We analyze a model of media bias under government capture and a free press. The government wants citizens to invest in a project. Citizens gain from investing only if the state of the economy is good. The state is unobserved. The media firm receives a noisy signal about the actual state and makes a report about whether or not the state of the economy is good. Citizens read the report and decide whether or not to invest. In this context, we show that media bias under government capture may be smaller (greater) than that under free press if the cost of investment is sufficiently high (low) provided that the signal noise is below a certain threshold. Finally, we show that the difference between the bias under government capture and free press diverges (converges) when the cost of investment is sufficiently high (low) in response to a reduction in noise.
In equilibrium under free press, it is always optimal for the media firm to follow an editorial policy such that the signal s = g is reported truthfully.
Consider the following editorial policies:
Editorial policy A:
, , , and
Editorial Policy B:
, , , .
It is easy to see that the good signal is reported truthfully under editorial policy A and the bad signal is reported truthfully under editorial policy B. We will show that the media firm will always prefer editorial policy A over B. Now consider editorial policy B. Since citizens only gain from investing when the actual state is good, they calculate the likelihood of the good state following any report using Bayes’ theorem. Therefore, the likelihood of a good state given report r = b is given by:
Let be the minimum return required to justify investment following a report rP = b under editorial policy B. As a consequence, we must have:
It is easy to check that . Similarly, the likelihood of the good state given a report r = g under editorial policy B is given by the following:
As before, let be the minimum return to justify investment under editorial policy B which is given by:
It is straightforward to check that for . As before, consider the intervals and under editorial policy B. In the interval , citizens do not invest based on the prior but invest in the project if the media firm issues a report rP = g. In the interval , citizens always invest based on the prior but do not invest if the media firm reports rP = b. Therefore, the net benefit, , of subscribing to the media outlet in the interval is given by the following:
Recall that the cost of following news is captured by d. As a result, the minimum return required from the investment to justify subscribing to the news is given by:
Similarly, the minimum return to justify subscribing to news in the interval is given by:
Since anyone with an expected return less than does not invest in the project, they do not have any need to subscribe to the media outlet. Similarly, any citizen with a return above always invests in the project and do not subscribe to the news. Therefore, the expected number of subscribers under editorial policy B are citizens whose expected return lies in the interval , which, after a little algebra yields:
Whereas the expected number of subscribers under editorial policy A, given that the magnitude of the bias is the same under both editorial policies, is given by the following:
Since , we must have Therefore, . Further, since is not the optimal choice of bias under editorial policy A, the expected number of subscribers, in equilibrium, must be higher. Given the profit function is monotonic in the number of subscribers as in Equation (1), this must imply that the profit under editorial policy A are higher than that under B. Hence proved. The result of lemma 1 can be shown to remain unaltered even if we include subscription prices▪
For a sufficiently large, the equilibrium level of bias under free press.
Note that the payoff of the function of the media firm, from Equation (1), is given by:
Differentiating with respect to yields Equation (13) which is as follows:
where . Now consider the following:
Evaluating we get
Note that for a sufficiently large m, . Therefore, for a sufficiently large R0, . Differentiating the first order condition with respect to and some algebra yields:
Clearly, for a sufficiently large R0. Since , we must have □
The equilibrium level of media bias under capture,.
The objective function of the government from Equation (17), after some algebra, turns out to be:
After some algebra, we can show that VGov is strictly concave in . Further, since S(1) = 0, we must have □
For a sufficiently large, the equilibrium level of bias under free press with subscription price,.
Let p be the subscription price for the news outlet. Therefore, the payoff of the media firm is captured by the following equation:
where and . The media firm first determines what price to charge in equilibrium. Maximizing the objective function with respect to p yields:
which can be rewritten as . This yields . With a little bit of algebra, we can show that . Plugging in the objective function we now have:
The rest of the theorem is similar to the proof of lemma 2. We can show that for a sufficiently large , . Further, citizens do not subscribe to the news when since the news is completely uninformative. Therefore, . As a result, we must have (since is continuous in ). Further, we can show that is strictly concave if (sufficient but not neccessary) which implies that is unique □
Media bias under capture is greater (lesser) than under free press if the cost of investment is below (above) a threshold, i.e.,,and,wherefor everyand.
Media bias under capture decreases with the cost of investment, i.e.,
Note that from Equation (17) we have:
Differentiating Equation (17) with respect to and evaluating it at yields:
Now consider , for every , such that since . Since is increasing in c, such that . Therefore, , and , . Since VGov is concave in , and □
Differentiating Equation (17) with respect to yields:
It is easy to check that VGov is strictly concave with respect to . Differentiating Equation (37) with respect to c using the implicit function rule gives us the following:
Since VGov is strictly concave in , . Further, with a little algebra we can show that Dc < 0 which yields our desired result □
The difference between equilibrium media bias under capture and under free press increases with q, i.e.,.
First consider free media. Recall that, under free press, the first order condition for profit maximization with respect to from Equation (13) yields:
Using the implicit function rule, we get where Fq is as follows:
After some algebra, we can show that Fq < 0 provided that R0 is sufficiently large. Therefore, . Now consider the first order conditions for maximizing VGov under capture which is given by Equation (40):
Dividing both sides of Equation (40) by we get:
Using the implicit function theorem on Equation (40) we get
which yields . Since VGov is strictly concave with respect to , . Therefore, the sign of depends on the sign of Dq which is given by:
It is easy to check that , and are positive. Therefore increases with q □
such that welfare under capture is smaller (greater) than that under free press if the cost of investment is smaller (greater) than the threshold, i.e.,, WGov < WPand, WGov > WP.
From Equation (15), we have:
Differentiating WGov−WP with respect to yields:
Since and , we must have . Note that and since , using Proposition 1, we obtain our result □
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