Yes, you can have your cake and eat it too in economics. It all depends on what it is that you call cake and how you define eating the thing. That is, you can view money as an end in itself, something you can take from one person and give to another. Or you can view money as a means to an end, something you create to do a job and then destroy when the job is completed.
If money is an end in itself, then transferring it from one person to another will not stimulate the economy because you cannot have your cake and eat it too. But if money is a means to an end, then it can be used to stimulate the economy if you make stimulation the end you seek. And this will be like having your cake and eating it.
So then, is money an end in itself or is it a means to another end? Well, scientists have discovered a while ago that a few things in nature, such as light for example, have a dual sort of existence; they found that light behaves both like a particle and like a wave. In a similar manner, money has a dual character in that it is both the end and the means to another end. In one sense it is the cake you can have or eat but not both; in another sense it is the cake you can both eat and have at the same time.
Some people hoard money because they think of it as an end in itself. To these people, the transfer of money from one place to another is a zero sum game; what you add to one pot you must subtract from another. When these people think of a stimulus package, they think in terms of money being "redistributed" in the sense that it is taken from those that have it and given to those that ask for it regardless of need or merit.
Other people understand that money is being created and that it is made to vanish all the time by the mere fact that credit is given and that it is circulated by the banks, by other financial institutions, by businesses and the public. These people make a distinction between money which they regard as the vehicle by which you create wealth, and the wealth itself which cannot be made to vanish without a violent occurrence such as an accident or a natural disaster.
To give an example in this regard, you borrow money to build a house. Until you do, the money remains the promise of wealth but not the wealth itself. Now you start building the house and by the time it is completed, the money will have vanished because in one way or another, it will have circulated through the system and returned to the bank where it will be destroyed.
By contrast, the house will be standing for a long time to come, perhaps as long as a hundred years or more. And in this sense, the house, the other edifices like it and all the goods and services that are created by industry represent the real wealth. In your case, the money you borrowed was utilized as a means to create a wealth that was not there before. And it was specifically distributed to you because someone believed you will be most effective at creating the wealth you promised to create.
When you have this comprehensive view of money in mind, you will not be alarmed at the sight of the government injecting a rich stimulus package into the marketplace in response to a man-made disaster that caused the financial system to freeze, and caused the circulation of the money to come to a halt. You now anticipate that the borrowed portion of the stimulus will eventually be paid back to the lenders (whether they reside at home or abroad) having created new wealth for society as well as prevented old wealth from vanishing.
And you will be relieved to know that the lenders had no better use for the money in the first place or they would have used it there, and that they will probably have no use for it again until someone borrows it once more. As for the printed portion of the stimulus, it will be sponged back by the central bank which printed it, and where it will be destroyed so as not to dilute the value of the currency.
All in all, both the borrowed and the printed portions of the money will have served as a means to an end which is to revive the economy and to get it back in shape. Unfortunately however, a number of individuals and institutions will get their hands on some of the money and will hoard it. That is, they will make the possession of money a desirable end in itself. This will have a deleterious effect of an intensity and a duration that is proportional to the level of confidence they have in the current economic situation. But the Fed which supervises the financial institutions has tools at its disposal that can mitigate the effect of such happening.
So far so good except for one small consideration. The central bank can create the money that is necessary to do a job, and it can destroy the money when the job is completed but what the bank cannot do is eliminate the distortions it will have itself created in the marketplace by its undertakings.
And here is how the distortions are created. When the bank buys treasury and/or commercial papers, it pays for them with money that sooner or later will be diffused throughout the economy. This happens because the money is used in most part to build colossal infrastructure projects such as airports and terminals, bridges and tunnels, schools and hospitals et cetera where the work is done by people who will spend the money on the goods and services they buy. In so doing, they will pay for the wages and salaries of those who made those goods and services, who in turn will buy other goods and services, and so on without end.
Thus, after a period of time, all monies will have been translated into wages and salaries which will be used to buy everyday goods and services among other things. The problem arises from the fact that those goods and services will not have increased to match the increase in the money that is chasing them because while people get paid to build airports, terminals, bridges, tunnels, schools and hospitals, they do not buy them. The result is the appearance of an inflationary bout which tends to push all prices upward. If this situation is allowed to go on for an extended period of time, the distortion thus created will damage the economy or even kill it which is what happened to the Soviet and to the other socialist systems.
Whether or not the stimulus packages now being injected into the economies of the world by various countries will be sufficient to damage the system to a serious degree remains to be seen. But one way or the other, the massive amounts of money being injected into infrastructure projects to rescue the capitalist system from its current predicament will require an extra effort to be made by everyone if only as a cautionary measure.
What can be done is the imposition of a user fee on the airports, terminals, bridges and tunnels that will be constructed. Also, the schools can make space available after hour to be rented out for such things as concerts, meetings and conventions. As for the government run hospitals, they could dedicate a section where the public may come to do fitness exercises for a fee. The hospitals could also use some of the space to set up a clinic for doing cosmetic surgery on a paying clientele.
Of course, many more similar ideas can be devised and implemented to increase the revenue without the governments having to raise taxes. But in the end, and certainly after the economies begin to perk up again, taxes will have to be gradually raised so as to help pay back the borrowed money and to firm up the value of the currency.
And there is one more action that can be taken. It is something that should be implemented in the name of fairness and not taken as a punitive measure. There is in the law something called false enrichment. When fully fleshed out, it says that if by direct, indirect or inadvertent means someone receives money to which he or she is not entitled, the injured party may sue to recoup all or part of the money.
Now, given that society was injured as a result of someone getting falsely enriched for whatever reason and by whatever means, the government should have the right to sue these people on behalf of society and to recoup as much as possible. The money thus raised can then be used to pay back the debt and to firm up the currency.