In general, efficiency is a ratio: output divided by input. The efficiency of a gasoline engine, for example, is the mechanical energy produced at the drive shaft (in joules) divided by the energy contained in the gasoline burned (also in joules). Because engines are lossy, the ratio will be less than one. Another way to measure efficiency is miles driven (output) divided by gallons of gasoline (input).
There are two ways of looking at economic efficiency. The efficiency of a capitalist company is usually the revenue divided by the total costs (excluding dividends and reinvestment). A company that operates with an efficiency greater than one is profitable. (If we include dividends (the cost of capital) and reinvestment, then this measure of efficiency can never be greater than one.) So a company can be more efficient, i.e. more profitable, if it can get more revenue for the same costs, or lower the cost to receive the same amount of revenue. The advantage of this conception of efficiency is that (the complexities of accountancy notwithstanding) it's relatively easy to measure. Since both the numerator and denominator are measured in nominal dollars, I'll call this the nominal efficiency.
Another way of looking at economic efficiency is use-value produced divided abstract labor time. This measure has intuitive appeal because it directly states what we think we should really be doing economically: using human time and effort to make our lives better. This sense of efficiency is enormously difficult to measure directly. Use-value is completely subjective, and abstract labor time itself has subjective components. One of the chief tasks of economists (and one reason economics is so difficult) is trying to extract some rational sense of this measure of efficiency from the raw data. The difficulties notwithstanding, we have an intuitive sense that improving this sense of efficiency is what we're really trying to do, so I'll call it the real efficiency.
One of the big problems with nominal efficiency is that there are two different methods of lowering costs: using less abstract labor time, or by paying the workers less for the same amount of work. The first method, while it sometimes causes local problems for displaced workers, raises the real efficiency of the economy (assuming the company produces the same amount of use-value).
The second method — paying workers less — actually reduces real efficiency. Similarly, paying workers more increases real efficiency while reducing nominal efficiency. (And, similarly, raising and lowering revenue has opposite effects on nominal and real efficiency.) The reason for the opposite effect is the falling marginal value of consumption.
Economists often make a simplifying assumption at the macroeconomic level that all dollars are equal: one dollar buys the same amount of use-value regardless of who spends it. But at the microeconomic level, the concept of the falling marginal value of consumption is well-understood. Margin in economics simply means "the effect of one more". If I already have nine widgets, then there is some value — the marginal value — specifically attached to obtaining the tenth. The marginal value of the tenth widget is different from the marginal value of the ninth; all my widgets are not alike. If Donald McCapitalist buys a hat-making machine for $1,000,000.00, and it takes one minute of abstract labor time (paid at $12/hour) to operate the machine to make one hat, then the marginal cost of the first hat (the difference between one hat and zero hats) is $1,000,000.20 and the marginal cost of the second hat is $0.20.
To understand the falling marginal value of consumption, imagine that you walk into a fast food joint around lunchtime on Monday. You're hungry, so you buy a hamburger for $1 and you eat (consume) it; you're no longer as hungry as when you walked in. You have just obtained use-value: you're less hungry and you had the pleasure of eating a burger. The marginal use-value of consuming the first hamburger is rather high, and the cost is $1, or 5 minutes of labor if you're the guy making hats. You're still a little hungry, so you buy and eat another hamburger. You weren't quite as hungry as you were a minute ago, so the value of relieving your hunger is a little lower. You also just had a hamburger, so we can imagine that the pleasure of eating another hamburger is also reduced. After two hamburgers, you're not hungry, but you're not really full, so you buy a third. There's really no point to eating a fourth, and after a fifth you're in Mr. Creosote territory. The more hamburgers you eat (in a short period of time), the smaller the pleasure you derive from eating the next one: the marginal value of consumption is falling.
The real efficiency of eating the hamburger is the output (the use-value) divided by the input (cost). It's hard to assign an actual number to the use-value, but we can order the marginal use-values: the use-value of the second hamburger is definitely less than that of the first, and the third is less than the second. Since the cost ($1 or 5 minutes of labor) remains the same, so the marginal efficiency of buying and eating each hamburger likewise falls.
You walk into work on Tuesday morning, and your boss tells you that they're cutting your wages to $6/hour (grumble grumble). When you walk into the fast food joint on Tuesday noon the marginal use-value of eating hamburgers is about the same, but the cost has doubled: a hamburger now costs you 10 minutes of labor. So your real marginal efficiency of consumption has been halved.
(There's another measure of efficiency: use-value per transaction. When you have less money (things cost more labor time), you're going to concentrate your individual purchases on high value items. On Monday you might have bought three hamburgers; on Tuesday you'll only buy one or two. If you have to cut spending, you'll cut out the lower value purchases. Lowering wages thus increases the transactional efficiency.)
Since presumably Acme Hats is still charging the same price for hats, their nominal efficiency has increased. More importantly, their revenue is still going somewhere, presumably paid to Donald McCapitalist, who owns the hat-making machine. But Donald McCapitalist already has a lot of money and he already consumes a lot. If it's really true that the more you consume, the lower your marginal use-value (and thus marginal efficiency), then the increased use-value of Don's additional consumption should be in some sense lower than the loss of use-value caused by your falling wages: Don can now afford to buy the 20th hamburger at lunch, but so what?
There are, of course, a lot of other factors. If Don lowers the wages at Acme Hats, then presumably all the other hat makers can lower their wages too. Eventually someone will lower their prices, forcing Don to lower his own prices, thus decreasing his revenue and bringing his nominal efficiency back to where it was. If everyone follows suit, you'll only be making $6/hour, but a hamburger will cost only $0.50, and your consumption efficiency will eventually also return to where it was. But there's a catch! The hat making machine, bought when wages were $12/hour, still has a nominal cost of $1,000,000 regardless of deflation. Even though his nominal marginal cost has been cut from $0.20 to $0.10, the $1,000,000 for the machine still has to be amortized across, say, a million hats. Although prices have halved, Don still has to charge more than $1.10 per hat instead of $1.20 per hat to make a profit. Overall prices "ought" to be cut in half, but Don can cut his own prices only ~9%!
Worse yet, a new competitor can buy the exact same machine for only $500,000, and he has to charge more than only $0.60 per hat to make a nominal profit. If Don is clever, though, he'll put Acme Hats in receivership, start a new company, buy the used machine for $400,000, and the bank that lent him the original $1,000,000 will be holding the bag. But of course the banker is not stupid either: he'll just raise your credit card interest, the credit card you're using to survive on $6/hour until all the prices eventually lower themselves. For the worker, capitalism is heads I win, tails you lose: they get you coming, going and standing still.