How long can I – coming from country X – live in country Y by spending my last monthly salary converted by nominal exchange rate:
1 as a backpacker or as a convenience tourist?
2 adapting to the other country's standards which may be lower?
3 adapting to higher standards than I am used to?
4 How much does this period deviate from a month?
My question is: Where do I find this approach taken?
There is a problem with this question, the size of the country. This is a more straightforward question if Country X is Luxembourg, and Country Y is Bolivia.
For a larger country, like the United States, the internal variability is extraordinary. To provide an example, the price of a home I used to own was one-fifth of the price of what it would cost me in another part of the United States.
A person backpacking in New York faces radically different costs than one backpacking the Appalachian Trail, the Big Island in Hawaii, or crossing Alaska. Of course, in Alaska, you would need things such as bear spray and a high powered weapon so as to minimize the risk of being eaten. There are really good brands of bear spray, so you should ask a local rather than buy it before you got to the United States. You cannot fix being eaten.
The United States, like the European Union, could be thought of as a custom's union combined with a monetary union. Gross aggregates do not reflect internal costs.
Two states, side-by-side, could be like day and night in terms of living standards and costs. Also, they can create a range of comparison problems.
For example, if you decided to drive from the District of Columbia to Bangor Maine, you would cross around ten states and be near tens of millions of people. The same driving distance would get you diagonally across the State of Montana. Although there are a few more people in Montana and the District, Montana is about the size of the American Northeast, and DC is about 69 square miles (177 sq km). Montana is about the same size as the island of Great Britain at approximately 147,000 square miles(381000 sq km).
Montana has stretches that go for hundreds of miles without gas stations or other stores of any kind. DC goes for blocks without gas stations.
In some parts of the United States, such as West Virginia, you could live on half your German salary and save the rest. In some parts of California, you will be homeless.
One of the problems with "representative agent" models, which is at least in part what any discussion of inflation, PPP or similar topics really imply or require, is that they reduce everything down to one number.
Your problem is closer to a personal finance question. For it to be answered, greater specification of the events likely to happen must occur.
The representative American doesn't exist in this sense. The American with the representative gross income is likely not paying the representative tax rate and is not the person paying representative housing prices, gasoline or health care costs. The median wage isn't paying the median tax, the median insurance premium, or the median cost of food. They are all different people.
I did a search for three-bedroom, two-bath homes in different parts of the United States. One sells for \$109,000 with 1.25 acres of land in Arthurdale WV. The other sells for \$918,000 with 7000 square feet of land. I also looked at a few other cities, villages, reservations and towns but these two seemed to capture the variability.
You will find your approach taken, approximately, in personal finance textbooks, minus the exchange rates. They ask these specific questions. The conversion to be taken place would be in nominal currency.
Traveling from a small country to a small country allows representative agent questions to be meaningful. When traveling from a large country to a large country, it is better to compare states or counties(parishes) to states or counties(parishes).