Question

I have the following problem. Of the problem, I think about (a) as follows, but I cannot understand (b). Please tell me the solution to the problem of (b) .

the problem:

Suppose you are in charge of setting the price for commercial advertisements shown during Enemies, a top network television show. There is a 60-minute slot for the show. However, the running time for the show itself is only 30 minutes. The rest of the time can be sold to other companies to advertise their products or donated for public service announcements.

Demand for advertising is given by: Q_d=30-0.0002P+26V

where Q_d = quantity demanded for advertising on the show (minutes), P = the price per minute that you charge for advertising, and V is the number of viewers expected to watch the advertisements (in millions).

(a). All your costs are fixed and your goal is to maximize the total revenue received from selling advertising. Suppose that the expected number of viewers is one million people. What price should you charge? How many minutes of advertising will you sell? What is total revenue?

I think:

Q_d=30-0.0002P+26V

P=280000-5000Q_d

TR=280000Q_d-5000Q_d²

Revenue maximization occurs where MR=280000-10000Q_d=0, thus  Q_d=28, P=140000

And total revenue : multiply "the price per minute that you charge for advertising" and "quantity demanded for advertising on the show (minutes)"

(b). Suppose price is held constant at the value from part (a). What will happen to the quantity demanded if due to PVRs the number of expected viewers falls to 0.5 million? Calculate the “viewer elasticity” based on the two points. Explain in words what this value means.

Answer 1

It is given that Qd=30-0.0002P+26V

As found out by you in part A, Qd is 28 and P=140000. Putting these numbers in, we get the value of V as

28=30-.0002*140000+26V

28=30-28+26V

28=2+26V

V=1

Now, if V becomes .5 while rest remain same, the new Qd will be

Qd=30-28+26*.5

Qd=30-28+13

Qd=43-28

Qd=15.

We know that any elasticity is a measure of how one thing changes when the other changes. In our case, we can say that viewer elasticity is

=%change in demand/%change in viewers

We have calculated that %change in demand=(15-28)/28=-13/28=-46.43%
%change in viewers=(.5-1)/.5=-50%

So,

viewer elasticity=-46.43/-50=.9286

What this means is that when viewer numbers changes by 1, demand changes by .9286.