What are two opposing theories on racial inequality? (With theorists)

Two theories that hold distinctly juxtaposing views on racial inequality are Marxist and Functionalist theory. (These theories can be set against each other in most essays as they are on distinctly different ends of the political spectrum.)
Marxism, as a macro conflict theory takes a pessimistic view on race relations. They stress that immigration exists to serve the capitalist class's need for labour and that racial tensions are deliberately built up by this capitalist class to divide workers from each other so they are easy to control. Marxist theorists would therefore argue that racial inequality is not a natural byproduct of the differing nature of various ethnic groups, but rather argue that it has been socially constructed by the Bourgeoisie to benefit their capitalist interests. Cox (1970) stressed the idea that 'race' itself was a human creation and is always something created to exploit. Cox, like many Marxist theorists, argues that racism has its origins in the development of capitalism, with its inherent need to exploit labour power. Cox cites the earliest example of this as colonialism, where the argument of the racial superiority of white Europeans over other races meant that their exploitation for the benefit of the empires economic situation was seemingly justifiable. Cox further argues that only white people are capable of racism in the UK as, as racism is used to justify exploitation it can only be constructed by the individuals with the power to control the narrative, not the exploited themselves- to Cox, the individuals with this power (in the context of racism in the UK which we are looking at) is always the white economic elite. To Marxist theorists like Cox racism is dependant on capitalism, and without capitalism there would be no racial inequality.
As a consensus theory- Functionalism takes a distinctly different approach to racial inequality to Marxism. Functionalists argue that the early ethnic inequalities experienced by immigrants were the product of their cultural difference and relatively low level of skills- placing the origins of racial inequality much more on individuals and personal choice, rather than on a more abstract and inescapable social force like capitalism, as the Marxists have done. Functionalists are also much more optimistic that Marxists, arguing that in a meritocratic society ethnic inequalities would decline as immigrants adopted the norms and values of mainstream British society and climbed up the social hierarchy. The functionalist Patterson (1965) offers a very different account of racial inequality than Cox in his host immigrant model. Patterson viewed Britain as a stable, homogeneous society with an established degree of consensus over the established norms and values. However, this equilibrium was disrupted by the arrival of immigrants in the 1950's who subscribed to very different norms and values, resulting in a culture clash. Patterson argued that the hosts were not actually racist, just unsure of how to act towards the newcomers. Patterson argues that there were 3 causes of ethnic inequality therefore: The first being the hosts fear of the cultural difference these 'strangers' may bring with them. Secondly, the hosts resentment over having to compete with immigrants for scarce resources such as jobs and housing and thirdly, the immigrants failure to assimilate. Here we see, the functionalist approach implies that immigrants who continue to practice their native culture may encounter racial prejudice through their actions, rather than that of a socially constructed system of prejudice. This is a key difference between the functionalist and Marxist approach, the most notable other being their differing views on whether racial prejudice will ever subside, with functionalists taking the optimistic approach that prejudice will naturally decline as immigrants assimilate and Marxists claiming that such discrimination will only fall away with the destruction of capitalism.