Chapter 11, Problem 11.6P

a)

To determine

To describe: Profits are maximized are to be shown for a downward sloping linear demand curve

Answer to Problem 11.6P

The level of output in market is 60.

Explanation of Solution

In market of monopoly, when price is fixed with the marginal cost, the outcome will be equal to the competitive market.

P is the price

Q is the output demand

MC is the marginal cost

So, equalization of the marginal cost in each market is,

  $\begin{array}{l}{P}_1=MC\\ 55-Q_1=5\\ Q_1=50\end{array}$

So, the level of output in market 1 is 50.

In market-2, the quantity would be,

  $\begin{array}{l}{P}_2=MC\\ 35-0.5Q_2=5\\ Q_2=60\end{array}$

The level of output is 60

Economics Concept Introduction

Introduction:

Monopoly competition occurs when many companies offer similar but not the same product in an industry.Companies in competition with monopolies usually try to differentiate their product to obtain market returns.

b)

To determine

To calcute: Total profit.

Answer to Problem 11.6P

Total profit is equal to $825.

Explanation of Solution

In case of monopolist maintains separation in the market, then profit maximizing price would be set as corresponding following equality,

  $M{R}_1=M{R}_2=MC$

Here, MR = Marginal Revenue

MC= Marginal Cost

Now to find out the profit maximizing output and the price in market-1,

  $\begin{array}{l}M{R}_1=MC\\ \frac{dR}{d{Q}_1}=5\\ \frac{d}{d{Q}_1}\left[\left(55-Q_1\right)Q_1\right]=5\\ 55-2Q_1=5\\ Q_1=25\end{array}$

So, the profit maximizing quantity in market is 25

Now to calculate the price charged in market-1 as,

  $\begin{array}{l}{P}_1=55-Q_1\\ =55-25\\ =20\end{array}$

So, the maximizing price is $20 in market 1

Now to find out the profit maximizing output and the price market 2,

  $\begin{array}{l}M{R}_2=MC\\ \frac{dR}{d{Q}_2}=5\\ \frac{d}{d{Q}_1}\left[\left(35-0.5Q_2\right)Q_2\right]=5\\ 35-Q_2=5\\ Q_2=30\end{array}$

So, the profit maximizing quantity in market-2 is 30

Now to calculate the price charged in market-2 as,

  $\begin{array}{l}{P}_2=35-0.5Q_2\\ =35-15\\ =20\end{array}$

So, the maximizing price is $20 in market 2

Now, total profit is calculated as,

  $\begin{array}{l}\pi =P_1{Q}_1+P_2{Q}_2-\left(Q_1+Q_2\right)MC\\ =500+600-55\times 5\\ =825\end{array}$

Therefore total profit is equal to $825

Economics Concept Introduction

Introduction:

Monopoly competition occurs when many companies offer similar but not the same product in an industry.Companiesin competition with monopolies usually try to differentiate their product to obtain market returns.

c)

To determine

To describe: The new profit level of the monopolist.

Answer to Problem 11.6P

The total profit is $\$1143.75$

Explanation of Solution

As the monopolist maintains the separation in the market, the profit maximizing price would be, set as,

  $M{R}_1=M{R}_2=MC$

Here, MR = Marginal Revenue

MC= Marginal Cost

Now to find out the profit maximizing output and the price in market-2,

  $\begin{array}{l}M{R}_2=MC\\ \frac{dR}{d{Q}_2}=3\\ \frac{d}{d{Q}_1}\left[\left(35-0.5Q_2\right)Q_2\right]=3\\ 35-Q_2=3\\ Q_2=32\end{array}$

So, the profit maximizing quantity in market is 32

Now to calculate the price charged in market-2 as,

  $\begin{array}{l}{P}_2=35-0.5Q_2\\ =35-16\\ =19\end{array}$

So, the maximizing price is $19 in market 2

Now, total profit is calculated as,

  $\begin{array}{l}\pi =P_1{Q}_1+P_2{Q}_2-\left(Q_1+Q_2\right)MC\\ =19\times 26+19\times 32-58\times 5\\ =812\end{array}$

Therefore, the total profit is $812

Now to find out the profit maximizing output and the price market 2,

  $\begin{array}{l}M{R}_1=MC\\ \frac{dR}{d{Q}_1}=0\\ \frac{d}{d{Q}_1}\left[\left(55-Q_1\right)Q_1\right]=0\\ 55-2Q_1=0\\ Q_1=\frac{55}{2}\end{array}$

So, the profit maximizing quantity in market-1 is $\frac{55}{2}$

Now to calculate the price charged in market-2 as,

  $\begin{array}{l}{P}_1=55-Q_1\\ =55-\frac{55}{2}\\ =\frac{55}{2}\end{array}$

So, the maximizing price is $\$\frac{55}{2}$ in market 1

Now to find out the profit maximizing output and the price in market-2,

  $\begin{array}{l}M{R}_2=MC\\ \frac{dR}{d{Q}_2}=0\\ \frac{d}{d{Q}_1}\left[\left(35-0.5Q_2\right)Q_2\right]=0\\ 35-Q_2=0\\ Q_2=35\end{array}$

So, the profit maximizing quantity in market is 35

Now to calculate the price charged in market-1 as,

  $\begin{array}{l}{P}_2=35-0.5Q_2\\ =35-\frac{35}{2}\\ =\frac{35}{2}\end{array}$

So, the maximizing price is $\$\frac{35}{2}$ in market 1

Now, total profit is calculated as,

  $\begin{array}{l}\pi =P_1{Q}_1+P_2{Q}_2-\left(Q_1+Q_2\right)MC\\ =\frac{55}{2}\times \frac{55}{2}+\frac{35}{2}\times 35-\left(\frac{55}{2}+\frac{35}{2}\right)\times 5\\ =1143.75\end{array}$

Therefore, the total profit is $\$1143.75$

Economics Concept Introduction

Introduction:

Monopoly competition occurs when many companies offer similar but not the same product in an industry.Companies in competition with monopolies usually try to differentiate their product to obtain market returns.