The rear wheel needs more friction for traction purposes so they are large but front wheels are only for stirring purposes so they are small.

To bear the load

The tractor has large wheels on the back for traction and to carry the weight of heavy implements, plows, cultivators and a larger surface area which helps to prevent sinking in soft soil and mud. Small wheels on the front for steering.
Disc brakes can't be locked for parking, so they work really well on the front, but band brakes can be set by lever lock on inclines for parking. Also, about 90% of the braking power is on the front brakes, more weight and more tire traction. If the front wheels do not need to drive, then:

1. It's cheaper to use smaller wheels at the front; and

2. It's much easier to steer smaller tyres with manual steering.

With all-wheel drive, and power steering, it makes sense to use the same tyre size all around for simplicity and equal traction power, and the power steering can exert the extra effort needed for the full-size front tyres
The back wheels are larger on commercial vehicles because that's where the majority of the load is held. The wheel ...more