Why is the road to the king called Mozi?

Not only the emperor is qualified, about purple:

From which dynasty did wearing purple clothes become a priority?

The respectability of Purple Clothes comes from Qi Huangong, and it comes from Han Feizi's "The Foreign Reserve Says Left".

During the Spring and Autumn Period, Qi Huangong liked to wear purple clothes. As a result, purple swept the country, making the value of purple cloth double. Qi Huangong asked Guan Zhong how to solve this problem. Guan Zhong said, "Don't wear it yourself. If someone enters the palace in purple, you should keep him away from you. " Qi Huangong accepted his suggestion. As a result, the courtiers and maids in the palace didn't wear purple clothes that day. No one wore it in the capital the next day; On the third day, the whole state of Qi could no longer see people wearing purple clothes.

In which dynasty did purple clothes become popular?

Popular in the Wei and Jin Dynasties, when it was stipulated that the palace should take red and often purple.

There is another reason why purple is expensive:

Purple paint is not commonly used. It can be used to increase the blue tone of red paint and increase the red tone of blue paint without affecting the color intensity. Purple can also turn the yellow of titanium dioxide into white. Violet dioxide is the most commonly used purple pigment in coating industry.

However, Zimo is just a path outside the capital referred to by scholars, so I don't quite understand it.