Archive for the 'Costs of production' Category

Nov 16 2010

Lesson Plan – Testing the Law of Diminishing Marginal Returns in a Paper Chain Factory

The law of diminishing returns is a basic microeconomic concept that explains how a firm’s costs of production change in the short-run as it varies the amount of labor employed. As workers are added to a fixed amount of capital, the productivity of additional workers decreases beyond a certain point due to the lack of available capital.

To test the law of diminishing returns, it is possible to create a factory floor right in your own classroom. Follow the instructions below to determine whether the law applies to your own imaginary firm.

Introduction: Your classroom is about to turn into a factory that manufactures paper chains (to hold paper anchors for paper boats, of course!). A paper chain is made by taking two long, narrow strips of paper, folding one into a ring and stapling the ends together, then folding the other into a ring and connecting it to the first ring to make a chain. Two loops of paper stapled together make a chain. The longer your chain, the more productive your factory and its workers are. The goal of your paper chain factory, of course, is to make the longest chain possible in a fixed amount of time using a fixed amount of land and capital, with labor as your only variable resource. This is therefore an experiment to test the short-run law of diminishing marginal returns.

Resource:

  • Land resources: You will need one table or a couple of desks pushed together. This is your factory floor. Additionally, you will need a box of paper, preferably recycled or used paper. These are your land resources.
  • Capital resources: Every factory needs tools. The tools you’ll have for this activity are two pairs of scissors and two staplers. Since this is a short-run simulation, the amount of land and capital cannot be varied, therefore you may NOT use more scissors and staplers as more workers join the production process.
  • Labor resources: These will consist of the members of your class. The simulation will start with just one worker, and in each successive round one additonal worker will be added until at least eight members of your class have joined the factory floor.

TIME: The time for each round of production is limited to one minute. Your teacher or a member of your class should be designated as time keeper.

Data Collection: Each student in the class should recored the following down in a data table. If you have access to laptops, the data can be collected in Microsoft Excel or in Google Spreadsheets. This way you can create graphs of the data to assist with your analysis later on. Each student should record the following data during the simulation.

# of Workers (QL) Total Product (TP): Marginal Product (=change in TP): Average Product (TP/QL)

Conducting the simulation: When your land and capital resources are ready and your recorder and time keeper have been designated, you may begin the simulation.

Mr. Welker’s students hard at work in the paper chain factory

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  1. In round one, only one student should come to the table. The timekeeper must start the clock and give the worker one minute to cut and staple as many links into one paper chain as he or she can. At the end of the minute the recorder must count the number of links in the chain, record it in the production table, and then take the chain and any links that were cut but not stapled aside in preparation for the next round.
  2. In round two, a second worker should join the first and the two may work together for one minute to make as long a chain as they can. Again, the recorder will count the number of links in the chain at the end of one minute, record this under “total product”, then remove the chain and any unstapled links from the table.
  3. In rounds three through eight, an additional worker is added in each round and the new production team is given exactly one minute to make as long a chain as they can. At the end of each round, the recorder must count the number of links and record this under “total product”.
  4. At the end of the eighth round the factory must close its doors and the simulation is over. Now the class as a whole should look at the total product data and together help the recorder calculate the marginal product and average product for each of the eight rounds.

Data analysis: With your productivity data tables complete, you may now plot your data for total, marginal and average product on a graph similar to those earlier in this chapter, with the quantity of labor on the x-axis and the firm’s output on the y-axis. Using Microsoft Excel or Google Spreadsheets you can create a graph that should look something like the following (created using real data from Mr. Welker’s class recorded in a Google Spreadsheet):

  • As a class, analyze the relationships between total and marginal product.
  • Determine whether your paper chain factory ever experienced increasing returns and whether it ever experienced diminishing returns.
  • Discuss the reasons for the changes in total product during each round of production.

  • The graph above illustrates just marginal and average products. Discuss the meanings of marginal product and average product and determine how they changed as workers were added to your factory floor.
  • What is the relationship between marginal product and average product?
  • Decide whether the law of diminishing marginal returns applied to your factory. If so, why? If not, why not?

4 responses so far

Nov 15 2010

Diminishing returns and the short-run costs of production – “Econ Concepts in 60 Seconds”

YouTube – Econ Concepts in 60 Seconds: The Law of Diminishing Marginal Returns

Mr. Clifford, an AP Economics teacher from San Diego, demonstrates the law of diminishing returns by deriving a total product and marginal product curve using production data from a student’s lawn mowing business.

Econ Concepts in 60 Seconds: The Law of Diminishing Marginal Returns The video above is most useful to Econ students because it enforces the Law of Diminishing Returns. The more important application of this basic economic concept, however, is the short-run per-unit cost curve, Marginal Cost, Average Variable Cost and Average Total Cost. Mr. Clifford offers his quick explanation of the relationships between a firm’s short-run costs in the following video.

Econ Concepts in 60 Seconds: Per Unit Costs Curves

Discussion Questions:

  1. Mr. Clifford derives a Marginal Product Curve in the first video and a Marginal Cost Curve in the second video. What is the relationship between the marginal product of a firm’s variable resource and the firm’s marginal cost of production? How are the shapes of both these curves determined by the law of diminishing marginal returns?
  2. Why does a firm care about its costs of production? Which of the four per-unit cost curves in the second video would a firm be most concerned with when determining whether or not it is earning profits or losses?
  3. What can cause a firm’s cost curves to shift up or down? How would a shift of the cost curves affect a firm’s profits?
  4. What is the primary economic goal of firms, and how can understanding their short-run costs of production help them achieve this goal?

22 responses so far

Mar 03 2009

Recession’s effects on small vs. large companies: some evidence in support of the Classical view of self-correction

Why Are Large Companies Losing More Jobs Than Small Ones? – TIME

This is a fascinating, short article from TIME. Before reading it, see if you can answer the multiple choice question below:

Q: Why do small companies lay off proportionately fewer workers during a recession than large companies?

A) Because small firms are less likely to be in the industries hardest hit by a recession (such as manufacturing)?
B) Because small firms are less focused on maintaining profits to satisfy greedy shareholders?
C) Because small companies are able to hang on to employees and even hire new ones during a recession because of all the talent being laid off by big firms.

Still thinking? Well, it’s likely that all three are true to some extent. But it’s the third one that seems most intriguing as a student of economics. Here’s what the article says:

…small companies hire disproportionately more early on in an economic recovery because it’s easy for these firms to find good workers while unemployment is still high—and easy for workers to come across small companies since there are so many of them. Once the economy is chugging along at full-steam and the labor market is tight, larger companies regain the advantage, since they’re likely able to offer more money—and poach from smaller outfits.

Seems pretty straight forward, right? Sure, but the fact that small firms are likely to hire when unemployment is high supports one side in a long-running economic debate over the economy’s ability to “self-correct” in times of recession.

As any student of Macroeconomics learns early on, there are two dominant theories of macroeconomics, both which are represented in the aggregate demand/aggregate supply diagram that we learn and use in AP and IB Economics.

The two models below represent the two opposing views of macroeconomics. First we see the Keynesian model, which shows that when overall demand in an economy falls, unemployment increases drastically and output tanks, plunging the economy into a deep recession. This is primarily because of the “inflexible” nature of wages, meaning that even when unemployment rises, workers are unwilling to accept lower wages and firms therefore are unwilling to hire more workers.

According to Keynesians, the only way to get the economy out of the recession is by increasing overall demand through heavy doses of government spending (case in point, the $775 billion stimulus in the US).

Next is the Classical AD/AS model with a vertical long-run aggregate supply curve. The implication of the vertical AS curve is that regardless of the level of overall demand in the economy, output will always return to the full-employment level, and thus unemployment will always return to its natural level. The major assumption underlying the Classical model is that wages are in fact flexible in times of recession. As unemployment rises, workers will accept lower wages since they’d rather be making less than making nothing at all. As wages fall firms will begin hiring more workers, increasing overall output and decreasing unemployment until full-employment output is restored.

The implication of the model on the right is that government is NOT needed to get the economy out of a recession, because it will self-correct due to the new hiring and production by firms in response to falling wages in the labor market.

The reason this article stood out to me was that it seems to offer some evidence in support of the flexible-wage, Classical model of macroeconomic self-correction. There has been surprisingly little talk among news anchors, pundits and politicians about the likelihood of the US or ANY economy suffering in the global slowdown “self-correcting” as the Classical model would suggest it should. But the fact that small businesses are less likely to lay off workers in a recession and more likely to begin hiring them due to the large number of workers being laid of by big companies offers at least an inkling of evidence in support of the Classical model of flexible wages and macroeconomic self-correction.

Discussion Questions:

  1. Why is laying off workers the first thing big companies do when faced with falling demand for their products? Why don’t they shut down factories instead?
  2. What pressures does a publicly traded company (one that sells stocks to investors) face in times of recession that a small, privately owned business does not?
  3. When the global recession is finally over, do you think more people or fewer people will be working for small companies (less than 50 people) than before the recession? What would you rather work for, a small firm or a large one? Why?

257 responses so far

Feb 11 2009

Will the economy self-correct?

Does the Economy Self-Correct? – Welker’s Wikinomics Page
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The debate in Washington over Obama’s fiscal stimulus package, which has now been re-written by both the House and the Senate, is ultimately one of the validity of orthodox economic theories. By voting for a nearly $1 trillion government spending bill, the Obama administration and Congress are clearly taking the position that an economy in recession will either not be able to correct itself, or will take too long to self-correct, thus the government is needed to accellerate the recovery process.

Washington’s stimulus package presents students and teachers of economics with an all too rare opportunity to put to the test the two competing hypotheses of macroeconomics: the Demand-side Theory versus the Supply-side Theory.

At the core of the long-running macroeconomic debate is the simple question, “Does the economy self-correct in times of recession?” The supply-side theory, attributed to the “classical” economists dating back to Adam Smith and David Ricardo, argues that the answer to this question is YES. The rationale between this laissez faire approach to macroeconomics is the following:

  1. Falling demand in an economy means less output by firms, forcing them to lay off workers.
  2. As inventories build up due to their inability to sell their output, firms will be forced to lower their prices, putting downward pressure on the price level in the economy (deflation).
  3. High unemployment and falling prices eventually lead to workers in the economy being willing to accept lower wages.
  4. Weak demand for commodities such as oil and minerals put downward pressure on raw material and energy prices faced by firms.
  5. Falling wages and raw material prices mean more potential for profits for firms in various enterprises, even as overall demand in the economy is weak. Firms begin hiring workers at lower wages, and increase production to take advantage of lower input costs. Overall supply of goods and services in the economy begins to increase due to lower costs faced by firms in all sectors.
  6. The downward spiral caused by weak aggregate demand, rising unemployment, falling prices for output, falling wages and commodity prices, is eventually reversed and turns into an upward spiral as firms hire more workers, employ more resources, creating more income and spending, moving the economy towards recovery and economic growth.

The supply-side theory of self-correction (so called because recovery results due to an outward shift of aggregate supply) outlined above depends on the downward flexibility of wages. If wages do NOT fall, as some demand-siders propose, then the idea that firms will eventually begin to hire more workers is busted, and unemployment will only continue to increase as overall demand remains weak.

Today, there is some evidence that wages in the United States may in fact be downwardly flexible.

GM Slashing 10,000 White-Collar Jobs, Cutting Pay – washingtonpost.com

…the base pay of higher-level U.S. executives will be lowered by 10 percent, while other salaried employees will face cuts of between 3 and 7 percent.

General Motors employees are beginning to accept lower wages. Rising unemployment, especially in the white collar sector, mean that the number of highly educated and skilled American workers unable to find work will grow as corporate layoffs continue.

A “shovel-ready” stimulus package from Washington may indeed help to “create or save” 3 million jobs, as Obama claims, but it is the self-correcting nature of markets due to flexible commodity prices and wages that will ultimately contribute to a recovery of the US economy. As prices of commodities fall, combined with lower wages for white collar workers and deflation in the overall economy, firms will find it profitable to begin employing resources at their lower costs, putting people back to work, stimulating spending through market forces.

Fiscal stimulus may accellerate the recovery process, but the threat it poses is the same threat posed by all forms of government intervention in the free market: that the nearly trillion dollars will go towards satisfying the priorities of politicians rather than the wants and needs of society as a whole, resulting in a misallocation of the nation’s resources towards goods, services, and infrastructure projects that are chosen by legislators, not the market itself. Stimulus is needed, but only the right kind. The recognition by politicians and the media that markets may also self-correct is also needed. News like GM’s wage cuts may sound dire, but the underlying implication of falling wages may be a sign that the US economy is already on the path to recovery, even before Washington has spent a single dollar on stimlus.

2 responses so far

Feb 07 2009

McAfee on Price Discrimination: a must-read for teachers of Microeconomics

Professor Preston McAfee on Price Discrimination

(you must have RealPlayer to view this video. Mac users can download it here)

CalTech Economics professor Preston McAfee is an expert on prices. His research spans three decades and examines the pricing behavior of firms in various market structures. In the lecture linked above the professor shares several examples of firms practicing price discrimination. I was surprised to see that many of the examples he discusses are ones that I have been using in my own lectures on price discrimination for the last few years.

McAfee presents a mathematical formula for monopoly pricing, which no AP or IB text that I’ve seen has included:

Monopoly Price = [PED/(1-PED)] x MC where PED is the price elasticity of demand of the customer and MC is the firm’s marginal cost of production.

The basic idea is that the more inelastic the customer’s demand, the higher price the monopolist should charge over its marginal cost. The implication, therefore, is that a monopolist prefers to charge higher prices to customer’s whose demand is inelastic and lower prices to customers who are “price sensitive” or whose demand is elastic. The charging of different prices to different consumers for the exact same product is what economists call price discrimination.

McAfee begins talking about price discrimination at minute 8:44 in the video. His examples include:

  • Movie theaters: Charge different prices based on age. Seniors and youth pay less since they tend to be more price sensitive.
  • Gas stations: Gas stations will charge different prices in different neighborhoods based on relative demand and location.
  • Grocery stores: Offer coupons to price sensitive consumers (people whose demand is inelastic won’t bother to cut coupons, thus will pay more for the same products as price sensitive consumers who take the time to collect coupons).
  • Quantity discounts: Grocery stores give discounts for bulk purchases by customers who are price sensitive (think “buy one gallon of milk, get a second gallon free”… the family of six is price sensitive and is likely to pay less per gallon than the dual income couple with no kids who would never buy two gallons of milk).
  • Dell Computers: Dell price discriminates based on customer answers to questions during the online shopping process. Dell charges higher prices to large business and government agencies than to households and small businesses for the exact same product!
  • Hotel room rates: Some hotels will charge less for customers who bother to ask about special room rates than to those who don’t even bother to ask.
  • Telephone plans: Some customers who ask their provider for special rates will find it incredibly easy to get better calling rates than if they don’t bother to ask.
  • Damaged goods discounts: When a company creates  and sells two products that are essentially identical except one has fewer features and costs significantly less to capture more price-sensitive consumers.
  • Book publishers: Some paperbacks cost more to manufacture but sell to consumers for significantly less than hard covers. Price sensitive consumers will buy the paperback while those with inelastic demand will pay more for the hard cover.
  • Airline ticket prices: Weekend stayover discounts for leisure travelers mean business people, whose demand for flights is highly inelastic, but who will rarely stay over a weekend, pay far more for a roundtrip ticket that departs and returns during the week.

McAfee also goes into a fascinating discussion of price dispersion which is essentially a theory of oligopoly pricing. All Econ teachers should watch this video and find examples of price discrimination and oligopoly pricing that they can incorporate into their own class.

If you’re up for a challenge, try deciphering some of the mathematics in McAfee’s free, downloadable intro to economics text, available here.

5 responses so far

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