First, a useful definition for understanding the following.
Rent-seeking is a concept in public choice theory, as well as in economics, that involves seeking to increase one's share of existing wealth without creating new wealth. Rent-seeking results in reduced economic efficiency through misallocation of resources, reduced wealth-creation, lost government revenue, heightened income inequality, and potential national decline.
National Review: The Conservative Inequality Paradox
Conservatives have two intellectual commitments that are increasingly incompatible. They believe that the American economy is clogged up with crony-capitalist corruption that hands out special favors and protections to organized interests. They also hold that economic inequality — in particular, the surging share of total income earned by those at the very top — is morally justified by the rights of property and the tendency of free markets to raise living standards overall.
So, it looks like (at least some) conservatives are of the belief that income inequality is not necessarily an issue that needs to be tackled, but the current state of inequality came about via corrupt influences over the market, and that situation is something worth fixing.
[W]e argue that conservatives are not mistaken about the extent of what we call “regressive regulation” — government-created distortions of markets that have the effect of funneling income and wealth up the socioeconomic scale. Such schemes of upward redistribution have proliferated in the past few decades, an era that is often misunderstood as one of unceasing deregulation. And because these reverse–Robin Hood policies work by squelching and misdirecting competition, they exert a powerful downward drag on output and growth as well.
They define these corrupt influences as being rooted in too much government intervention in the markets.
In the best of all worlds, conservatives would respond to this state of affairs by attacking rent-derived inequality at its source. Their economic agenda would focus on curtailing subsidies for finance, excessive protection of intellectual property, the licensing of high-end professionals, and overly restrictive land-use regulation. Doing so wouldn’t require conservatives to become crusading egalitarians, as these reforms would also unleash economic dynamism, innovation, and growth — familiar conservative priorities.
This article argues that the best solution would thus be to tackle the issue of undue government influence in the markets so that wealth can be redistributed naturally by the marketplace in accordance to ability rather than through rent-seeking behavior.
Nevertheless, making regressive regulation a conservative priority would be a distinct change in approach. Too often, conservatives’ idea of a pro-growth policy agenda starts and ends with tax cuts, despite the overwhelming evidence that moderate increases or decreases in the top rate have little effect on growth. When conservatives do turn their attention to regulation, they usually think about providing “regulatory relief” for business by lightening health, safety, environmental, and labor regulations. In our view, though, the regulations with the most pernicious economic effects are the ones that subsidize business by blocking competition or by otherwise distorting markets.
However, this article makes clear that this is not the typical approach taken by conservative policy makers. Rather, the typical approach would be to focus on a pro-growth agenda through the use of tax cuts. Furthermore, when typical conservative policy turns to deregulation, it tends to focus on regulations that are more burdensome for businesses rather than on those regulations that distort the market effects.
Many conservatives did not look carefully at the evidence behind these dodgy empirical claims because they believed that they held the moral trump card: By cutting taxes, they were returning wealth to its rightful owners. But in the “captured economy” we’re currently living in, this belief is due for reexamination. Not only is a significant fraction of the rich’s income morally tainted by government favoritism, but it is also used to fund yet more rounds of regressive rent-seeking.
This article argues against the traditional solution of tax cuts because this returns wealth to the current holders of wealth rather than the rightful owners. That is, the wealthy have engaged in rent-seeking behavior to promote government intervention into the markets so that they can maintain or grow their wealth. By cutting taxes, the wealth returns to these individuals that corrupted the market so that they can in turn use their wealth to further corrupt the markets. However, in an ideal market, rent-seeking behavior should be discouraged and wealth should be distributed according to ability and ones contributions to the marketplace.
One way to begin solving this problem would be to build a veritable bonfire of the deductions that the wealthy use to shield their income from taxation. The exclusion from taxes of employer-paid health insurance, retirement savings through 401(k)s and IRAs, and education savings accounts could either be scrapped or converted into refundable tax credits. We could also consider a financial-transaction tax, which could raise a lot of revenue while also reducing the incentives for excessive trading of assets. Changes such as these would allow us to claw back some of the rents at the top of the economy without increasing the marginal income-tax rates that conservatives are so concerned with.
Some proposed solutions would be to do away with some of the financial instruments that promote rent-seeking behavior in the wealthy so that their assets are more likely to re-enter the marketplace for redistribution via market forces.
If conservatives took seriously the presence of ill-gotten gains at the top of the income spectrum, they might also look at immigration policy in a new light. Over the past few decades, the United States has exposed those at the bottom of the economic pile to intense global competition, whether in the form of products from China or workers from Mexico. As Dean Baker has argued, it is high time to expose the wealthy to those same bracing forces of competition by opening up the economy to more high-skilled immigrants, especially in protected professions such as medicine and dentistry.
Some further proposed solutions are in promoting more high-skilled immigration to the United States in order to bring more competition into the top end of the marketplace.
It looks like the general conservative viewpoint is that inequality is natural and a consequence of a healthy marketplace. Some conservatives presumably view the current situation as a natural consequence that does not require fixing. However, as is argued in this article, some conservatives view the current inequality as unnatural and a result of too much government intervention, so the solution would be to reduce the government influences on the markets. Overall, in regards to this latter argument, there is a lot that liberals would agree with: most notably that the wealthy elites have used their economic positions to influence government in their favor.
It might be worthwhile to note that I am on the political left, so it's possible that this summary is distorted by my viewpoint (however, I've tried to avoid this).