Question

Using Supply and Demand to Analyze Markets — End of Chapter Problem

Consider the demand for broadband internet service, given as ??=224−4?. Q is the number of subscribers in a given area (in hundreds), and P is the price in dollars per month. This demand relationship is illustrated in the diagram below. Assume the price of broadband service is $25 per month.

a. What will the total number of subscribers be at a price of $25? ______ subscribers

b. What is the total amount paid by broadband subscribers for the service (i.e., Area B)? _____ dollars per month

c. What is the consumer surplus received by the subscribers (i.e., Area A)? ______ dollars per month

d. What is the total value to subscribers of broadband service (i.e., Areas A and B)? ______ dollars per month

Answer 1

Solution :-

(a) :-

The demand for broadband internet service, given as QD =224−4P

Q = number of subscribers.

P = price in dollar per month.

The price of broadband service = $25 per month.

QD = 224 - 4P

QD = 224 - 4 x 25

QD = 224 - 100

QD = 124

So,

The total number of subscribers be at a price of $25 is = 124 subscribers.

(b) :-

The price(P) of broadband service = $25 per month.

Number of subscribers(Q) = 124

So, the total revenue is -

Total revenue = P x Q

= 25 x 124

= $3100

So,

The total amount paid by broadband subscribers for the service (i.e., Area B) is = $3100.

(c) :-

Now, calculating the price at Q = zero

QD = 224 - 4P

0 = 224 - 4P

224 = 4P

224/4 = P

P = $56

Now , the consumer surplus :-

CS = 1/2 x ( price at which Q is zero - current price) x Quantity

CS = 1/2 x ( 56 - 25) x 124

= 1/2 x 31 x 124

= 31 x 62

CS = $1922

So,

The consumer surplus received by the subscribers (i.e., Area A) is =$1922.

(d) :-

The total value to subscribers:-

Total value = area A + area B

= 1922 + 3100

= $5022

So,

The total value to subscribers of broadband service (i.e., Areas A and B) is = $5022.