Chapter 14, Problem 10TPS

Subpart (a):

To determine

The profit from the price discrimination.

Explanation of Solution

The market is a structure where there are buyers who buy and sellers who sell, and the exchange of goods and services takes place between them. The price is determined by the interaction of the demand and supply in the market.  The price discrimination is the practice of charging different prices for the exact same commodity for different consumers in the market.

The profit maximizing point of a firm is the point where the firms’ marginal cost is equal to the marginal revenue. Here, it is given that the marginal revenue of senior citizens is $50-\text{Q}$, and the marginal revenue from others is $100-2\text{Q}$. The profit maximizing output can be calculated by equating the marginal revenue with the marginal cost, which is given as 10 in both the cases.

Thus, the profit maximizing quantity by the seniors can be calculated by equating MR equal to Mc as follows:

$\begin{array}{c}{\text{Marginal cost}}_{\text{Seniors}}={\text{Marginal revenue}}_{\text{Seniors}}\\ 10=50-\text{Q}\\ \text{Q}=50-10\\ \text{Q}=40\end{array}$

The profit maximizing price can be calculated by substituting the profit maximizing quantity in the equation for price as follows:

$\begin{array}{c}{\text{Price}}_{\text{Seniors}}=\text{50}-0.5\text{Q}\\ =50-\left(0.5\times 40\right)\\ =50-20\\ =30\end{array}$

Thus, the profit maximizing price for seniors is $30, and the quantity is 40. Similarly, the items for the others can be calculated as follows:

$\begin{array}{c}{\text{Marginal cost}}_{\text{Others}}={\text{Marginal revenue}}_{\text{Others}}\\ 10=100-2\text{Q}\\ \text{2Q}=100-10\\ \text{Q}=\frac{90}{2}\\ =45\end{array}$

The profit maximizing price can be calculated by substituting the profit maximizing quantity in the equation for price as follows:

$\begin{array}{c}{\text{Price}}_{\text{Seniors}}=\text{100}-\text{Q}\\ =100-45\\ =55\end{array}$

Thus, the profit maximizing price for others is $55, and the quantity is 45.

Economics Concept Introduction

Concept introduction:

Price discrimination: The price discrimination is the practice of charging different prices for the exact same commodity for different consumers in the market.

Subpart (b):

To determine

The profit from the price discrimination.

Explanation of Solution

When the percentage of discount that have to be offered to the seniors have to be calculated, the price that the seniors are charged must be subtracted from the price charged for others and divided with the price charged for others as follows:

$\begin{array}{c}\text{Percentage discount offered to seniors}=\frac{\left(\text{Price for others}-\text{Price for seniors}\right)}{\text{Price for others}}\times 100\\ =\frac{\left(55-30\right)}{55}\times 100\\ =45\end{array}$

Thus, the seniors will be offered a discount of 45 percent.

Economics Concept Introduction

Concept introduction:

Price discrimination: The price discrimination is the practice of charging different prices for the exact same commodity for different consumers in the market.

Subpart (c):

To determine

The profit from the price discrimination.

Explanation of Solution

The total cost of the firm can be calculated by multiplying the total quantity with the marginal cost, and the total revenue of the firm can be calculated by multiplying the quantities demanded by seniors and others with their respective prices and adding them together. By subtracting the total cost from the total revenue, the total profit of the firm can be calculated. This can be done as follows:

$\begin{array}{c}\text{Total Profit }=\left[\begin{array}{l}\left\{\left({\text{Quantity}}_{\text{Seniors}}\times {\text{Price}}_{\text{Seniors}}\right)+\left({\text{Quantity}}_{\text{Others}}\times {\text{Price}}_{\text{Others}}\right)\right\}\\ -\left\{\text{Total output}\times \text{Marginal cost}\right\}\end{array}\right]\\ =\left[\left\{\left(40\times 30\right)+\left(45\times 55\right)\right\}-\left\{85\times 10\right\}\right]\\ =\left[\left\{1,200+2,475\right\}-\left\{850\right\}\right]\\ =3,675-850\\ =2,825\end{array}$

Thus, the total profit of the firm is $2,825.

Economics Concept Introduction

Concept introduction:

Price discrimination: The price discrimination is the practice of charging different prices for the exact same commodity for different consumers in the market.

Subpart (d):

To determine

The profit from the price discrimination.

Explanation of Solution

When there is no possibility of price discrimination in the market, the firm faces only one single marginal revenue and market demand. Since there is no change in the marginal cost of the firm, the profit maximizing quantity can be calculated by equating the marginal revenue and marginal cost as follows:

$\begin{array}{c}\text{Marginal cos}=\text{Marginal revenue}\\ 10=67-\frac{2}{3}\text{Q}\\ \frac{\text{2}}{3}\text{Q}=67-10\\ \text{Q}=\frac{57}{2}\times 3\\ =85.5\end{array}$

The profit maximizing price can be calculated by substituting the profit maximizing quantity in the equation for price as follows:

$\begin{array}{c}\text{Price}=\text{67}-\frac{1}{3}\text{Q}\\ =67-\frac{1}{3}\times 85.5\\ =67-28.5\\ =38.5\end{array}$

Thus, the profit maximizing price for others is $38.5 and since the quantity cannot be a fraction, it is 86.

Economics Concept Introduction

Concept introduction:

Price discrimination: The price discrimination is the practice of charging different prices for the exact same commodity for different consumers in the market.

Subpart (e):

To determine

The profit from the price discrimination.

Explanation of Solution

The profit of the market can be calculated by subtracting the total cost from the total revenue as follows:

$\begin{array}{c}\text{Total profit}=\text{Total revenue}-\text{Total cost}\\ =\left(85.5\times 38.5\right)-\left(85.5\times 10\right)\\ =3,291.75-855\\ =2,436.75\end{array}$

Thus, the profit of the market is $2,436.75, which means that the total profit is less than the previous level profit when the market was able to price discriminate on the basis of age.

Economics Concept Introduction

Concept introduction:

Price discrimination: The price discrimination is the practice of charging different prices for the exact same commodity for different consumers in the market.