Economics 211

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Economics 211

• Microeconomic Principles
• Fall 2005

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Basics of Supply

• Thinking in terms of resource allocation we know
  that supply will be limited by
  
• Limited resources
• Given technology (at a particular time)
• A first step is to think about what we can do
  with those objective limits -- and how do we
  think about that?
  
• production function

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Production Function
The "production function." is a relationship
between quantities of input and quantities of
output that tells us, for each quantity of input,
the greatest output that can be produced with
those inputs. Here is an example in the form o
f a table, with labor as the only input.
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Diminishing Returns

• This production function provides an example of
  diminishing returns, and important principle
  for our understanding of production.
  
• With labor as the only variable input -- with
  other inputs, such as land and capital, fixed,
  even if only for the short run -- the law of
  diminishing returns will be applicable.
• This law was originally proposed by the first
  professor of economics in history -- Thomas
  Malthus.

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Malthus
Malthus published the Essay on Population, 1798,
which made him a controversial celebrity. In
1905, he took a position at the East India
College in Haileybury, thereby becoming the
England's first academic economist. A great
pessimist, he originated the idea of diminishing
returns in the Essay and of unemployment and
insufficient aggregate demand in his Principles
of Political Economy.
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Law of Diminishing Returns
The Law of Diminishing Returns when a fixed
input is combined in production with a variable
input, using a given technology, increases in the
quantity of the variable input will eventually
lead to decreasing productivity of the variable
input. Malthus argued that land is the fixed inp
ut, labor the variable input, and that decreasing
productivity of labor would depress incomes.
Malthus knew that technological progress could
reverse this prediction, but probably
underestimated the real impact of technology.
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Productivity

• In most statistical discussions of productivity,
  we refer to the average productivity of labor
  
• In microeconomics, however, we will focus more on
  the marginal productivity.

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In other words,

• marginal productivity of labor is
• the additional output as a result of adding one
  unit of labor, with all other inputs held steady
  and ceteris paribus.
  
• is an approximation to this.

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Remember --
When 300 labor-days per week are employed the
firm produces 2505 units of output per week.
When 400 labor-days per week are employed the
firm produces 3120 units of output per week.
It follows that the change in labor input,
?Labor, is 100. It also follows that the change
in output, ?Output, is 615.
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So
Applying the formula above, we approximate the
marginal productivity of labor by the quotient
615/100 6.15. We can interpret this result as
follows over the range of 300 to 400 man-days of
labor per week, each additional worker adds
approximately 6.15 units to output.
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Diminishing Returns, Again

• Law of Diminishing Returns (Modern Statement)
• When the technology of production and some of the
  inputs are held constant and the quantity of a
  variable input increases continually, the
  marginal productivity of the variable input will
  eventually decline.
• The inputs that are held steady are called the
  "fixed inputs." We are treating land and capital
  as fixed inputs. Labor is the variable input.

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Average and Marginal Productivity
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Visualizing -- Total output
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Visualizing -- AP and MP
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Average and Marginal Productivity

• Average and marginal productivity will not always
  have the same slope. In general,
  
• whenever average productivity is greater than
  marginal productivity, average productivity will
  slope downward.
  
• whenever average productivity is less than
  marginal productivity, average productivity will
  slope upward.
  
• as we add labor input, one unit after another, we
  add a bit more to output at each step. When the
  addition is greater than the average, it pulls
  the average up toward it. When the addition is
  less than the average, it pulls the average down
  toward it.

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Application Efficient Allocation of Resources

• Diminishing returns plays an important part in
  the efficient allocation of resources.
  
• For efficiency, of course, we want to give more
  resources to the use in which they are more
  productive.
  
• But, as we give more resources to a particular
  use, we will observe diminishing returns -- that
  use will become less productive.
  
• Does that sound a little frustrating? Not really
  --

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An Example

• Ajit is a farmer who grows lentils on two fields
  in North India.
  
• He has a field on a hill and a field beside a
  small river.
  
• The riverside field is more fertile than the
  hilltop field.
  
• Ajit has only a limited amount of labor to divide
  between the two fields.
  
• He can work at most 300 days, total, on both
  fields.
  
• He wants to get the largest possible crop of
  lentils from his two fields.
  
• How should he 'allocate his labor' between the
  hilltop field and the riverside field?

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The Production Functions
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Here are the Numbers
What happens is when Ajit allocates more labor
to the river field, marginal productivity on
that field decreases, and eventually it is less
productive at the margin.
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Visualizing --
We can visualize the efficient allocation of
resources with a graph like this one.
Labor on the more fertile field
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Marginal Productivity
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Implication

• Allocating 215 to the river field produces the
  largest output.
  
• If you start from any other quantity, moving
  toward 215 increases output at the margin.
  
• Rule -- equimarginal principle
• When the same product or service is being
  produced in two or more units of production, in
  order to get the maximum total output, resources
  should be allocated among the units of production
  in such a way that the marginal productivity of
  each resource is the same in each unit of
  production.

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Interim Summary

• Supply depends on productivity
• For many economic applications, it is marginal
  productivity that is more important.
  
• When there is a single variable resource, it is
  subject to diminishing marginal productivity.
  
• This leads to and important principle of resource
  allocation
  
• Make MP equal in every use of the resource.

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Productivity is important -- BUT

• To understand businesses better we need to think
  in terms of costs.
  
• This is central to what we call the theory of
  the firm
  
• Lets move on to some details.

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Firms

• A firm is a unit that does business on its own
  account.
  
• There are three main kinds of firms in modern
  market economies
  
• Proprietorships
• Partnerships
• Corporations
• Limited liability
• Anonymous ownership

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Objectives

• We will follow the neoclassical tradition by
  assuming that firms aim at maximizing their
  profits.
  
• Profit is defined as revenue minus cost, that is,
  as the price of output times the quantity sold
  (revenue) minus the cost of producing that
  quantity of output.
• But dont forget opportunity cost!

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Dont Forget Opportunity Cost!

• Some of the costs may not correspond exactly to
  money outlays.
  
• Consider, for example, a taxi driver who is
• Self-employed
• Withdrew savings from his MM account to buy his
  cab
  
• All the same, his labor and capital are costs --
  opportunity costs.

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The Neoclassical Model of the Firm

• Labor is homogenous and variable in the short
  run.
  
• Nonhuman inputs (land and capital) are homogenous
  and given in the short run.
  
• Labor is adjusted to maximize profit.

Thanx to John Bates Clark (1847-1938).
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Long and Short Run

• Some inputs are fixed in the short run. Capital
  goods, for example, may be very specialized and
  durable.
  
• The long run is a period long enough so that all
  inputs are variable, and firms can enter or exit.

Thanx to Alfred Marshall (1842-1924).
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From the Point of View of the Individual Firm

• The price of output is a given constant.
• The wage (the price of labor per labor hour) is a
  given constant.

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Maximize Profits
Here is the relationship of profits to labor
input in our numerical example from earlier
lectures
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Analytic Approach 1

• Profit is the difference of revenue minus cost.
• What does one additional labor unit add to cost?
• What does one additional labor unit add to
  revenue?
  
• The first question is relatively easy. What one
  additional labor unit will add to cost is the
  wage paid to recruit the one additional unit.

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Analytic Approach 2

• What does one additional labor unit add to
  revenue?
  
• What does one additional labor unit add to
  production?
  
• By definition, that's the marginal product.
• Put that in money terms
• Value of the Marginal Product
• The Value of the Marginal Product is the product
  of the marginal product times the price of
  output. It is abbreviated VMP.

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VMP and Profit
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The Equimarginal Principle, Again

• The way to maximize profits then is to hire
  enough labor so that
  
• VMPwage
• where
• p is the price of output
• MP marginal product and
• VMP pMP

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Cost Version

• Taking the same numerical example, lets put it
  in terms of cost.
  
• Since we have fixed and variable inputs in the
  short run, we will also have fixed and variable
  costs.

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Cost Curves
Here is a picture of the fixed and variable costs
for our example
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Economists (Sometimes) Prefer to Work With
Averages

• Average fixed cost (AFC)
• This is the quotient of fixed cost divided by
  output.
  
• Average variable cost (AVC)
• This is the quotient of average cost divided by
  output
  
• Average total cost (ATC or AC)
• This is the quotient of total cost divided by
  output.

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Picture
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Marginal Cost
Marginal cost can be interpreted as the
additional cost of producing just one more
("marginal") unit of output.
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Picture
This is a fairly typical example of nonlinear
cost curves as shown in most economics textbooks.
Note the relation of MC to AC in particular.
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Profit Maximization 1

• Assumptions
• Price is given -- determined by the market.
• The businessperson has control only over the
  quantity produced.
  
• Therefore, the objective is to adjust output to
  give max profits under those assumptions

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Profit Maximization 2
p MC
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Supply Curve

• Implication The supply curve for an individual
  firm is the firms marginal cost curve (if it
  produces any output at all).

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Long Run

• All of this is short run.
• Some inputs, and their respective costs, are
  fixed.
  
• Thats why variable and marginal costs rise.
• In the long run, all inputs are variable.
• Nevertheless, cost conditions may be complex in
  the long run as well.

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Jargon Guide Returns to Scale

• increasing returns to scale decreasing cost
• average cost decreases as output increases in the
  long run
  
• constant returns to scale constant costs
• average cost is unchanged as output varies in the
  long run
  
• decreasing returns to scale increasing costs
• average cost increases as output increases in the
  long run

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SEPTA and Increasing Returns
If SEPTA really is of benefit to the people of
greater Philadelphia, why cant it pay its own
way? Increasing returns may be the answer.
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Increasing Returns

• The cost of the first ride (in the picture we
  just saw) is enormous -- about 35,000.
  
• From that point on, the marginal cost is much
  less -- from 0.20 for the second ride to about
  0.10 for the 25000 and first.
  
• Benefits are greater than costs if something over
  6000 can be served.

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Deficit
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How Can That Be?
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Long Run Average Cost 1
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Long Run Average Cost 2
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Implications

• Where increasing returns to scale are dominant,
• Bigger firms can outsell smaller --
• Competition tends to break down to monopoly
• Big, bureaucratic organizations are inevitable
• But costs are low
• If decreasing returns to scale are dominant, then
  small is beautiful.

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May the Force be With You
I personally believe that (other than in
agriculture) increasing returns to scale are very
important. The good news is this means products
can be very cheap if you can operate on a large
enough scale. But the force of increasing
returns has a dark side organizations get very
big and complex and there just are no simple
rules for running them efficiently!
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Summary

• In a market economy, most production is organized
  in profit-seeking firms.
  
• Taking the marginal productivity approach, the
  rule is VMPwage
  
• Taking the cost approach it is pMC
• If there are increasing returns to scale in the
  long run, things will get a bit complicated.