I'd like to speak to you today on a topic, which is both timely about the pandemic, and also I think very relevant for the theme of the conference, which is the interaction between government and the economy. The title is mechanism design for pandemics.

        We are all familiar with how well competitive markets work under normal circumstances. Let's imagine that there are many consumers and many producers of some good. If each consumer i gets benefit bi (xi) from consuming quantity xi and each producer incurs a cost cj (yj) from producing a quantity y j ，then the net social benefit from the good is just the sum of the benefits minus the sum of the costs. And for a social optimum, for the economy to achieve an optimum, this of course wants to maximize the net benefit, the sum of the benefits minus the costs subject to feasibility. Feasibility means getting the sum of the consumptions equal to the sum of the supplies. Now, this maximization involves getting a number of things right. You have to get total production right. You have to get each producer j's production right. And you have to get each consumer i's consumption right. That sounds as though it might be a complicated thing, but a competitive market solves this through the simple device of prices. So let p be the price of the good that's being bought and sold. Each consumer is going to want to maximize her benefits minus the price that she has to pay for consumption xi, and that means that the first order condition for her maximization equates the marginal benefit and the price. Similarly, each producer is going to want to maximize its net profit which is revenue from selling a quantity yj minus the cost of producing yj , and the first order condition for that is price equals marginal cost. A market outcome achieves the constraint maximum. It achieves the maximization of net benefits, which is sum of the benefits minus cost subject to feasibility.

        That's a simple result, but a very powerful one because it means that in many circumstances we can rely on the market alone for a good allocation. But let's imagine that we're in a pandemic, and there are some goods for which there are no markets because there are some goods that may not even have been created yet. Virus test kits, for example, the corona virus wasn't even heard of a year ago. So when the pandemic struck there was no market for a virus test. Furthermore, some of the most important goods in a pandemic are public goods in the sense that they are created for the benefit of the entire society. They are not created so much for individual consumers. And so if you left it up to ordinary markets to have consumers buy test kits, they might not buy enough because they don't take into account that when they get tested they are also conferring a benefit on the rest of society. Clearly some sort of intervention is needed into the market for virus test kits, and the best candidate for that intervention is from the governments. The government first needs to somehow stimulate production and has to get the right number of those virus tests produced, then it has to get those virus test kits to consumers.

        Now, how should the government behave with respect to production? One thing the government could do is simply to order companies to produce some quantity of test kits. A problem with that strategy is that the government doesn't know how much it's going to cost for different companies to produce the kits. And so if it comes up with an arbitrary figure, a hundred thousand test kits, it doesn't know whether that makes sense. There could be other companies that could produce those test kits far more cheaply. Another thing that the government could do is simply set a price that it will pay for each test kit produced and then leave it up to companies to decide how much to produce. But again, if the government doesn't know what different companies' cost function is, it doesn't really have a good idea of what price to set, doesn't know how much will be produced. And so it may set the price too high or set the price too low.

        So some severe informational problems face the governments. But here is where a judicious application of mechanism design can come to the rescue. What I'm going to propose is a variation of a well-known mechanism, the Vickrey-Clarke-Groves mechanism that the government could use in order to get the right quantity of test kits produced.

        First the government has to decide what is the benefits of having a total production of the sum of the yj produced. And then as in the model I started with, the government will be interested in maximizing the total gross benefits minus the total cost of production. In other words, the government wants to maximize the net benefit. The problem is that it doesn't know what the costs are, though the costs are known to the producers, but not to the government. So what can the government do? What it can do is to have each firm report its cost function. And when I say report its cost function, I mean, these might be firms which have never produced test kits before. What the government can do is to advertise ahead of time that any firm that wants to produce test kits is welcome to enter as long as it reports its cost function. And then once the government gets all these reports, what it can do is to find production levels for each firm, which maximize the total net benefits, and then it will tell each firm k, you should produce y k*. Now, how does it get firm k to report its true cost function that clearly is critical to this exercise because the government wants to be maximizing the true net benefits. So it has to induce firm k to report its true cost function.

        It turns out that there's a simple idea which will indeed get firms to report their true cost functions and it's this. Suppose firm k is paid this expression here. Now there are two parts to this expression.

        The first two terms correspond to the gross benefits of all of the production that has happened. This second term subtracts off the costs of all of the other firms. So firm k is not included. And this second term is the net benefits that would accrue to society if firm k weren't around at all. So let's imagine that the government does this maximization, but leaves firm k out. Then these two terms minus this parenthetic term is simply the marginal effects that firm k has on net social benefit by being presence. This is what society obtains if firm k is there. This is what society gets if firm k is not there. Firm k is paid the difference. Now I claim that this will actually induce firm k to report its true cost function.

        Then after all of the production is taking place, the government can take these test kits and simply distribute them, either freeof charge or at a low price to citizens. Remember test kits are public goods, so it's important that as many citizens as is feasible to use these test kits. So the government is quite willing and should be willing to subsidize the cost of using the test kits, it will charge at most a low price for the testkits.

        Now that the last remaining thing that I have to show you is why if firm k is paid this amount here, it will actually report its true cost function. And the secret is that this parenthetic term doesn't depend at all on firm k's report. So this parenthetic term will not influence firm k at all. Furthermore, if we look at the first two terms, that's net benefits of society, except for firm k's own cost. So if we take net benefits and we subtract off what firm k will actually have to pay, its true cost, then we have firm k maximizing that social benefits. But if it's maximizing net social benefit, it's going to want to use its actual cost because by using its actual cost in its report, it will be maximizing the true net social benefit. And that's all there is to the argument.

        This gets at a key idea in mechanism design, which is to get private agents like firms or consumers to act in a socially responsible way to maximize a social objective. Just give them an objective function which looks like the social objective. This is the social objective that was given to firm k, so naturally, if firm k is presented with this objective, it will maximize that social welfare. This is an idea which could have been used. Sadly, it wasn't used when the pandemic hit the United States. I'm sorry to say that the American response to the pandemic is pretty disgraceful. It was very bad. One reason it was so bad is because the government ignored arguments like this, but there will be other emergencies in the future. And in those future emergencies, I hope that someone will remember mechanism design. It could be very useful in such circumstances. Thank you very much.