Chapter 3, Problem 10E

a)

To determine

To determine the price elasticity of demand for the year 2006 and 2007.

Answer to Problem 10E

The final result derived from the calculation for price elasticity of demand for the year 2006 and 2007 is -0.21.

Explanation of Solution

The price elasticity of demand for the year 2006 and 2007 can be calculated as follows:

  $\frac{PercentageChangeinQuantityDemanded}{Percentagechangeinprice}$

% change in quantity demanded:

  $\begin{array}{l}=\frac{450-525}{\raisebox{1ex}{$\left(450+525\right)$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}\times 100\\ =\frac{-75}{487.50}\times 100\\ =-15.38\%\end{array}$

% change in price:

  $\begin{array}{l}=\frac{8000-17200}{\raisebox{1ex}{$\left(8000+17200\right)$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}\times 100\\ =\frac{-9200}{12600}\times 100\\ =-73.02\%\end{array}$

Price elasticity of demand:

  $\begin{array}{l}=\frac{-15.38}{-73.02}\\ =-0.21\end{array}$

b)

To determine

To determine the income elasticity of demand for the year 2007 and 2008.

Answer to Problem 10E

The final result derived from the calculation for income elasticity of demand for the year 2007 and 2008 is -3.53.

Explanation of Solution

  $\frac{Percentagechangeinquantitydemanded}{Percentagechangeinincome}$

% change in quantity demanded:

  $\begin{array}{l}=\frac{400-450}{\raisebox{1ex}{$\left(400+450\right)$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}\times 100\\ =\frac{-50}{425}\times 100\\ =-11.76\%\end{array}$

% change in income:

  $\begin{array}{l}=\frac{590-610}{\raisebox{1ex}{$\left(590+610\right)$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}\times 100\\ =\frac{-20}{600}\times 100\\ =-3.33\%\end{array}$

Income elasticity of demand:

  $\begin{array}{l}=\frac{-11.76}{-3.33}\\ =-3.53\end{array}$

c)

To determine

To determine the sales forecast for the year 2009.

Answer to Problem 10E

The final result derived from the calculation for sales forecast for the year 2009 is 316.

Explanation of Solution

  $\begin{array}{l}Q2=Q1(1+ED(\%\Delta P)+Ey(\%\Delta Y)\\ Q2=400(1+(0.21)(0)+(-3.53)(0.06)\\ Q2=316\end{array}$

Sales forecast for the year 2009 has been calculated against the income and price elasticities for the previous years and has been calculated as 316 that is a reduction when compared to the previous year.

d)

To determine

To determine the Sales for the year 2009, with an increase in the price and income levels.

Answer to Problem 10E

The final result derived from the calculation the Sales for the year 2009, with an increase in the price and income levels is 320.

Explanation of Solution

  $\begin{array}{l}Q2=Q1(1+ED(\%\Delta P)+Ey(\%\Delta Y)\\ Q2=400(1+(0.21)(0.06)+(-3.53)(0.06)\\ Q2=320\end{array}$

Sales forecast for the year 2009 has been calculated against the income and price elasticities for the previous years and has been calculated as 320 that is a reduction when compared to the previous year.