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CHAPTER 7

WHY ARE THERE MORE MEMBERS OF A BAND THAN PROFESSORS IN A CLASS?

Diminishing Marginal Returns and the Demand for Labor

Guitarist Eric Clapton was inducted into the Rock & Roll Hall of Fame as a solo artist, and yet he seldom plays alone. He was also inducted into the Hall of Fame as a member of both the Yardbirds and Cream. Ladysmith Black Mambazo tours with 10 singers, whereas their friend Paul Simon often performs solo. Like any employer, bands could always add more people to their workforce or lay a few people off, or a band member could go it alone as a professor does. In this chapter you will learn how these decisions are made, and how rockers and professors differ in spite of the remarkable similarities in their lifestyles, wardrobes, and value to society.

When bandleaders, businesses, and colleges contemplate taking on new personnel, they want to know what hiring additional workers could do for them. The contribution of 1 more worker to the level of output per period is called the marginal product of labor. If adding a professor at a college with 100 professors allows 30 more students to be taught each year, the marginal product of the 101st professor is 30 students per year. If another barista (coffee bartender) at Starbucks allows the store to serve 12 more lattes per hour, those 12 lattes are the last-hired barista’s marginal product. And if a new band member would improve the band’s sound and lead to 1,000 more CD sales per year, the marginal product of that band member is 1,000 CDs per year.

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In the classic film Mary Poppins, actor Dick Van Dyke becomes a one-man band by strapping instruments onto his body. Modern one-man bands, such as Bernard Snyder,¹ appear at popular tourist destinations. The problem with such bands is that the one player is unlikely to gain mastery of the many instruments. Likewise, if you were the only worker in an espresso bar, you would have to divide your efforts among making coffee, serving customers, cleaning, stocking, running the cash register, and the many other tasks involved. With the first worker wearing many hats, each of the first few additional workers might contribute more to total product (the total number of drinks made per hour) than the previous worker, meaning that marginal product is increasing.

¹ See www.onemanband.org.

If going from 1 to 2 workers allows 1 person to get really good at making drinks while the other person can develop cash register and cleanup efficiency, the marginal product of the second worker can exceed that of the first. On working-joe.com, the staff of Working Joe Espresso suggests that a worker with divided attention can serve 10 drinks an hour, whereas a focused barista can serve 40 drinks an hour. The marginal product of the first worker is 10 because the total product increases from 0 to 10 when the first worker is hired. The second hire allows 1 person to focus on espresso-making skills and deliver 40 drinks per hour. The marginal product of the second worker is 30, because total product increases by 30, from 10 to 40, when the second worker is hired.

Alas, marginal product can’t keep increasing forever. According to the “law” of diminishing marginal returns, as more of one input—such as land, labor, or equipment—is added to fixed amounts of technology and other inputs, the marginal product must eventually fall. The short run is defined as the period of time during which the quantity of at least one input cannot change. The amount of fixed inputs, including machinery and buildings, is fixed in the short run because of the length of time it takes to make such changes as installing new equipment, building buildings, and getting out of leases. The amount of variable inputs, such as labor and ingredients, is always adjustable. It doesn’t take long to hire or fire an employee or to order a new sack of coffee beans. Every input is variable in the long run.

In accordance with the law of diminishing marginal returns, the path of marginal benefits from myriad economic pursuits turns downward sooner or later. Efficiency dictates that each activity should be carried out until the marginal benefit no longer exceeds the marginal cost, and it is the fall of marginal benefits that brings a halt to many a virtuous endeavor. Other chapters in this book discuss how the marginal utility that consumers seek and the marginal revenue that firms seek generally fall. Marginal product falls sooner or later, too, as opportunities for specialization run out, redundancy sets in, and the usefulness of fixed inputs (such as stages, espresso bars, and classrooms) is spread thin by growing quantities of variable inputs (such as musicians, baristas, and professors).

Let’s extend the previous section’s example of the espresso bar, in which the marginal product is 10 for the first worker and 30 for the second. The accompanying table presents production levels for each quantity of workers. With 1 person already working the cash register and another working the espresso machine, a third worker may be useful for keeping beverage ingredients stocked and helping to make drinks, contributing a marginal product of 20. A fourth worker wouldn’t have a lot of equipment to work with but could increase sales by 15 espressos per hour by covering other workers’ breaks, wiping tables, and helping the other workers stay focused on their specialized roles. A fifth worker would have less important tasks to complete but might increase sales by 5 espressos per hour by helping to take customer orders, checking in new shipments, and washing dishes. In similar ways, diminishing marginal product would be observed as more band members were added to a stage with a fixed number of instruments and as more professors were added to a fixed number of classrooms. Notice in the table that total product increases even as marginal product decreases; any positive marginal product represents a contribution to the total level of production.

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Can marginal product be negative? Yes, indeed: At some point another worker simply gets in the way. A second barista at the drive-through Java Hut in the mall parking lot would make things cozy, and a third might deny all of them enough space to take a deep breath. When additional workers don’t have much to do, their boredom invites distracting conversations and horseplay. When office workers are bored, they go on-line, often to send messages to other people who should be working. As evidence that such problems are real, increasing numbers of employers are using filtering services from companies such as Websense.com to block employees’ access to anything from instant messaging and Internet porn to eBay and peer-to-peer services for sharing music files.

Seventy-six trombones led the big parade,

With a hundred and ten cornets close at hand.

They were followed by rows and rows of the finest virtuosos—

The cream of every famous band.

—From “76 Trombones” in The Music Man

Not all bands, espresso bars, colleges, and factories are alike. The rate at which marginal product decreases depends on the situation and the amount of the fixed input. There may be 76 trombones in the big parade, but a folksinger can sing and play the guitar with little need for accompaniment. One player cannot make an orchestra, however, and the marginal product of the players needed to fill out the critical strings, brass, percussion, and woodwind sections is large. The contribution of a guitarist, backup vocalist, or drummer for singer Alanis Morrisette is positive but not so large. If you’re looking for really big sound, consider William Havergal Brian’s “Gothic” symphony (Symphony No. 1, 1919–1927), the largest symphony ever written. It requires 200 players in the orchestra itself, plus 4 brass bands and 4 large mixed choirs, for a total of more than 1,000 musicians and singers.

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Why does guitarist Keith Richards appear with Mick Jagger and the other Rolling Stones, whereas Brandeis University professor and former U.S. Labor Secretary Robert Reich takes the stage alone at his lectures? It’s not because additional professors cost more than additional rock stars; it’s because additional professors contribute less than additional rockers do. That is, professors’ marginal product plummets as more of them are added. The first professor brings intellectual intrigue to the audience. A second professor at a lecture could perhaps take over the diagram-drawing duties of the first and prevent those awkward moments when the speaker’s back is turned to the audience. A third could run around glaring at students who aren’t paying attention. These extra professors may not be worthless, but their contributions aren’t on the same scale as adding a drumbeat and harmony to vocals. The negligible marginal product of professors beyond the first in a classroom explains why there are more members of a band than professors in a class.

No employer wants to hire another worker after marginal product has become negative, meaning that additional workers will actually reduce output levels. However, there’s a big difference between negative marginal product and diminishing marginal product. Employers generally do want to keep hiring after marginal product starts falling. The important reason is that any positive marginal product represents a contribution to total product. Employers are wise to keep hiring as long as the marginal product of an additional worker brings in at least as much money as that worker must be paid.

The amount of money that an additional worker brings in is found by multiplying the marginal product of that worker by the marginal revenue of the good or service (meaning the additional dollars gained from each new unit sold). If another band member increases CD sales by 1,000 and each CD sells for $10, that last-hired band member contributes 1,000 × $10 = $10,000 to the revenues of the band. Economists call the additional revenues from hiring one more worker the marginal revenue product. As marginal product decreases, so does marginal revenue product. In order to maximize profits, an employer will hire until the marginal revenue product equals or falls below the wage rate.

Consider an espresso bar whose first 5 workers have marginal products of 10, 30, 20, 15, and 5 drinks per hour, respectively. If each espresso sells for $2, the marginal revenue product for these workers is $20, $60, $40, $30, and $10 per hour, respectively. If the wage rate is $12 per hour, 4 workers should be hired. The revenues generated by the first 4 workers exceed their $12 cost per hour, but there’s no sense in paying $12 for a fifth worker who will only bring in $10!

The demand for workers is linked directly to the demand for products. If the demand for espresso increases and drives the price up to $3 per espresso, the marginal revenue product of the first 5 workers will increase to $30, $90, $60, $45, and $15 per hour, respectively. With this higher demand for espresso, the fifth worker will be worthwhile to hire because he or she will bring in $15 worth of sales for a $12 wage. Because the demand for labor is based on the marginal revenue product of labor (the marginal product of labor times the output price), and the output price component of marginal revenue product is derived from the demand for the output, the demand for inputs is called a derived demand.

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This chapter explains the reasons for diminishing marginal product and provides several real-world implications. You will find more applications of this concept everywhere you look. Let’s consider one more example: Would you, could you, find diminishing marginal product in a boat?

If you’ve spent much time in a rowboat, you’ve probably seen that 1 person can row gently down the stream at about 2 mph. With 2 rowers in a boat with 2 oars, each can take an oar and the speed may increase to 3 mph, making the marginal product of the second rower a 1-mph increase in speed. A third person in the boat has no oar to work with but might increase the speed by 0.5 mph up to 3.5 mph by directing the back-facing rowers and preventing them from veering off course. A fourth person simply gets in the way and weighs down the boat, perhaps slowing the speed back down to 3 mph for a marginal product of 20.5 mph.

Diminishing marginal product affects everything from the speed of our progress while rowing to the decision about how many musicians the folk band Beggars Row should hire. And no matter what your economics professor’s ratings are on www.ratemyprofessor.com, a second professor in the same classroom probably wouldn’t be nearly as valuable.