Chapter 14, Problem 21C

Subpart (a):

To determine

Price discrimination and the quantity demanded for channels.

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 same commodity for different consumers in the market.

The given information are as follows: $10 for Lifetime and $7 for the food network. The maximum willingness to pay for a lifetime is higher than $10, only for two, namely Tyler and Alex. Since the maximum willingness to pay for a lifetime by Monique is $3, she will not subscribe to lifetime.

The maximum willingness to pay for the food network by Monique is $9 and by Alex is $7. Since the price for the food network is $7 and the maximum willingness to pay by Tyler is only $4, it will be subscribed by Alex and Monique only.

The profit of the cable operator can be calculated as follows:

$\begin{array}{c}\text{Profit of the cable operator}=\left[\begin{array}{l}\left({\text{Quantity demanded}}_{\text{Life time}}\times {\text{Price}}_{\text{Life time}}\right)+\\ \left({\text{Quantity demanded}}_{\text{food network}}\times {\text{Price}}_{\text{Food network}}\right)\end{array}\right]\\ =\left(2\times 10\right)+\left(2\times 7\right)\\ =20+14\\ =34\end{array}$

Thus, the profit of the cable operator is $34.

Economics Concept Introduction

Concept introduction:

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

Subpart (b):

To determine

Price discrimination and the quantity demanded for channels.

Explanation of Solution

When the price of the lifetime becomes $11 and that of the Food network is $8, the person subscribing to the lifetime will be only Tyler because he is the one who has the willingness to pay $11 for the lifetime. In the case of the food network, only Monique has the willingness to pay $8 for it and thus, only Monique will subscribe to the food network. Alex will not subscribe to any channel. Thus, the total profit of the market can be calculated as follows:

$\begin{array}{c}\text{Profit of the cable operator}=\left[\begin{array}{l}\left({\text{Quantity demanded}}_{\text{Life time}}\times {\text{Price}}_{\text{Life time}}\right)+\\ \left({\text{Quantity demanded}}_{\text{food network}}\times {\text{Price}}_{\text{Food network}}\right)\end{array}\right]\\ =\left(1\times 11\right)+\left(1\times 8\right)\\ =11+8\\ =19\end{array}$

Thus, the profit of the cable operator is $19 which is lower than the previous level price by $15. Thus, the increased price reduces the number of subscribers and thus, the cable operator should avoid such issue when the marginal cost of serving an additional viewer is zero.

Economics Concept Introduction

Concept introduction:

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

Subpart (c):

To determine

Price discrimination and the quantity demanded for channels.

Explanation of Solution

When the profit maximizing price is $10 for the lifetime and $7 for the food network, Alex values lifetime by $10 and pays $10 for it which means there is no consumer surplus. Tyler values it as $15 and pays only $10, which means there is a consumer surplus of $5. Monique values food network by $9 whereas pay only $7, which means there is a consumer surplus of $2. Alex values and pays $7 for food network which means there is no consumer surplus. Thus, the summation of the entire individual consumer surplus will be the total surplus which can be calculated as follows:

$\begin{array}{c}\text{Total consumer surplus}={\text{Consumer surplus}}_{\text{Alex}}+{\text{Consumer surplus}}_{\text{Tyler}}+{\text{Consumer surplus}}_{\text{Monique}}\\ =0+5+2\\ =7\end{array}$

Thus, the total consumer surplus is $7.

Economics Concept Introduction

Concept introduction:

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

Subpart (d):

To determine

Price discrimination and the quantity demanded for channels.

Explanation of Solution

When the price of the lifetime and food network bundle becomes $12, everyone is willing to pay $12 for the bundle. This means that all the three will subscribe to the bundle. Thus, the total profit of the cable operator can be calculated as follows:

$\begin{array}{c}\text{Profit of the cable operator}={\text{Quantity demanded}}_{\text{Bundle}}\times {\text{Price}}_{\text{Bundle}}\\ =3\times 12\\ =36\end{array}$

Thus, the profit of the cable operator increases to $36. When Alex values the bundle by $17 and pays $12, there will be a consumer surplus of $5 and Tyler values the bundle by $19 and pays $12 means there is a consumer surplus of $7 to Tyler. Since Monique values and pays the bundle of $12, there will be no consumer surplus for her. Thus, the total consumer surplus can be calculated by adding their consumer surplus together as follows:

$\begin{array}{c}\text{Total consumer surplus}={\text{Consumer surplus}}_{\text{Alex}}+{\text{Consumer surplus}}_{\text{Tyler}}+{\text{Consumer surplus}}_{\text{Monique}}\\ =5+7+0\\ =12\end{array}$

Thus, the total consumer surplus is $12.

When the cable operator increases the price of the bundle to $13, Monique will not subscribe to the bundle and the total profit of the cable operator becomes $26 which is lower than the previous level price by $12.

Thus, the profit of the cable operator is $19 which is lower than the previous level price by $15.

Economics Concept Introduction

Concept introduction:

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