Compare and contrast the functionalist and conflict views of social stratification in relation to ascribed status and achieved status that leads wealth and wages inequalities.

The conflict perspective and the functionalist perspective of social stratification are fundamentally at odds. Conflict theorists argue that social stratification that leads to wage gaps is the result of ascribed statuses like a person's socioeconomic background. Functionalists argue that different jobs have different values and are thus compensated differently -- looking more at the achieved status of a worker rather than their ascribed socioeconomic status. At its heart, conflict theory says that social stratification is not necessary or healthy for societies while functional theory says that it is.
The functionalist perspective on social stratification says that because jobs are inherently unequal in difficulty and skill level, they will be compensated differently. For example, it is more difficult to acquire the skills to be an engineer than to acquire the skills to be a janitor. Kingsley Davis and Wilbert Moore, proponents of this theory, believe that wealth inequalities are justified because the people making the most money decided to work hard and acquire the training necessary to do work that is compensated more highly. 
A conflict theorist's perspective on social stratification argues that it is the result of the owners controlling and exploiting workers. They believe it is not good for society to be so stratified because it only benefits some -- but not all -- of the members of society. Conflict theory is informed by the principles of Karl Marx, who believed that inequalities stemmed from whether a person was a member of the elite who owned the means of production or a member of the proletariat who worked for the owners. 
It's also important to consider that a functional theorist believes social stratification is necessary to motivate people with the right skills and intelligence to work in specialized positions. Conflict theory considers social stratification to result from a lack of opportunity to unprivileged people. 
Both theories can be further understood through a study of achieved and ascribed status.
Achieved status is a role or recognition granted by a person's own effort. For example, a college degree holder studied and worked to get that degree. A doctor went to medical school and completed his rotations and residencies.
Ascribed status is something that a person gets simply by being born, such as, a person's race, religion, or gender. A person can also be assigned a status later in life that they adopt as an ascribed status. 
Sometimes ascribed versus achieved status can even differ between family members. If a person worked hard to have a high economic status, it may be achieved. Their children, however, would be born into that status. So the children would have that economic position as an ascribed status. 
Having many positive ascribed statuses may help you successfully collect achieved statuses more easily. For example, a person with many economic resources and an excellent childhood education is more likely to attend college than someone who grows up poor and has to help raise their siblings. Major differences exist between people of different races, genders, and socioeconomic backgrounds that are explainable by those people's ascribed statuses.
Conflict theory argues that people are able to reach higher wages and better economic positions because of statuses which are ascribed to them and not achieved by them. A boy born to a king is destined to become a king himself, while a person born into poverty has relatively little chance of ever becoming a monarch. Conflict theory holds that these stratifications between groups are unfair and have negative implications for society because they contribute to wealth and wage inequality across racial and socioeconomic lines. Conflict theorists recognize the barriers that less-favorable ascribed statuses can present to people. For example, a person with a low socioeconomic status is less likely to have the resources to attend college. On the other hand, a person with a large trust fund can easily choose to become a doctor, a lawyer, or another professional with a favorable achieved status. Therefore, people born with more favorable ascribed statuses are more likely from birth to get high earnings. Ascribed statuses help explain and sustain wealth inequalities and the wage gap in societies between people of different backgrounds.
Functionalism, however, argues that all positions are important for society to work -- but that when you've achieved a status, you should be compensated for the value of that status. Because pro football players generate more money in advertisements and ticket sales than teachers do, their pay is millions more. Because medical training is a specialized skill that not everyone is capable of or willing to train to do, it is more highly compensated than a job that can be learned in a day. Functionalism says that social stratification, as well as wealth and wage inequalities, are the expected results of the unequal value of different jobs.For functionalists, education helps bridge the gap between ascribed and achieved status. People have the opportunity to gain knowledge and then train for a career that helps them move up from some of their socioeconomic ascribed statuses. A girl born into a poor rural family can, through hard work and education, end up with an achieved status of a high socioeconomic position. Functionalism doesn't ignore the fact that ascribed statuses may present barriers to certain achieved statuses, but it also doesn't account for it when considering the wage gap between different professions. 
Conflict and functionalist views have different opinions of social stratification. Conflict theorists point at the barriers for people with less favorable ascribed statuses and what they see as the unfair wage gap between different types of work. Functionalists, however, are more inclined to look at achieved statuses -- like education or job training -- as the reason for the wage gap that leads to wealth inequalities between groups. Conflict theorists would argue that functionalists need to consider that social stratification isn't a pure meritocracy, but rather a mix of a person's ascribed and achieved status. 
 
https://open.lib.umn.edu/sociology/chapter/8-2-explaining-stratification/

https://philschatz.com/sociology-book/contents/m42845.html

https://www.radford.edu/~junnever/articles/davis_moore.htm