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According to economists, minimum wages are very bad, especially for lower-paid workers that are supposed to benefit from them. Here's the reasoning.
In plain English terms, the idea is that if I tell you you have to pay your worker $8 per hour, you'll hire fewer people than if you were allowed to pay $5 per hour. Imagine if you could afford to pay $10 per hour for your workers. If minimum wage is $8, you pay one worker where you could have hired two at $5 without the minimum wage. So that other worker you could have hired is hurt by the minimum wage.
In economic terms, a minimum wage creates a surplus of workers because it makes businesses demand fewer workers (lowers quantity demanded) and it makes more workers want to work (increases quantity supplied).
The wording of the question is some what confusing. Perhaps what is implied that "whether according to law of demand and supply, minimum wages are good or harmful for an economy". Before, I get down to even answering this question some clarification should be made about some popular misconceptions about laws of demand and supply in economics.
There is no single universally applicable law of demand and supply in economics. There are several different laws of economics dealing with demand, supply, and prices. One law says that quantity demanded of a product increases as price is reduce. Another law says that quantities offered for supply decreases as the price reduced. A third law says that an a market the price of a product or service stabilize at a price at which quantity demanded equals quantity offered for supply. There are many other laws which explain impact the of other factors like utility, cost, and nature of competition on demand, supplies and prices. Further is should be noted that all these laws make some assumptions which may or may not be true. Also there are some exceptions to the rule. For example quantity demanded of some prestige goods may actually increase with increase in price.
What is popularly called the law of demand and supply by laymen, is usually an indirect reference to the concept of the invisible hand, first propounded by Adam Smith in his book Wealth of Nations first published in 1776. As per this concept in a competitive market, the mechanism of market price that affect the demand and supply in a market, ensures that combined effect of individual behavior of consumer and supplier in the economy pursues the selfish goal of maximising personal benefits, leads to maximizing the benefit for the whole society. This is a very old theory which no longer represents the ultimate and final opinion of economists. This theory assumes the existence of a perfect market which does not exist in reality, and therefore is not valid in practice.
Imposition of minimum wages, which is just an instance of a wider policy of fixing floor prices of goods and services is now a commonly accepted practice for protecting some interest of some specific groups in society. This is considered not only to ensure more equitable division of income among different sections of society but also to promote long term growth and prosperity of economy as a whole.
While some economist may be opposed to minimum wages in principle. Most of the economists accept the need for minimum wages under some conditions.
In the case of labour markets, a minimum wage can cause unemployment. If the minimum wage exceeds the equilibrium wage, the number of workers demanded at that wage is less than the number of workers who are willing to work. Even though some workers would be willing to work for less than the minimum wage, employers are not permitted to pay them less than minimum wage. Therefor there is surplus of unemployed workers at the minimum wage.
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