But is it really a tradeoff? Only if we believe that "6. markets are usually a good way to organize economic activity," because then any government efforts to achieve greater equality through promoting a more secure society (better healthcare, government programs to protect the unemployed) are confounded by "leaky buckets" because they are outside of the market. But what if these measures for greater equality led to greater efficiency because we are a stronger, more stable community?
I guess we can't think like that -- "4. people respond to incentives" after all, so unemployment insurance reduces the incentive for "3. rational people [who] think at the margin" to enter the workforce. And since "2. the cost of something is what you give up to get it," unemployment insurance makes your leisure time cheaper than it would have been otherwise, causing you to misallocate your time between work and leisure.
Let's think about this "market" in the broad picture.
When Marx addressed to workers whether they should be for or against free trade, i.e., whether "5. Trade can make everyone better off," he came out neither for nor against it -- it was, he argued, simply not on the table of worker concerns, since in capitalism the fundamental point of reform is the labor process and who controls various aspects of it. That is, economics today -- certainly not an abstract idea which has existed in its same form since the Greek's gave the term "oikonomos, which means 'one who manages a household,'" -- is not "the study of how society manages its scarce resources," (pg. 1) it is about who has control and rights and property in the workplace -- that is, after all, what distinguishes capitalist economics from former economic systems (e.g., hunter-gatherer, feudalism) in the first place.
And so the so-called "principles" that "9. prices rise when government produces too much money" and that "10. society faces a short-run trade-off between inflation and unemployment" are far from god-given facts and concerns of all of economics: they are products of a unique way of thinking about the economy which is rooted in concepts particular to the market-oriented view of society, and not necessarily real concerns of workers fighting for better living standards (because productivity does not give it to them), women searching for equal treatment in the household (because they could care less about incentives for entering the workforce), or even big financiers (who are far from rational people at their margins).
All principles from Mankiw, Principles of Economics (4e, 2007)