A true conservative would do his/her best to see that middle-class and lower-class (economically) people would get favorable tax treatment, since they spend most of their disposable income and their consumerism is the engine behind economic growth in the US. Giving tax cuts to the wealthy, and to businesses that export jobs overseas is NOT conservatism. It is not rational behavior based on concern for the common good, but short-sighted bias to benefit the wealthiest and most powerful.
There's at least three different Republican Party economic philosophies. I'm not sure which would be considered the "true conservative policy", but I'd guess Reagan's supply-side tax cuts for the wealthy and business wouldn't be it - or at least not the traditional conservative approach since it was still a very new Republican idea when Reagan ran in '80 (it started to become popular in the mid-70's).Reagan didn't bloat government. He wanted to cut a lot of government spending, and was criticized for the amount he was able to get cut. In fact, the establishment Republican party actually fought against him on some of this, because they were benefiting from some of the big-government he wanted to cut.
1) Monetarism, or balanced budgets. The government should never spend more money than it takes in. I think this is the traditional conservative approach with no pre-determined doctrine over whether a specific tax increase/cut is worthwhile or not.
2) Keneysian tax cuts designed to increase demand. Tax cuts to middle class and lower income workers to increase disposable income that increases demand for products. If it's accompanied by cuts in government spending to avoid deficits, then it would qualify as a traditional conservative approach. If the tax cuts take priority over the spending cuts, then it wouldn't.
3) Supply-side economics with tax cuts designed to increase investment. Tax cuts to businesses/wealthy that increase the amounts of products created, thereby lowering prices and making them more affordable. This was Reagan's economy and, if the idea hadn't come along during double digit inflation, would have been laughed off the stage. Why would someone create a product if there weren't a demand for it just because it became cheap to produce?
Obviously, the supply-side idea is slightly oversimplified and it was a good tactic for its time, in spite of contributing to large budget deficits. The unspoken part of the equation was that US manufacturing had old facilities and needed new investment to keep up with foreign competitors (aside from other disadvantages that just became worse later on). I think it would be kind of foolish to declare "Reaganomics" a magic bullet that applies to normal economic situations.
And, actually, Volcker's almost malicious manipulation of interest rates (at least malicious if you were a construction worker seeing the housing market come to a complete halt) may have done at least as much to curb inflation as Reagan's tax cuts.