# A beautifully simple illustration of how housing drives inequality

Dirk Baur over at the University of Western Australia has constructed a fantastically simple model, using the board game Monopoly to look at the interplay of housing and inequality.

For all its simplicity, the results bear a striking resemblance to empirical data.

"We assume a city with four suburbs each populated with five streets. There is one house in each street. The price of the houses (including the land) varies across streets and increases from 1 to 20 monotonically with the cheapest house being in the first street in the first suburb and the most expensive house being in the last street in the fourth suburb. The rental yield is assumed to be 5% and thus varies between 0.05 currency units for the cheapest house and 1 currency unit for the most expensive house."

"There are N players of the game. Each of them sequentially roll a die and buy the house (including the land it is built on) if the initial or remaining budget suffices. If the house has already been purchased by another player rent must be paid to the owner of the house.The default budget for each player is set equal to the amount that would be needed to buy x houses so that all houses can be sold on average."

Baur runs this simulation multiple ways, fiddling with starting capital, wages (the equivalent of passing Go), and rules around what causes the game to end. One thing is constant – the correlation between inequality and housing.

"Interestingly, the correlation between house ownership and budgets across players remains close to one even for positive regular income parameters. This means that the regular income can decrease the inequality in ownership and capital wealth but not change the ranking of the players based on the house ownership."

"…the simulations show that (i) inequality is a frequent phenomenon in the game, (ii) house prices increase both with higher starting capital and higher wages, (iii) wealth inequality falls if wages are sufficiently high relative to house price growth and (iv) inequality is extreme when players do not own any property. We compare the results with house prices and disposable income of eight industrial countries and find striking similarities with the model outcomes despite the model’s simplicity."

But my biggest takeaway is something this model makes implicit but is quite hidden in the real world – the real inequality is between those who are playing and those that haven’t started yet.

"Whatever the dynamics of the inequality among the players of the game are, the inequality measured with those that are not (yet) part of the game, i.e. future players or future generations, almost always increases and can easily reach extreme values."