.2+0.3\right)}\times 100\right)\\ =80\end{array}$

Thus, the percentage of tax borne by a demander is 80.

$\begin{array}{c}\text{Percentage of tax borne by supplier}=\left(\frac{{\text{E}}_{\text{D}}}{\left({\text{E}}_{\text{S}}+{\text{E}}_{\text{D}}\right)}\times 100\right)\\ =\left(\frac{\text{0}\text{.3}}{\left(1.2+0.3\right)}\times 100\right)\\ =20\end{array}$

Thus, the percentage of tax borne by a supplier is 20.

(b)

To determine

Determine the percentage of tax borne by a demander and a supplier if Es is 2 an ED is 3.

Explanation of Solution

If the elasticity of demand is 3 and elasticity of supply is 2, then the percentage of tax borne by a demander and a supplier can be calculated as follows:

$\begin{array}{c}\text{Percentage of tax borne by demander}=\left(\frac{{\text{E}}_{\text{S}}}{\left({\text{E}}_{\text{S}}+{\text{E}}_{\text{D}}\right)}\times 100\right)\\ =\left(\frac{\text{2}}{\left(2+3\right)}\times 100\right)\\ =40\end{array}$

Thus, the percentage of tax borne by a demander is 40.

$\begin{array}{c}\text{Percentage of tax borne by supplier}=\left(\frac{{\text{E}}_{\text{D}}}{\left({\text{E}}_{\text{S}}+{\text{E}}_{\text{D}}\right)}\times 100\right)\\ =\left(\frac{\text{3}}{\left(2+3\right)}\times 100\right)\\ =60\end{array}$

Thus, the percentage of tax borne by a supplier is 60.

(c)

To determine

Determine the percentage of tax borne by a demander and supplier if Es is 1 and ED is 0.5.

Explanation of Solution

If the elasticity of demand is 0.5 and elasticity of supply is 1, then the percentage of tax borne by a demander and supplier can be calculated as follows:

$\begin{array}{c}\text{Percentage of tax borne by demander}=\left(\frac{{\text{E}}_{\text{S}}}{\left({\text{E}}_{\text{S}}+{\text{E}}_{\text{D}}\right)}\times 100\right)\\ =\left(\frac{1}{\left(1+0.5\right)}\times 100\right)\\ =66.67\end{array}$

Thus, the percentage of tax borne by a demander is 66.67.

$\begin{array}{c}\text{Percentage of tax borne by supplier}=\left(\frac{{\text{E}}_{\text{D}}}{\left({\text{E}}_{\text{S}}+{\text{E}}_{\text{D}}\right)}\times 100\right)\\ =\left(\frac{0.5}{\left(1+0.5\right)}\times 100\right)\\ =33.33\end{array}$

Thus, the percentage of tax borne by a supplier is 33.33.

(c)

To determine

Determine the percentage of tax borne by a demander and supplier if Es is 1 an ED is 0.5.

Explanation of Solution

If the elasticity of demand is 0.5 and elasticity of supply is 1, then the percentage of tax borne by a demander and supplier can be calculated as follows:

$\begin{array}{c}\text{Percentage of tax borne by demander}=\left(\frac{{\text{E}}_{\text{S}}}{\left({\text{E}}_{\text{S}}+{\text{E}}_{\text{D}}\right)}\times 100\right)\\ =\left(\frac{1}{\left(1+0.5\right)}\times 100\right)\\ =66.67\end{array}$

Thus, the percentage of tax borne by a demander is 66.67.

$\begin{array}{c}\text{Percentage of tax borne by supplier}=\left(\frac{{\text{E}}_{\text{D}}}{\left({\text{E}}_{\text{S}}+{\text{E}}_{\text{D}}\right)}\times 100\right)\\ =\left(\frac{0.5}{\left(1+0.5\right)}\times 100\right)\\ =33.33\end{array}$

Thus, the percentage of tax borne by a supplier is 33.33.

(d)

To determine

Determine the percentage of tax borne by a demander and a supplier if Es is 0.5 and ED is 0.5.

Explanation of Solution

If the elasticity of demand is 0.5 and elasticity of supply is 0.5, then the percentage of tax borne by a demander and a supplier can be calculated as follows:

$\begin{array}{c}\text{Percentage of tax borne by demander}=\left(\frac{{\text{E}}_{\text{S}}}{\left({\text{E}}_{\text{S}}+{\text{E}}_{\text{D}}\right)}\times 100\right)\\ =\left(\frac{0.5}{\left(0.5+0.5\right)}\times 100\right)\\ =50\end{array}$

Thus, the percentage of tax borne by a demander is 50.

$\begin{array}{c}\text{Percentage of tax borne by supplier}=\left(\frac{{\text{E}}_{\text{D}}}{\left({\text{E}}_{\text{S}}+{\text{E}}_{\text{D}}\right)}\times 100\right)\\ =\left(\frac{0.5}{\left(0.5+0.5\right)}\times 100\right)\\ =50\end{array}$

Thus, the percentage of tax borne by a supplier is 50.

(e)

To determine

Explain the finding regarding relative elasticity and tax burden.

Explanation of Solution

Here, the consumers with relatively more elastic demand curve will bear a smaller percentage of the tax. Thus, if the elasticity of demand curves and supply curves eas equal, then the consumer and producer share the tax burden evenly.