Marginal Product of Capital

Analysts and economists...always thinking on the margin, and about inputs and outputs. (As do dieticians and proctologists.) “Thinking on the margin” means thinking about an additional unit of something.

Inputs, sometimes called “factors," are the things firms use to make stuff to sell. An output is the ending product that goes to the consumer market, called “product” by firms.

The marginal product of capital asks, “How much more product (the output) would we have if we added one more unit of capital to the production process?”

The marginal product of labor is the same, except we switch the input of “capital” with the input of “labor.” The marginal product of labor asks, “How much more output would we have if we added one more unit of labor into the system?”

With both of these, we’re not looking at total output, but rather how much more we get if we tinker around with our inputs a bit.

Let’s take a look at man’s best friend to see how marginal product of capital and marginal product of labor interact. No, not dogs...we’re talking about the one in your pocket. Um...your phone.

In a cell phone factory, you’ve got an assembly line with embryonic phones, making their way through the production process. On that assembly line, there’s a mix of humans and robots, each specialized in an area of phone production. A firm has the goal of increasing profits, which means reducing costs as much as possible. Sure, having the assembly line helps...but what mix of robots and humans will cost the least?

That’s where the “least-cost rule” comes into play. The least-cost rule says that, to minimize costs, find how much marginal product a dollar spent on each input-type makes...then set them equal to each other.

At the phone gestation factory, that means the firm can figure out how many workers to hire and how many machines to rent to minimize costs. If we were to look at the marginal product of laborers and the marginal product of machines, we'd see that each additional one of them yields less and less marginal output. That’s the law of diminishing marginal returns rearing its ugly head. If laborers cost $10 per hour and machines can be rented for $8 an hour, then we can calculate the marginal product-to-price ratio for each.

Quiz time: how many workers and how many robots will the firm hire? Remember, firms can get the most bang for their buck by employing the quantity of inputs where their marginal product-to-price ratio equals each other.

Depending on how much money the firm has, it has a few different options. The phone firm could hire one worker and two machines, each which have a marginal product-to-price ratio of 6. Let’s think about what that means for a minute. The first worker hired would result in a marginal product of 60...so, adding 60 more phones to total output. But at what cost?

$10. Six additional phones per dollar.

The first machine is adding 64 more phones to total output for $8, which means 8 more phones per dollar. Eight more phones per dollar is better than six phones per dollar, right? So...we hire a second robot.

A second robot will only bring in an additional 48 phones, and still costs $8 to rent. For the second phone-assembling robot, 48/$8 is 6 additional phones per buck spent. Wait a minute here. Same marginal product-to-price ratio as the first human.

You might be thinking: why not just hire all robots? Well, because hiring the first worker is a better deal than hiring the third robot. Hiring the first worker gets you 6 phones per dollar and the third robot gets you 4 phones per dollar. Which is why the least cost rule works: if your MP/Ps are unequal, it means you’re missing out on a more cost-effective input combo. If the phone firm has more money, it could hire where MP/P is 4, which means 2 workers and 3 machines. It could also hire where MP/P equals 2, which means 3 workers and 4 machines.

Firms have to know their marginal product of capital and marginal product of labor so they can tinker with the numbers, finding the least-cost way to produce their product. Otherwise, some other firm will be finding a lower-cost way to make the product, which could then use that advantage to undercut its competitors, pushing them out of the market.

It’s like Survivor, but with firms. Everybody’s gotta stay neck 'n' neck to keep their skin in the game, or else they’ll have to leave the island. So, if you’re a firm, tinker away with marginal product. And hopefully you’ll never hear the words “The tribe has spoken.”