Chapter 2, Problem 2.4P

To determine

(a)

To fill the given box.

Explanation of Solution

Use the following formula to find the elasticity of demand.

  $\begin{array}{c}{\text{ε}}_{\text{Q,P}}\text{ = }\frac{\text{ΔQ}}{\text{ΔP}}\frac{\text{P}}{{\text{Q}}^{}}\\ \text{Q = 300-100P}\\ \frac{\text{ΔQ}}{\text{ΔP}}\text{ = -100}\\ \text{= -100 × }\frac{\text{P}}{\text{300-100P}}\end{array}$.

  $\text{= }\frac{\text{P}}{P-3}$

Find the values of Q^dby inserting the values in $Q=300–100P$

P	0.10	0.45	0.50	0.55	2.50
Qd	290	255	250	245	50
eQ,P	−0.035	−0.176	−0.2	−0.225	−5

To determine

(b)

To draw the graph for demand function.

Explanation of Solution

To plot the graph just find out inverse demand function.

The inverse demand function, $P=3–\frac{1}{100}{Q}^d$

When price is zero then quantity is:

  $\begin{array}{c}P=3–\frac{1}{100}{Q}^d\\ 0=3–\frac{1}{100}{Q}^d\\ -3=–\frac{1}{100}{Q}^d\\ Q^d=300\end{array}$

Similarly, when quantity is zero then price is $3.

  

The Y axis of graph shows the price and x axis shows the quantity. When price is $3 then quantity demanded is zero. When price is zero then the quantity demanded is 300 units.

To determine

(c)

To find the price at which demand is unitary elastic.

Explanation of Solution

Elasticity of demand is equal to:

  $\begin{array}{c}{\text{ε}}_{\text{Q,P}}\text{ = }\frac{{\text{ΔQ}}^{\text{d}}}{\text{ΔP}}\frac{\text{P}}{{\text{Q}}^{\text{d}}}\\ \text{Q = 300-100P}\\ \frac{\text{ΔQ}}{\text{ΔP}}\text{ = -100}\\ \text{= -100 × }\frac{\text{P}}{\text{300-100P}}\end{array}$.

  $\text{= }\frac{\text{P}}{P-3}$

Let's take the price $1.50, then the elasticity of demand is -1.

  ${\epsilon }_{Q,P}=\frac{1.5}{1.5-3}=-1$.

Thus, at price $1.50 the demand will be unitary elastic.

To determine

(d)

To find the price at which demand is inelastic.

Explanation of Solution

Elasticity of demand is equal to:

  $\begin{array}{c}{\text{ε}}_{\text{Q,P}}\text{ = }\frac{{\text{ΔQ}}^{\text{d}}}{\text{ΔP}}\frac{\text{P}}{{\text{Q}}^{\text{d}}}\\ \text{Q = 300-100P}\\ \frac{\text{ΔQ}}{\text{ΔP}}\text{ = -100}\\ \text{= -100 × }\frac{\text{P}}{\text{300-100P}}\end{array}$.

  $\text{= }\frac{\text{P}}{P-3}$

Let's take the price $1.50, then the elasticity of demand is -1.

  ${\epsilon }_{Q,P}=\frac{1.5}{1.5-3}=-1$.

Here, all price below $1.50 will give inelastic demand.

To determine

(e)

To find the price at which demand is elastic.

Explanation of Solution

Elasticity of demand is equal to:

  $\begin{array}{c}{\text{ε}}_{\text{Q,P}}\text{ = }\frac{{\text{ΔQ}}^{\text{d}}}{\text{ΔP}}\frac{\text{P}}{{\text{Q}}^{\text{d}}}\\ \text{Q = 300-100P}\\ \frac{\text{ΔQ}}{\text{ΔP}}\text{ = -100}\\ \text{= -100 × }\frac{\text{P}}{\text{300-100P}}\end{array}$.

  $\text{= }\frac{\text{P}}{P-3}$

Let's take the price $1.50, then the elasticity of demand is -1.

  ${\epsilon }_{Q,P}=\frac{1.5}{1.5-3}=-1$.

Here, all prices above $1.50, will give the demand is elastic.