Chapter 11, Problem 1CE

To determine

The elasticity in the demand of beef.

Answer to Problem 1CE

Solution:

The elasticity of the beef is inelastic.

Explanation of Solution

Given:

The monthly demand for beef in a given region is expressed in an equation

$q=-3.003p+675.23$

Where $q$ is the monthly demand in tons and $p$ is the price in dollars per $100$ pounds.

Formula used:

The equation of elasticity is:

$E=-\frac{p}{q}\cdot \frac{dq}{dp}$

Where $p$ states the price of the goods and $q$ states the demand for the goods.

Explanation:

The equation of elasticity is:

$E=-\frac{p}{q}\cdot \frac{dq}{dp}$

Where, $p$ states the price of the goods and $q$ states the demand for the goods.

The demand is governed by the equation

$q=-3.003p+675.23$

Where, $p$ is the price in dollars per $100$ pounds.

Differentiate the function with respect to $p$,

$\frac{dq}{dp}=-3.003$

Substituting the values in the equation of Elasticity,

$\begin{array}{c}E=-\frac{p}{-3.003p+675.23}\cdot \left(-3.003\right)\\ =\frac{3.003p}{-3.003p+675.33}\end{array}$

Now, elasticity for the price of $\$70$ will be substituted in the above-mentioned elasticity equation.

$\begin{array}{c}E=\frac{3.003\cdot 70}{-3.003\cdot 70+675.33}\\ =\frac{210.21}{465.12}\\ =0.45\end{array}$

The elasticity is less than $1$. So the demand is inelastic.