My understanding about Shadow Price in Economic

Several times, I heard the word shadow price. I remeber hearing this word last time from Yanagi hara sensei. What I did get from his explanation is whenever we talk about shadow price it is not the price of goods or service but it is named shadow price because it is the price of constraint facing by individual who wish to maximize or minimize some objective. Prof. Yanagihara gave a mathematical example of a consumer about maximization of utility with budget contraint where he refere to the so-called Lagrang multiplier of that complicated mathematical model as shadow price. But what is the simple meaning in our daily life?

A simple example, a consumer who wish to buy cloth he is facing some constraint. His objective is to get the best qualities and durable cloth, but his under the constraint of his income and price. Then, given price of the cloth if his income decrease by one dollar what will he choose to buy more, less or no cloth. Or let say if the price of cloth decline then he will buy more cloth because the constraint is less restrictive to him.

In labor market, workers wish to have higher salary so that he can support there life but as wage rise and price also rise then the shadow price is higher because the constraint is even serious for workers to purhcase goods on market.

In short, I can summarize that shadow price is price of the constraint facing consume, firm, government or a country while pursuing some objective.