Chapter 12, Problem 11C

Subpart (a):

To determine

The elimination principle application.

Explanation of Solution

The market equation with ‘n’ number of firm is given as follows:

${\text{Q}}_{\text{S}}=0.5\text{n}+\text{0}\text{.1nP}$ (1)

Substitute the respective values in equation (1) to calculate the market supply with 24 firms.

$\begin{array}{c}{\text{Q}}_{\text{S}}=0.5\text{n}+\text{0}\text{.1nP}\\ =0.5\left(24\right)+0.1\left(24\right)\text{P}\\ =12+2.4\text{P}\end{array}$

The market supply equation with 24 firm is ${\text{Q}}_{\text{S}}=12+2.4\text{P}$.

The equilibrium price can be calculated as follows:

$\begin{array}{c}\text{Demand}=\text{Supply}\\ 100-2\text{P}=12+2.4\text{P}\\ \text{2}\text{.4P}+2\text{P}=1\text{00}-\text{12}\\ 4.4\text{P}=88\\ \text{P}=\frac{88}{4.4}\\ =20\end{array}$

The equilibrium price is $20.

Substitute the equilibrium price in the demand equation to calculate the equilibrium quantity.

$\begin{array}{c}{\text{Q}}_{\text{D}}=100-2\text{P}\\ =100-2\left(\text{20}\right)\\ =100-40\\ =60\end{array}$

The equilibrium quantity is 60 units.

 Individual firm output can be calculated as follows:

$\begin{array}{c}{\text{Output}}_{\text{Individyual firm}}=\frac{\text{Market output}}{\text{Number of firm}}\\ =\frac{60}{24}\\ =2.5\end{array}$

Each individual firm produces 2.5 units of output.

Individual firm profit can be calculated as follows:

$\begin{array}{c}\text{Profit}=\left(\text{Price}-\left(\left(\text{5}\times {\text{Output}}_{\text{Individual firm}}\right)-5+\frac{24.2}{{\text{Output}}_{\text{Individual firm}}}\right)\times {\text{Output}}_{\text{Individual firm}}\right)\\ =\left(20-\left(\left(\text{5}\times \text{2}\text{.5}\right)-5+\frac{24.2}{\text{2}\text{.5}}\right)\right)\times 2.5\\ =\left(20-\left(12.5-5+9.68\right)\right)\times 2.5\\ =\left(20-17.18\right)\times 2.5\\ =7.05\end{array}$

Individual firm’s profit is $7.05. Since there is a positive profit, there will be a new entry in to the industry.

Economics Concept Introduction

Concept Introduction:

Elimination principle: According to the elimination principle above, normal profit are eliminated by a new entry and below normal profit are eliminated by an exit.

Subpart (b):

To determine

The elimination principle application.

Explanation of Solution

Substitute the respective values in equation (1) to calculate the market supply with 35 firms.

$\begin{array}{c}{\text{Q}}_{\text{S}}=0.5\text{n}+\text{0}\text{.1nP}\\ =0.5\left(35\right)+0.1\left(35\right)\text{P}\\ =17.5+3.5\text{P}\end{array}$

The market supply equation with 24 firm is ${\text{Q}}_{\text{S}}=17.5+3.5\text{P}$.

The equilibrium price can be calculated as follows:

$\begin{array}{c}\text{Demand}=\text{Supply}\\ 100-2\text{P}=17.5+3.5\text{P}\\ \text{3}\text{.5P}+2\text{P}=1\text{00}-\text{17}\text{.5}\\ 5.5\text{P}=88\\ \text{P}=\frac{82.5}{5.5}\\ =15\end{array}$

The equilibrium price is $15.

Substitute the equilibrium price in the demand equation to calculate the equilibrium quantity.

$\begin{array}{c}{\text{Q}}_{\text{D}}=100-2\text{P}\\ =100-2\left(\text{15}\right)\\ =100-30\\ =70\end{array}$

The equilibrium quantity is 70 units.

 Individual firm output can be calculated as follows:

$\begin{array}{c}{\text{Output}}_{\text{Individyual firm}}=\frac{\text{Market output}}{\text{Number of firm}}\\ =\frac{70}{35}\\ =2\end{array}$

Each individual firm produces 2 units of output.

Individual firm profit can be calculated as follows:

$\begin{array}{c}\text{Profit}=\left(\text{Price}-\left(\left(\text{5}\times {\text{Output}}_{\text{Individual firm}}\right)-5+\frac{24.2}{{\text{Output}}_{\text{Individual firm}}}\right)\times {\text{Output}}_{\text{Individual firm}}\right)\\ =\left(15-\left(\left(\text{5}\times \text{2}\right)-5+\frac{24.2}{\text{2}}\right)\right)\times 2\\ =\left(15-\left(10-5+12.1\right)\right)\times 2\\ =\left(15-17.1\right)\times 2\\ =-4.2\end{array}$

Individual firm’s profit is -$4.2. Since there is a negative profit, there will be a few exits entry in to the industry.

Economics Concept Introduction

Concept Introduction:

Elimination principle: According to the elimination principle above, normal profit are eliminated by a new entry and below normal profit are eliminated by an exit.

Subpart (c):

To determine

The elimination principle application.

Explanation of Solution

Rearrange the individual equation ${\text{q}}_{\text{S}}=0.5+\text{0}\text{.1P}$ in terms of Price. This can be done as follows:

$\begin{array}{c}{\text{q}}_{\text{S}}=0.5+\text{0}\text{.1P}\\ \text{0}\text{.1P}=-0.5+{\text{q}}_{\text{S}}\\ \text{P}=\frac{-0.5}{0.1}+\frac{1}{0.1}{\text{q}}_{\text{S}}\\ =-5+10{\text{q}}_{\text{S}}\end{array}$

Individual supply equation is $\text{P}=-5+10{\text{q}}_{\text{S}}$.

The quantity can be calculated by equating price equation with average cost equation. This is done as follows:

$\begin{array}{c}{\text{Individual supply}}_{\text{Interms of price}}=\text{Average cost}\\ -5+10{\text{q}}_{\text{S}}=5{\text{q}}_{\text{S}}-5+\frac{24.2}{{\text{q}}_{\text{S}}}\\ 10{\text{q}}_{\text{S}}-5{\text{q}}_{\text{S}}=-5+5+\frac{24.2}{{\text{q}}_{\text{S}}}\\ 5{\text{q}}_{\text{S}}=\frac{24.2}{{\text{q}}_{\text{S}}}\\ \left(5{\text{q}}_{\text{S}}\right){\text{q}}_{\text{S}}=24.2\\ {\text{q}}_{\text{S}}{}^2=\frac{24.2}{5}\\ {\text{q}}_{\text{S}}=\sqrt{4.84}\\ =2.2\end{array}$

Individual firm output is 2.2 units.

The equilibrium price can be calculated by substituting the equilibrium quantity in to the individual supply equation.

$\begin{array}{c}\text{P}=-5+10{\text{q}}_{\text{S}}\\ =-5+10\left(2.2\right)\\ =17\end{array}$

The equilibrium price is $17.

The equilibrium market quantity (Output) can be calculated by substituting the equilibrium price in to the demand equation.

$\begin{array}{c}{\text{Q}}_{\text{D}}=100-2\text{P}\\ =100-2\left(\text{17}\right)\\ =100-34\\ =66\end{array}$

The market equilibrium quantity is 66 units.

The number of firms in the industry (Optimum number) can be calculated as follows:

$\begin{array}{c}\text{Number of firm}=\frac{\text{Market quantity}}{\text{Individual firms output}}\\ =\frac{66}{2.2}\\ =30\end{array}$

The number of firms in the industry (Optimum number) is 30. Since the number of firms in the industry is less than the 35 and greater than the 24, it is possible to get normal profit by the 30 firms.

Economics Concept Introduction

Concept Introduction:

Elimination principle: According to the elimination principle above, normal profit are eliminated by a new entry and below normal profit are eliminated by an exit.