Do rising inequalities create inflation? When the "richs"* get richers, the "poors"* get poorer... assuming:

h1) a constant volume of money,

h2) a constant volume of people,

h3) a close separation between the two groups of people,

h4) a constant influx of money from rich to poors (salaries) c1, and a constant influx of money from poors to rich (profits from stuff sold to poors) c2, such that c2 > c1

this means that the volume of money the richs have access to gets bigger over time and the volume of money the poors have access two gets smaller, therefore, also assuming:

h5) constant prices,

this means each person in this poor group has individually access to a smaller amount of money. Therefore despite a constant salary, they can afford to buy less things.

Could we therefore says that richs experiment a deflation and poors an inflation? If not, is there a more befitting name to describe this phenomenon?

Are the assumption realistics, or is the reasonment flawed?

Example:


100 persons, divided in R and P, with respectively 20 and 80 persons
1000 euros total volume of money
time t1: R has 500 euros, P has 500 euros
time t2: R has 700 euros, P has 300 euros
the prices remain constant at t1 and t2, e.g. 1 euros bread, 2 euros meat, 3 euros gas


at t1: people in P and R have on average respectively 25 and 6.25 euros

at t2: people in P and R have on average respectively 35 and 3.75 euros

therefore, despite constant salaries for people in P:

at t1 they can afford both bread, meat and gas

at t2 they can afford only bread and meat

*: I put quotation marks, because being rich or poor is subjective, but within a closed social group we can assume that such a distinction can be agreed upon.
This is not an answer that will state exactly which assumptions are valid/invalid but rather a guide to find answers to your question.

Here are various scientific articles about the topic:

These first two papers take what is called a Political Economy perspective on the matter. They assume that the central bank controls inflation, but the central bank is to some extent controlled by the population. If the population has higher income inequality, it prefers higher inflation and thus countries with higher inequality will face higher inflation.

Albanesi, Stefania. "Inflation and inequality." Journal of Monetary Economics 54.4 (2007): 1088-1114.

Dolmas, Jim, Gregory W. Huffman, and Mark A. Wynne. "Inequality, inflation, and central bank independence." Canadian Journal of Economics/Revue canadienne d'économique 33.1 (2000): 271-287.

This paper is also interesting, since it considers the different inflation faced by different income classes. It is somewhat orthogonal to your question, however.

Hobijn, Bart, and David Lagakos. "Inflation inequality in the United States." review of income and Wealth 51.4 (2005): 581-606.

However, to my knowledge, there are no papers written on income inequality as a direct cause of inflation without the involvement of the Political Economy argument above. This is mainly because in Economics our models usually tell us that the central bank has almost perfect control over inflation (except for negative inflation rates).

PS: If you find the readings above too difficult, consider reading a textbook on monetary economics:
Mishkin, Frederic S. The economics of money, banking, and financial markets. Pearson education, 2007.