The New Zealand-born economist, Bill Phillips, is best known for identifying an empirical relationship between a country’s inflation rate and its unemployment, the so-called Phillips curve.  However, before becoming an economist, Phillips had been an engineer, and in 1949 he built one of the first models of a national economy, the MONIAC.  MONIAC used flows of coloured water to represent money flows through an economy, and perhaps explains (or is a reflection of) traditional economics’ obsession with distinguishing stocks from flows.
In the 1970s, the Australian cartoonist Bruce Petty also built a physical model of a national economy, but this time with seats for several human operators, representing variously The Government, The Unions, Big Business, etc.   Instead of the hydraulic flows used by Phillips, Petty’s model used mechanical levers and pulleys, which impacted in convoluted ways on the machine and on the other operators.   This model looked something built by Heath Robinson or Rube Goldberg, and was immense fun to watch it at work.   I’ve not yet been able to find a video of Petty’s model at work.