Prices and wages

Let's see if we can figure out what effect lower wages would have on prices, and the possible welfare gains from those lower prices. Remember, the reason we import manufactured goods probably has more to do with the wages in countries like China, India, Indonesia, Mexico, etc. than anything else. Arguing that there is comparative advantage is, in my opinion, a very long stretch. So, how big an effect do lower wages have on prices?

Let's organize our thinking as follows. First, what will the price of a good be? What determines that? Well, as you should know, if there are constant returns to scale and free entry,

price = average cost

Average cost is the cost of the inputs used + normal profit divided by the quantity of the good produced. (Remember, normal profit is profit when the firm's rate of return in the going rate of return, the ROR that anyone with money to invest can get.)

For example. Suppose 2 million tons of steel are produced. Suppose the workers are paid $100 million (including fringe benefits, etc.), all the other inputs cost $120 million, and the firms producing the steel make a profit of $30 million on that steel. Then the cost of producing that 2 million tons of steel is $100 + $120 + $30 = $250 million. Therefore, the average cost of a ton of steel is $250 million divided by 2 million tons = $125. And that would end up being the price of steel, in equilibrium.

So, if firms pay workers less (lower wages), then one component of cost goes down and that lowers average cost and in turn price. By how much, percentage-wise? Let's figure that out. We're going to make a very strong assumption and so what we end up with is what we would call a benchmark. (Think of a benchmark as a starting point for discussion.) That assumption is an assumption about the technology being used. We'll assume there are fixed proportions. That means the quantity of a good produced divided by the quantity of one of the inputs used to produce it will always be the same. That ratio doesn't change as output changes or as input prices change.

For example, suppose a good is produced using X poundsof a raw material and a machine that is operated by two workers. If the machine is run for 8 hours, 1000 units are produced. No more, no less. What happens to production if you add a worker, ceteris paribus? Answer: nothing. (In fact, maybe it goes down, since the worker with nothing to do distracts the two individuals actually working.) What happens if we add a machine, ceteris paribus? Answer: again, nothing; there's no one to operate it. Let's look at the ratio: output over pounds of raw material used to produce that output. What is that ratio? Answer: X. It doesn't matter how much is produced, or what the price of the raw material is. The existing technology converts X pounds of raw material into 1 unit of product using 2 workers and a machine. End of discussion.

All right. Let's suppose that we have two workers and one machine. And from those inputs, we get 1000 units. (We'll forget about raw materials, to keep it simple.) Then if 2Q units are produced, 4 workers and 2 machines will be employed etc. That means that average cost is

(wage x 2 workers + price of a machine x 1 + profit)/1000

if 1000 units are produced, and

(wage x 4 workers + price of a machine x 2 + 2 x profit)/2000

when 2000 units are produced. Convince yourself that the 2 average costs are the same. (Look at the one right above and cancel out a 2 from both the denominator and numerator, i.e. bottom and top.)

Now let's go back to our steel example.

production = 2 million tons of steel

labor cost = $100 million

all the other input costs = $120 million

profit = $30 million

total cost = $250 million

average cost = price = total cost/quantity produced = $250 million/2 million = $125 a ton

Note that labor cost is 40% of total cost: $100 million/$250million = .4, or 40%. That's what we would refer to as labor's cost share. OK, what if there are lower wages in the steel industry, for whatever reason? Say wages go down by 50%. That means they are .5 x what they were.

Well, that has no effect on other input costs and profit. It just lowers that $100 million labor cost to $50 million. Remember, steel makers can't change how much labor they use to produce 2 million tons of steel. So, what does this change do to average cost and in turn, price?

Let's see. Now we have

production = 2 million tons of steel

labor cost = $50 million

all the other input costs = $120 million

profit = $30 million

total cost = $200 million

average cost = price = $200 million/2 million = $100 a ton

What do we see here? Answer: a 50% decrease in wages only lowers the price of steel by $25/$125 x 100% = .2 x 100% = 20%. Why is that? Because labor cost is only part of the cost. If there were only labor costs, then a 50% decrease in labor cost would translate into a 50% decrease in average cost and thus, a 50% decrease in price. Here's the moral to this figuring: the effect of a change in wages on price depends on what part of total cost labor cost is.

Now you do the figuring. Using the amounts below, figure total cost = 1) ; average cost = price = 2) ; labor cost/total cost = 3)

production = 2 million tons of steel

labor cost = $70 million

all the other input costs = $180 million

profit = $30 million

All right, now suppose wages are cut by 50%, what will the percentage decrease in price be now that labor's cost share is less? Put that percentage in 4)

OK, let's think about how lower wages affect price, more generally. As it turns out, we can use the following formula:

% change in price = labor's share of costs x % change in wage

Thus, if you find that labor's share is .2 and wages go down by 60%, price will go down by .2 x 60% = 12%.