Derived Demand for Inputs

I. Introduction and Review

NOTE: For those of you planning to take the CLEP exam, the study guide put out by Princeton Review on Economics has an excellent treatment of Microeconomics. There are also excellent online testing materials.

First, let’s talk about our midterm exam that we just completed. The main cause of answering economics questions incorrectly is misunderstanding the question. Often, once the student understands the question, the answer is obvious. But there are many careless errors made in taking economics exams. Reduce those errors, and you will increase your score. Read the question, and reread it if necessary, in order to understand it.

Most questions have a purpose to them. Look for that purpose. For example, the most difficult question on our exam was its last question:

  1. Suppose the demand curve is this: P = $100/Q . Its price elasticity of demand is:

(a) inelastic

(b) unit elasticity

(c) elastic

(d) none of the above

What is the purpose of that question? To see how good a mathematician you are? Of course not. It must be getting at something else.

When P = $100/Q, then (PxQ) = $100. But PxQ is simply revenue. So the revenue is the same amount ($100) no matter how much the price is changed. That is the special characteristic of something that has unit elasticity.

Consider the graphed questions on the exam. There were many four different points for selling the good to the public. But the public is not going to buy anything unless it is on the demand curve. So any point not on the demand curve could be eliminated as an answer.

My favorite question was this:

  1. Matt, Anthony and Bill were studying for their only final exam, which is in economics. After studying a while, Matt said he’s not going to study any more because he’s reached the point of diminishing returns. Anthony said he’s not going to study any more because he’s reached the point of maximum marginal returns. Bill said he’s not going to study any more because he’s reached the point of minimum marginal returns. Who’s right if they want to do their best?

(a) All of them

(b) Anthony and Bill

(c) Matt and Bill

(d) Bill, maybe

The correct answer is (d). To do one’s best, one keeps studying as long as the marginal returns are greater than zero. Only when the marginal returns are less than zero is there a negative benefit. Bill hit his minimum returns, which may or may not be less than zero. Matt reached the point of diminishing returns, but returns are still positive when they start diminishing. Anthony has reached his peak at the point of maximum marginal returns, where he is obtaining maximum benefit.

Everyone does poorly on exams from time to time. The key is to turn the negative into a positive. A saying in business is that when you get a lemon, figure out how to turn it into lemonade and sell it. Learn from your errors, and be much stronger next time.

II. Inputs

Until now, when we discussed what a company does we have usually talked about its output. How many goods will it sell at what price? The price elasticity of its demand, for example, looks at how demand for its output changes based on a change in its price.

Marketing and sales also focus on the output of a company. Marketing consists of advertising and promoting the goods. Sales, the most important aspect of almost any company, consists of persuading customers to buy the company’s good or service. The most valued employees of almost any company are its top salesmen and saleswomen. They are the ones that bring in the money to the company.

For the planned homeschool dinner, the output are the seats at the dinner and the sales effort consists of selling the spots and receiving money in return. In a homeschool course, the output are the lectures and the sales effort consists of selling places in the course. Colleges compete for students who can pay their tuition and fees. Many colleges struggle because they have a difficult time attracting enough students to pay tuition. In fact, very few new colleges have begun in the past twenty years.

But there is another side to every company: its own inputs and the costs they incur. For the homeschool dinner, the inputs include a speaker’s fee, a facility fee, and a catering fee. For a homeschool course, the inputs include a teacher’s fee, perhaps a facility fee, and expenses for materials such as handouts or textbooks. Lowering the costs of those inputs increases the profitability of the project.

This is like offense and defense in sports. The people on offense are the salesmen, trying to score points. The people on defense are the buyers of inputs for the company, trying to keep the expenses down. They are opposite jobs, often requiring opposite personalities. Extravagant people make for better salesmen; frugal people are often better buyers of inputs for a company.

Experienced businessmen will emphasize: profits are made by keeping expenses down. After all, profits are the main goal of a typical business. If it is buying food from supplier number one and can reduce costs by going to supplier number two, then the rational action is to change suppliers.

Keeping costs down was what made Wal-Mart so powerful. Its marketing and advertising have only been mediocre. But it is the best in reducing costs. It pays its employees relatively little; opposes unions forming among its workers; and is ruthless in bargaining down the costs of its suppliers. Wal-Mart has made immense profits as a result.

Does that seem unfair? No one has to supply Wal-Mart goods at a low price. If a supplier does not want to do business with Wal-Mart, then it doesn’t have to.

In general, the demand for inputs by firms is called the derived demand for inputs, because it is derived from the consumer demand for the products the company sells. You want to buy gas from a gas station, and your demand in turns creates a demand by the station for its inputs: the gas and labor.

III. Monopsony

In some areas, however, Wal-Mart may be so dominant that it is almost a monopsony. A monopsony means only one buyer. A buyer holds a monopoly on purchases.

The most obvious example of a monopsony is a small town where there is only one employer. If you want a job in that town, then your only place to work is at that company. Of course, very few towns are actually limited to just one employer. But for certain types of jobs, there may be only one employer, and it has a monopsony over those jobs.

A monopsony is different from a competitively hiring firm in one significant way. When a monopsony needs to hire an additional worker, then it has to raise the wages for all its workers at that level to hire an additional one. Its marginal cost for paying for this factor (its marginal factor cost, or MFC) is more than the wage of the additional worker. MFC equals the W of the additional worker PLUS the increased wage of all the other workers.

For example, if a monopsony can hire 10 workers at $6 or 11 workers at $7, then its MFC of hiring an 11th worker is $7 + (10 x ($7-$6)) = $17.

For a competitive firm, in contrast, MFC=W because it can hire all the workers it needs at the market wage, without causing the market wage to rise for all its workers.

IV. Elasticity of Derived Demand for Inputs

Just as we had price elasticity of demand for buying goods, we can also look at the elasticity of demand for inputs such as labor. The definition is what you might expect:

Elasticity of input demand = (Percent change in quantity of input demanded)

divided by (percent change of input’s price)

Both changes are typically stated in positive numbers, as in the example of price elasticity of demand.

Usually questions ask about the firm’s demand for the input of labor. If wages increase by 10% and the demand for labor falls by only 5%, then the elasticity of labor demand is 0.5. Because it is less than one, this is an inelastic demand for labor.

If, on the other hand, when wages increase by 10% then the demand for labor falls by $20%, then the elasticity of labor demand is 2 and this is greater than one. This is an elastic demand.

When the labor demand is elastic, then wage and the overall payments as wages move in the opposite direction. In other words, when the wage increases, the overall wage expense to companies decreases. That is because an increase in wage causes a greater decrease in demand for labor, and overall wage payments decrease.

But when the labor demand is inelastic, then wage and the overall payments as wages move in the same direction. That is because an increase in wage does not decrease the labor demand by companies much, and thus their overall labor costs increase also.

Assembly line workers at car manufacturing plants typically have inelastic labor demand. As labor unions were successful in increasing the wages of assembly line workers in the early 1970s, car manufacturers overall labor costs increased dramatically. Only competition by foreign manufacturers was successful in stopping the upward climb in car prices due to increasing labor costs.

V. Example

Let’s start with this simple equation: Profits = Total revenue – Total cost

That’s easy enough. Now let’s break it down:

Profits = (P x Q) – (W x L) – other non-labor input costs

Now suppose we add one more worker to our company. We will have to pay him a wage of W, so the marginal factor cost of one more worker is W (assuming a competitive market). What is his marginal benefit to our company? P x MP

When does a company hire that additional worker? When the change in profit is greater than zero. That occurs when (P x MP) > W

Let’s apply this to an example. Suppose a firm has a declining marginal product for each additional laborer hired, such that:

Labor Units (L)           Marginal Product (MP)

1                                                    20

2                                                    18

3                                                    16

4                                                    14

5                                                    12

6                                                    10

7                                                     8

Suppose the wage W for each employee is $70 and the price the output is sold for is $5. How many workers should you hire?

If you hired just one employee, then you would make 20 x $5 = $100 in revenue. But your cost was only W=$70, so you made a profit of $30! You’ll hire at least one employee.

If you hire a second employee, then you would make (20+18) x $5 = $190. But your cost was only $70 x 2 = $140, so your profit is $50! You’re doing even better, so you hire the second employee.

Skip down to hiring employee number 6. Then you make (20+18+16+14+12+10) x $5 = 90 x $5 = $450 . What’s your cost? 6 x $70 = $420. It’s barely profitable.

Should you hire one more employee? That additional employee costs you $70, but only brings in 8 x $5 = $40 in revenue. You’d be losing money on him. DON’T HIRE HIM. Or if you hired him, then fire him and give him a good job reference.

Let’s back up and see if it makes sense to keep employee number 6 around. His marginal cost is $70, and he brings in marginal revenue of 10 x 5= $50. He’s losing money for you also. You don’t want him on your staff.

How about employee number 5? His marginal cost is $70, and he brings in marginal revenue of 12 x 5 = $60. He’s losing money for you also. Fire him too.

Your firm hires four workers and no more. Anyone beyond your fourth employee is a money-loser for you. This is because of declining marginal product of labor.

VI. Review

Monopoly is a single seller.

Monopsony is a single buyer.

If the firm is competitive:

then marginal factor cost (MFC) of labor equals the wage of the extra worker: MFC = W. What is the benefit of that extra worker? Marginal benefit (MB) of L is P x MP (price times marginal product)

What, then, is the marginal profit of hiring one more worker ? It is (P x MP) – W

So when does a competitive firm hire an additional worker? When P x MP exceeds W.

Labor demand:

If Q increases, then labor demand increases.

What causes Q to increase? Increased demand by consumers

Now, here is the ultimate brain teaser: what is the effect of consumer demand for output on the labor demand by the company? When consumer demand (demand for output) is more elastic, then labor demand by a company tends to be more elastic. When it is easy to substitute other inputs for labor (such as machines replacing humans), then labor demand also tends to be more elastic. Finally, when other inputs are in more elastic supply, then labor demand tends to be more elastic. And don’t worry if you don’t understand all that.

VII.     Assignment

Review the topics that gave you difficulty on the exam. Then read, and reread, the above lecture. Then answer the problems below, which use many concepts from the course.

  1. A ____________ is one and only one buyer in a market.
  1. In terms of P, MP, and W, state when a company in a competitive market hires an additional worker at wage W.
  1. What is the marginal factor cost of a monopsony when it increases is wage for 10 employees from $11 to $12 in hiring an 11th employee? Show your work.
  1. Kevin owns a company and notices that he receives fewer applications for jobs, and that his employees quit at a higher rate, than his competitors. What would you first look at as the possible reason?
  1. Brandon unionized all the employees in an industry and then tried to both increase their wages and the number of people employed. Is this possible? Are there conditions which would make it possible?
  1. Suppose a Masters of Business Administration (MBA) costs $30,000 a year for two years and full time studying. How much would someone already making $40,000 a year have to earn upon graduation to make it worthwhile?
  1. Suppose you run the local phone monopoly, and want to know the short-run and long-run conditions for shutting down. Explain them in terms of average variable cost (AVC), average total cost (ATC) and price (P).
  1. Abigail has to pay $10.50 to hire nine workers, and must increase the wage to $11 to hire a tenth worker. But the tenth worker will bring in $13 extra to the firm’s revenue. Does Abigail hire the tenth worker?
  1. Marginal revenue product is the change in total revenue resulting from a unit change in the quantity of a variable unit employed. Now redo and explain question 46 on the exam:   Factor of production is any input (e.g., land, labor and capital) used to produce output. A monopolist will continue to purchase a particular factor of production until:

(a) average factor cost equals average revenue product

(b) marginal factor cost equals marginal revenue

(c) marginal factor cost equals marginal revenue product

(d) average factor cost equals marginal favor cost

Extra Credit (4 points for 10 and 11; 6 points for 12)

  1. If our class is a monopsony with respect to dinner speakers addressing large classes of high school homeschoolers, can we set the fee at whatever we like? Do we have leverage with respect to setting a fee?
  1. Explain: when consumer demand (demand for output) is more elastic, then demand for labor by a company tends to be more elastic.
  1. Imagine yourself as a powerful regulator who can set the price of a certain good in a certain industry wherever you want. Suppose that the free market, competitive equilibrium would have the price settle at P=$5. Where would you set the price if you diabolically wanted to cause a shortage of goods? Where would you set it if you diabolically wanted to cause a surplus of goods? Explain.