Simulate population wealth over time

Suppose you're given the following information about a population and its wealth distribution:

• Population size: 2500
• Mean income (in USD, thousands): 50
• Standard deviation of income (in USD, thousands): 12.5
• The population wealth is initially normally distributed

Additionally, you're told that economic transactions occur randomly between two individuals in the population. In a transaction, two parties come together and there is an exchange of wealth. For the purposes of this question, the transactions can be modeled in the following way:

• Two individuals come together at random
• When they interact, their wealth is put into a pot, and is then split randomly and uniformly between the two parties

Given this information, write a simulation to show how the wealth of the population will change over time. You can simulate 50 time steps (or transactions per individual).