Question

there is a tradeoff between equality and economic efficiency. why might, say the redistribution of income in order to increase economic equality reduce efficiency?

Answer 1

Equality in economics ussually refers to government intervention in the free market in the form of taxation, subsidies, payment transfers and so on but we'll just focus on taxes. In welfare economics, governments levy taxes which extracts capital/cash from the market and places it into the hands of the government.

Now, the government's supposed mandate is that it can put the the money to better use than the free market could have. The government may also believe that it can increase "equality" among market participants by taking money and using it for other ventures that may not have been pursued by the free market at will. For example, education and military defense spending. Education has a net benefit to society because it gives the next generation of consumers and workers all the updated knowledge of the current generation. Defense spending on the other hand protects a country from losing it's capital generating potential due to external threats.

After World War 2, capital in post-war countries in Europe was destroyed due to loss in war. Just to clarify, capital refers to industry, machinery and basically anything which can be used to produce goods. That capital loss had negative economic ramifications, but with a strong military a country could have come out rather unscathed in terms of its capital generating capability, like the United States. Just as a sidenote, a strong military gives the perception of stability and safety and makes foreign capital more attractive to be invested.

Disregarding that tangent we took, it is unlikely the free market would have spontaneously provided both education and military defence better than a centralized federal government could have. That is one arguement in favour of taxation.

However, if the government levies too high a tax, companies may forgo investing or buying new capital because they will have less money left over. As a result, economic efficiency will decline - high levels of taxation have the cost on efficiency because it might interfere with a company's ability to conduct business. A balance is needed, and thus there exists tradeoffs between equality and efficiency.

Just as another side note, taxation creates something called "externalities" which is money lost forever so to speak - neither the companies nor the government can make use of that money. You may not have covered it yet, so I didn't discuss it.