Can't government experiment on price in the case of a monopoly?

In the lecture given by Jon Gruber at MIT, he talks about the governmental regulations on monopolies, and he states that

(in short)

for government to regulate a monopoly, it needs to know the price of that good in the case of a perfectly competitive market.However, in reality, the government does not know the demand and supply curve. Nevertheless, to get the demand curve the government can do experiments on the consumer and get the demand curve.

If so, can't the government do experiment on the monopolist ? I mean, it can set a price first, and then change the price. Doing so, observing how much the firm produce, we can learn the supply curve of the monopolist. Of course, this would in some sense be not logical, but in the long run, you the government could set all the monopolies in the optimal price.

Moreover, if we look from a broader picture, this can be accomplished more easily by cooperation of different governments on collecting the data.

• What do you think "experiments on the consumer" mean? Mar 25, 2018 at 14:22
• @denesp The government can give different prices for similar consumers, and see how much they consume that good, and get the demand curve.
– Our
Mar 25, 2018 at 15:02
• I think earlier I misunderstood your question and thought that you are recommending experimenting on the monopoly instead of on the consumers. Your proposal is to experiment on both the monopoly and the consumers, right? Mar 25, 2018 at 17:17
• If the monopolist knows that the outcome of the experiment will influence its own future profitability, then it is unlikely to act as if it is operating in a competitive market during the experiment. It's more likely to behave in whatever way it expects to lead the government to set prices in its favour.
– Dan
Mar 25, 2018 at 17:21
• The government doesn't needs to know the perfect competition equilibrium price to regulate a monopoly, it's just unlikely that the regulation will be "optimal" in the absence of this information. Also, being the government, it would be possible to use some legal process to mandate that the monopolist provide sufficient information rather than adopt some experimental procedure to figure it out. Mar 25, 2018 at 23:04

If I understand your question correctly, you are proposing that the government sets prices and observes the behavior of market actors to elicit the demand and supply functions.

I see two possible concerns:
Unless the monopoly is obligated to serve all customers, the market may not be in equilibrium, full demand may not be observed. Similarly the government would have to buy any unsold goods, otherwise a too large $p$ could result supply being larger then demand, resulting in a loss for the monopoly.

The other concern is that the monopoly's behavior significantly affects the government's observations. It could potentially benefit by behaving suboptimally now and earning more in the regulated future. One way it could do that is to make the government believe it has higher costs by supplying lower quantities given any price $p$.
-While I was writing this answer, @Dan has posted the same idea in a comment.

• Yeah but the goverment does not have to inform the monopolist about the experiment. I mean, as I have said, this is a long term plan for the goverment, so in theory, this can be accomplished without informing any party in the market.
– Our
Mar 26, 2018 at 7:08
• @onurcanbektas How does the government set the prices of a company's products without informing them? Apple would be much surprised to find they are selling iPhones for \\$10. Mar 26, 2018 at 7:24
• I meant the experiment not the price. I mean if the company knows that the goverment is experimenting on the market, then the company will set in higher price of their product during the experiment to make profit in the long run.
– Our
Mar 26, 2018 at 10:52