Production Function

Production Function – a function that defines the maximum amount of output that can be produced with a given set of inputs.

Q = f(K,L)Where K = Capital and L = Labor

Various Production Functions

Linear Production FunctionQ = aK + bL Inputs are perfect substitutesMarginal Product of Labor = b

Leontief Production FunctionQ = min(bk, cL)Also called the fixed proportions production

function Inputs are perfect complements

Cobb-Douglas Production Function

Q = KaLb

Capital and Labor are both substitutes and complements for each other.

Productivity of each input depends upon the amount of the other input employed

Marginal Product of Labor = bKaLb-1

Lesson of Production Functions

Output of a firm is produced by capital and labor.

The owner of the firm provides the capital.

Workers provide the labor.How much should each input be paid?

And what determines those payments?

Two Views on Rights

Natural Rights – the idea that there exists universal rights the exist independent of social organizations.

“Nonsense on Stilts” – Jeremy Bentham’s reaction to the notion of natural rights. For Bentham, there is no such thing as natural rights.

Bentham’s ideas are also echoed in the work of John Stuart Mill

Distribution of Resources “The things once there mankind, individually or collectively,

can do with them as they please. They can place them at the disposal of whomsoever they please, and on whatever terms..... Even what a person has produced by his individual toil, unaided by anyone, he cannot keep, unless by the permission of society. Not only can society take it from him, but individuals would and could take it from him, if society ... did not employ and pay people for the purpose of preventing him from being disturbed in [his] possession. The distribution of wealth, therefore, depends on the laws and customs of society. The rules by which it is determined are what the opinions and feelings of the ruling portion of the community make them, and are very different in different ages and countries, and might be still more different, if mankind chose....” John Stuart Mill [Heilbroner: 129-130].

Hiring Workers in a COMPETITIVE Labor Market

Fundamental assumptions: The labor market is competitive and firms seek to maximize profits.

Firm’s maximize profits be equating marginal revenue and marginal cost.

With respect to inputs, firms will add inputs as long as the income generated by the input exceeds the expense of the input.

A firm will stop hiring inputs when the income an additional worker produces equals the expense of hiring the worker.

Marginal Revenue Product

• How do we measure the marginal income from an additional input?

• The value of a worker can be divided into two parts:▫ Marginal Product of Labor: the productivity of the

last unit of labor hired (i.e. the productivity of a worker).

▫ Marginal Revenue of Output: the revenue generated by the last unit sold (i.e. the value of a unit produced).

▫ Marginal Revenue Product = MP * MR• How do we measure the marginal expense of an

additional input?• In a perfectly competitive labor market, the marginal

expense of labor is the wage.• To maximize profits, the firm will equate the

worker’s MRP and Wage.

The Importance of Stage Two

• In what stage of production do firms operate? Only in stage two.

• In stage one, increases in the labor force will increase the MRP. If it made sense to hire the previous workers, and the next worker offers a higher MRP, then it makes sense to hire the next. Hence firms will not stop hiring workers in Stage Two.

The Law of Diminishing Returns and Profit Maximizing Hiring

• The Law of Diminishing Returns – As you, hire more workers, holding all else constant, the amount of output from each additional worker you add will eventually decline.

• Implications: As a firm expands the size of its labor force, the productivity of each additional worker declines. In other words, marginal product (and MRP) decline as the number of workers increases.

• If wages are set by the market, how many workers should the firm hire?

Adjusting your labor force

• If W > MRP What action should the firm take?

• If W < MRP What action should the firm take?

• The firm will maximize profits with respect to the hiring of workers when W = MRP

• Can a competitive firm pay a worker less than the worker’s MRP? No, because another firm would be willing to offer more.

A MonopsonyMonopsony – a single buyer in a market.

◦Contrast with a monopoly.A firm in a competitive labor market is

forced to pay a worker a wage equal to the worker’s marginal revenue product.

A monopsony, though, is the sole buyer in the market. Consequently the monopsonist can ask workers to accept wages below the worker’s marginal revenue product.

EXPLOITATION

•Implication: Monopsonistic firms exploit their workers.

•Joan Robinson (1933): “What is actually meant by exploitation is usually that the wage is less than the marginal revenue product.”

Offsets to Monopsony Power

•Another way of saying a firm has monopsonistic power: Firm has bargaining power in its negotiations with its workers.

•Two efforts to increasing workers’ bargaining power▫Minimum Wage Laws▫Labor Unions

Application: A Minimum Wage

McGraw-Hill/Irwin 15

S0

D0

P (wage per hour)

Q (quantity of workers)

W0

Wmin

QD QS

Excess supply = unemployment

Labor

Minimum wages theoretically causes

unemployment

A minimum wage is a type of price floor, it is the lowest wage a firm can legally pay an employee

Q0

Minimum Wage Basicshttp://www.dol.gov/whd/flsa/#minFair Labor Standards Act (FLSA) establishes

minimum wage, overtime pay, recordkeeping, and youth employment standards affecting employees in the private sector and in Federal, State, and local governments. Covered nonexempt workers are entitled to a minimum wage of not less than $7.25 per hour effective July 24, 2009. Overtime pay at a rate not less than one and one-half times the regular rate of pay is required after 40 hours of work in a workweek.

When federal law does not apply, the state minimum wage applies http://www.dol.gov/whd/minwage/america.htm

The History of the Federal Minimum Wage

Fair Labor Standards Act of 1938

Set the minimum wage at $0.25.

The federal minimum wage is not indexed to inflation. The wage only rises when Congress acts.

Consequently, the purchasing power of the wage declines in between the times Congress has raised its value.

Nominal vs. Real from

http://oregonstate.edu/instruct/anth484/minwage.html

A federal minimum wage was first set in 1938. The graph on the next slide shows nominal

(blue diamonds) and real (red squares) minimum wage values. Nominal values range from $0.25/hr in 1938 to the current $7.25/hr. The graph adjusts these wages to 2010 dollars (red squares) to show the real value of the minimum wage.

Calculated in real 2010 dollars, the 1968 minimum wage was the highest at $10.04. The real dollar minimum wage (red squares) falls during periods Congress does not raise the minimum wage to keep up with inflation.

The minimum wage increased in three $0.70 increments--to $5.85 in July, 2007, $6.55 in July, 2008, and to $7.25 in July 2009.

Problems in estimating the impact of the minimum wage

1. Nominal vs. Real wages: Cost of living must be adjusted over time and across economic regions. The lower the cost of living, the greater the impact of a minimum wage.

2. Ceteris paribus: The problem of a growing economy.

3. Effect of uncovered sectors: Unemployment may not be increased if workers can find work elsewhere.

1. Not every firm is covered (generally small, intrastate firms are not)

2. Noncompliance is an issue

The Empirical EvidenceDavid Card and Alan Krueger

(1994)Dube, Lester, and Reich (2010) We use policy discontinuities at state borders to identify the effects of

minimum wages on earnings and employment in restaurants and other low-wage sectors. Our approach generalizes the case study method by considering all local differences in minimum wage policies between 1990 and 2006. We compare all contiguous county pairs in the U.S. that straddle a state border and find no adverse employment effects. We show that traditional approaches that do not account for local economic conditions tend to produce spurious negative effects due to spatial heterogeneities in employment trends that are unrelated to minimum wage policies. Our findings are robust to allowing for long term effects of minimum wage changes.

CONCLUSION: For cross-state contiguous counties, we find strong earnings effects and no employment effects of minimum wage increases.

Why?

Economists SurveyedMinimum Wage Survey Question A: Raising the federal minimum wage

to $9 per hour would make it noticeably harder for low-skilled workers to find employment.

Question B: The distortionary costs of raising the federal minimum wage to $9 per hour and indexing it to inflation are sufficiently small compared with the benefits to low-skilled workers who can find employment that this would be a desirable policy.

The vanishing Labor Union movement in the United States

Craft Unions• Craft Unions - Workers who share a common skill.• The American Federation of Labor (AFL) is a

collection of craft unions. Craft unions were locally rooted, concerned mainly with the improvement of union members position, even if this meant that workers outside the union did not benefit.

• Craft unions increase wages by limiting access to the unions and to the required skills.

• The result is a fixed supply of labor, which increases wages and creates a deadweight loss.

Industrial Unions• Industrial Unions - Workers employed in a common

industry• The Council of Industrial Organization (CIO) is a

collection of industrial unions. Industrial unions tend to be organized over a wide geographic area. Furthermore, success is only achieved if the union is inclusive. All workers must participate in the union for the union to bargain successfully.

• Industrial unions, via strikes, negotiate for higher wages. The higher wages result in a reduction in labor employed and a deadweight loss.

Economic Impact of Unions• Negative Impact of Unions

▫ Unions create inefficiency (i.e. deadweight loss)▫ Unions also limit employment and thus output.

•  Positive Impact of Unions▫ Studies fail to show a link between unions and

productivity levels or productivity growth.▫ Unions serve as a countervailing force to the

monopsony power of employers.

• Is there evidence unions can counteract monopsony power? Sports unions

The Threat Point• The work of John Nash• Consider bargaining between a monopoly union and

a monopsonistic employer.• Wages will be determined via the bargaining process.

Bargaining power is directly related to its ability to walk away from the table.

• The value of opportunities that each side has outside the current contractual agreement as the bargainer’s threat point. The higher the threat point for either side, the greater its bargaining power, the more favorable a solution the side can achieve.

• Employer’s Threat Point rises the more readily it can access an alternative source of labor.

• The Union’s Threat Point rises when it is able to find other jobs elsewhere or it has sufficient financial resources.

The Objectives of Management

Managers seek to maximize utility (A.A. Berle and Gardner Means)

Focus of these authors is on the separation of ownership and management, which arose due to the rise of the corporation.

How would this impact market behavior? Studies have shown that managerial control is less profitable than owner control. Manager’s are more risk adverse, due to an inability to diversify.

A related view.... Managers seek to satisfice (Richard Cyret, James March and Herbert Simon)

In this class we assume that firms seek to maximize profits. This is a simplification.

WHY DO WE NEED TO ANSWER THIS QUESTION? We need to know the motivation of the people we study.

WHAT IS THE IMPACT OF MANAGERS?

Adam Smith on Managers The profits of stock, it may perhaps be thought are only a different name for the wages of a particular sort of labour, the labour of inspection and direction. They are, however, altogether different, are regulated by quite different principles, and bear no proportion to the quantity, the hardship, or the ingenuity of this supposed labour of inspection and direction. They are regulated altogether by the value of the stock employed, and are greater or smaller in proportion to the extent of this stock. Let us suppose, for example, that in some particular place, where the common annual profits of manufacturing stock are ten per cent, there are two different manufactures, in each of which twenty workmen are employed at the rate of fifteen pounds a year each, or at the expense of three hundred a year in each manufactory. Let us suppose, too, that the coarse materials annually wrought up in the one cost only seven hundred pounds, while the finer materials in the other cost seven thousand. The capital annually employed in the one will in this case amount only to one thousand pounds; whereas that employed in the other will amount to seven thousand three hundred pounds. At the rate of ten per cent, therefore, the undertaker of the one will expect a yearly profit of about one hundred pounds only; while that of the other will expect about seven hundred and thirty pounds. But though their profits are so very different, their labour of inspection and direction may be either altogether or very nearly the same. In many great works almost the whole labour of this kind is committed to some principal clerk. His wages properly express the value of this labour of inspection and direction. Though in settling them some regard is had commonly, not only to his labour and skill, but to the trust which is reposed in him, yet they never bear any regular proportion to the capital of which he oversees the management; and the owner of this capital, though he is thus discharged of almost all labour, still expects that his profits should bear a regular proportion to his capital. In the price of commodities, therefore, the profits of stock constitute a component part altogether different from the wages of labour, and regulated by quite different principles. [Chapter VI: Of the Component Parts of the Price of Commodities. pp. 54-55]

RED AUERBACH ON COACHING

“These guys today want you to believe that what they’re doing is some kind of science. Coaching is simple: you need good players who are good people. You have that, you win. You don’t have that, you can be the greatest coach who ever lived and you aren’t going to win.”

see John Feinstein and Red Auerbach (2004). “Let Me Tell You a Story: A Lifetime in the Game.” pp. 273.

Red Auerbach coached the Boston Celtics to nine NBA titles in the 1960s.

THE ASHENFELTER DIP

De Paola, Maria and Vincenzo Scoppa. 2012. “The Effects of Managerial Turnover: Evidence from Coach Dismissals in Italian Soccer Teams.” Journal of Sports Economics, v13, n2: 152-168.

Researchers must also account for what is called “regression to the mean” or the “Ashenfelter dip”.There is a tendency for outcomes that are far from the mean to be followed by those that are closer to the mean. With respect to coaching, there would be a tendency for teams to fire coaches when the team is performing well below average. Once the new coach is on board, performance regresses back to the mean. If this tendency in the data is not accounted for the researcher might conclude the new coach is the cause of the reversion. Ashenfelter, Orley. [(1978). “Estimating the Effect of Training Programs on Earnings.” Review of Economics and Statistics. 60: p. 47-57]

studied the earning of people in a training program. He found that earnings tended to dip right before entering the program. So comparing earnings before and after the training program would overstate the value of the training program.

A Comparison of Team Performance Under the Old and the New Coach in the Italian “Serie A” De Paola and Scoppa (2012). * - difference is statistically significant

Points Goals Scored Goals Conceded Old Coach 0.994 1.023 1.509 New Coach 1.122 1.15 1.455 Difference 0.128* 0.127* -0.054

MORE ON ASHENFELTER DIP IN SOCCER

DOES CHANGING COACHES HELP IN SOCCER? To control for this impact, the De Paola and

Scoppa (2012) estimated a series of regressions that examined the impact of changing a coach after controlling for the quality of the two teams in the match. Once quality is controlled for, the impact of changing the coach was not statistically significant.

As De Paola and Scoppa (2012) note, this result confirms studies of Belgium soccer and Dutch soccer. [seeBalduck, A., &Buelens, M. (2007). Does sacking the coach help or hinder the team in the short term? Evidence from Belgian soccer. Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 07/430 &Bruinshoofd, A., &TerWeel, B. (2004). Manager to go? Performance dips reconsidered with evidence from Dutch football. European Journal of Operational Research, 148, 233-246].

COACHES IN BASKETBALL AND BASEBALL

Berri, David J., Michael Leeds, Eva Marikova Leeds, and Michael Mondello (2009).”The Role of Managers in Team Performance.” International Journal of Sport Finance, 4, n2; (May): 75-93.

This study looked at the impact of 62 NBA coaches from 1977 to 2007. Of this sample, only 14 coaches had a statistically significant and positive impact on individual player performance.

Bradbury, J.C. 2010. “Hired to Be Fired: The Publicity Value of Coaches.” Presented at the Southern Economic Association Meeting. November, 2010.

Bradbury’s study included 134 managers. Of these, this study reports that just 21 managers has a statistically significant – at the “lenient ten-percent level benchmark” – on a hitter’s performance. For pitchers, only fifteen managers had a statistically significant and positive impact on performance. And there was not a single manager found to have a positive and statistically significant impact on player performance.

The Principal-Agent Problem A principal is the person who wants an action taken. In

the work environment, this is the owner of the firm. The agent is the person who takes the action. In the

work environment, this is the worker. If motivations differ between the principal and agent,

and information is not perfect, a principal-agent problem exists.

A specific example is the issue of moral hazard. Moral hazard occurs when the agent can take actions that the principal cannot directly observe that will reduce the welfare of the principal. For example, consider shirking.

How can the firm limit shirking?

Difficulty of Vertical IntegrationShirking of Workers

Shirking - the behavior of a worker who is putting forth less than the agreed to effort.

Efficiency Wages – Paying the worker a wage above the market wage.

Why is this necessary? Because workers can vary productivity, a firm may need to pay higher wages to ensure higher levels of output.

Why would firms pay efficiency wages? In other words, why do higher wages elicit higher productivity.

a. The Gift exchange hypothesisb. Worker turnoverc. Worker quality

Shirking Defense How do firms prevent the manager from shirking?

Make the manager a residual claimant.• Residual claimant - persons who share in the profits of the

firm. How do firms prevent workers from shirking?

• Profit sharing – mechanism used to enhance workers’ efforts that involve tying compensation to the underlying profitability of the firm

STOCK OPTIONS, etc..• Revenue sharing – mechanism used to enhance workers’

efforts that involve tying compensation to the underlying revenues of the firm

SALES COMMISSIONS, TIPS, etc... NO INCENTIVE TO LOWER COSTS

Teams and Productivity Teamwork is employed when a team of individuals can

produce more than the sum of individuals working alone.

Observing individual productivity is difficult, so shirking can occur: The Free Rider Problem

Profit Sharing: If team members share in the profits of the firm, then they have an incentive to monitor other team members. If the incentive to monitor exceeds the free-rider effect, profit sharing can increase productivity.

More Defense: Piece Rates Piece-Rate Compensation – Employee is paid

according to productivity. Such a compensation plan will increase

productivity. Will only work if productivity can be

measured. Problems

• Teamwork will diminish.• Quantity is easy to measure, quality is

not. Thus quality can suffer with this compensation plan.

Subjective Evaluations Why are subjective evaluations

employed? To encourage innovation, dependability, cooperation, etc...

Subjective evaluations can lead to rent-seeking by workers, or actions taken to re-distribute resources from others.

Subjective evaluations can also be quite inaccurate. Inaccurate evaluations can distort incentives.

The Long-Run

How does a firm decide to expand production? Profit maximizing output > average cost minimizing output.

Expanding productive facilities moves the firm from the short-run to the long-run.

Long run - the shortest period of time required to alter the amounts of all inputs used in a production process.

A period of time long enough for all inputs to be varied.

Economies of Scale

Economies of scale - reductions in the minimum average cost that come about through increasing plant size. specialization of labor. more efficient yet larger equipment. greater volume of output increase

efficiency from learning. Constant returns to scale - increases in plant

size do not affect minimum average cost.

Diseconomies of Scale

Diseconomies of scale - increases in plant size increase minimum average cost. supervision of workers more difficult

(morale declines). lengthening of the managerial chain leads to

disorganization. Long run average total cost is a summary

of our best short-run cost possibilities.

Long-Run Average Cost

Capacity – Output level at which short-run average costs are minimized.

If a firm moves beyond ‘capacity’ the firm may want to consider building a larger plant.

BE ABLE TO ILLUSTRATE THIS STORY IN THE SHORT-RUN

Minimum Efficient Scale – Output level at which long-run average costs are minimized.

BE ABLE TO ILLUSTRATE LONG-RUN AVERAGE COST AND IDENTIFY THE LEVEL OF OUTPUT CORRESPONDING TO MES.

Firm Size and Plant Size

Multi-plant Economies of Scale – Cost advantages from operating multiple facilities in the same line of business or industry.

Multi-plant Diseconomies of Scale – Cost disadvantages from operating multiple facilities in the same line of business or industry.

The Economics of Multi-Plant Operations

Elements needed for problem Equation for Demand Curve Short-run Total Cost Function

Steps in Solving the Problem Solve for profit maximizing output, price, and profit. Solve for average cost minimizing output. Solve for MC when firm produces at capacity. Set MR equal to MC at capacity to determine optimal

multi-plant operation. Determine the optimal number of plants. Determine price and profit when firm employs the

optimal number of plants.

Why Profits?

Why do firms make a profit? The story from classical economics Payment to the capitalist-entrepreneur (i.e. profit) is comprised of

three elements (according to classical economics) payment for the use of capital payment to the entrepreneur for managerial expertise payment as compensation for risk

What is profit in the long-run? How can profits persist? Again, we answered these questions earlier in the

course.

One Last View on Managers

1. Thorstein Veblen. (1904). Theory of the Business Enterprise

2. Classical and Neoclassical Economics: Hero of the play is the capitalist.

3. Veblen: The capitalist is the saboteur of the system.

4. Veblen glorified the machine, the engineer, the technician. What is the role of the businessman, who is not concerned with production, but with profit?

5. The capitalist sabotages the economy so that in confusion can come his profit. WE WILL REVIEW MONOPOLY THEORY!

6. For Veblen, society was divided between engineer and businessman. Between production and finance.

http://www.dilbert.com/

http://www.dilbert.com/

http://www.dilbert.com/ Dilbert illustrates the story Veblen tells The engineers understand what should be happening The manager, though, does not and constantly frustrates his engineers with poorly constructed plans and silly sayings. Remember! Don’t be the pointy-haired boss in the future!