Firm Theory: production functions, cost curves and profit maximization

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Firm Theory production functions, cost curves
and profit maximization
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Remarks

• Switching gears Theory of the Firm
• Embarking on an analysis of the firm.
• Note
• There are lots of different types of firms.
• There are lots of ways to organize
  entrepreneurial activity.
• There are lots of firm objectives.

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What We Assume

• For our analysis we assume that
• we have an owner manager,
• who has a business,
• with the primary and only objective to maximize
  economic profit.

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Whats a Business?

• A business is an organization producing goods or
  services, also called a firm.
• A business, or firm, is assumed to maximize its
  profits.
• Examples of businesses Microsoft, Kinkos, the
  Campus Store (a business within Cornell
  University).
• Examples of organizations that are not businesses
  in this sense Cornell University as a whole, US
  Department of Defense.
• Organizations that produce goods and services but
  are legally prohibited from using the profit
  motive are excluded from our formal model of a
  firm.

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Whats a Market?

• A collection of buyers and sellers organized for
  the purpose of exchanging goods and services for
  money.
• Markets can be global, national, regional, or
  local depending upon the item being bought and
  sold.

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Profit Maximization

• profit total revenue - total cost
• total revenue
• determined by the level and nature of competition
  in your market
• total cost
• costs are determined by factor market prices and
  the firms technology or production function

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Economic Profits

• Economic profits are the difference between total
  revenue and total costs.
• Economic total costs include the opportunity
  costs of all inputs to the production processin
  particular, the opportunity costs of the owners
  time and physical capital (equipment and space).
• Whenever we talk about profit we mean economic
  profit.

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Accounting Profits

• Accounting profits are defined as total sales
  revenue (the same as total revenue in the
  economic profits definition) minus operating
  costs (costs of goods sold administrative and
  sales costs for those who know some accounting).
• Accounting Profits Sales Revenue - Accounting
  Costs

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Production Cost Structures

• There are lots of ways to describe production and
  costs.
• You need to understand them all.
• For example
• total, fixed and variable concepts
• average and marginal concepts
• long run and short run concepts
• all related to each other

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Jonathans New York State Apple Farm

• The farm is a business organized to grow and sell
  apples.
• The owner/proprietor, Jonathan, tries to maximize
  his profits from the business.

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The U.S. Apple Market

• Americans consume 19 lbs. of apples per person
  annually, for a total consumption of 5 billion
  lbs.
• More than 6 billion lbs. of apples are grown in
  the US each year (mostly in Washington, New York
  and Michigan).
• Only about 234 million lbs. are imported, while
  more than 1.3 billion lbs. are exported.
• There are about 1,700 apple farms in the State of
  New York, with an average of 96 acres of orchards
  per farm and about 92,000/year in revenue from
  apple sales.
• 80 of the New York apple farms are individual or
  family owned.
• Markets like the US apple market are classic
  examples of competitive product markets.

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Production Functions

• The production function shows the input
  requirements for each level of production.
• For some businesses the production function is
  relatively simple--a few processes with little
  substitution.
• For some businesses the production function
  involves thousands of different processes and
  millions of substitution possibilities.
• The production function is the economists summary
  of the input requirements for each level of
  production.

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Jonathans Apple Farm Production Function

• The table describes Jonathans inputs for the
  annual production of apples shown in the first
  column.

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Fixed Factors

• A fixed factor is one that does not vary as the
  quantity produced increases or decreases.
• Some factors are fixed in the short run
  (managerial time).
• Some factors are fixed in the medium run
  (cultivated acreage).
• No factors are fixed in the long run.

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Jonathans Fixed Factors

• Jonathan has two fixed factors
• His cultivated acreage (100 acres)
• His own managerial time (1,100 hours)

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Variable Factors

• A variable factor is one that must be increased
  in order to increase output.
• The classic variable factor is labor.
• Variable factors usually exhibit diminishing
  marginal productivity--the amount of extra
  product generated by each additional unit of the
  input, holding other inputs constant, declines.

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Jonathans Variable Factors

• Jonathan must vary his labor input to increase
  his production of apples.
• At first this variation is modest going from 50
  tons/year to 100 tons/year requires an additional
  1,200 hours
• Going from 200 to 250 tons/year requires an
  additional 3,200 hours.
• Jonathan cannot increase the size of his farm,
  his acreage is fixed.

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Jonathans Marginal Product of Labor

• The graph shows how the marginal product of labor
  rises, then falls for Jonathans apple farm.
  Marginal product is in red.
• The marginal product is the extra amount of apple
  production (pounds/hour worked) that can be
  produced by an extra hour of work.
• Average product (in blue) is the ratio of output
  to labor used. Average product of labor is
  usually called labor productivity in the
  business press.

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The Average/Marginal Relation

• For product curves or any other average/marginal
  pair of curves
• If marginal product is above average product,
  then average product is rising.
• If marginal product is below average product,
  then average product is falling.
• Therefore, marginal product equals average
  product when average product is at a critical
  value, in this case a maximum.

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From Production Curves to Cost Curves

• By combining the production function and the
  factor prices, we produce the businesss cost
  curves.
• The total cost curve is the amount spent on all
  fixed and variable costs to produce the indicated
  output.
• The average cost curve is the ratio of total
  costs to units produced.

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Marginal Cost

• The most important cost concept is marginal cost.
• Marginal cost measures the amount by which costs
  increase as output increases by one unit.

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7 Short Run Cost Curves

• Total values
• fc fixed costs PK K where K is fixed
• vc variable costs PLL(x)
• srtc short run total costs fcvc
• Average values
• afc average fixed cost fc/x
• avc average variable cost vc/x
• sratcshort run average total costsrtc/xafcavc
• Marginal value
• srmcshort run marginal cost ?srtc/?x ?vc/?x

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Short Run Cost Curves

• Short run cost curves get their shape from the
  marginal productivity of the variable factor
  (except the fixed costs, of course).
• If capital is held constant (short run) then the
  marginal product of labor gives the short run
  cost curves their shape.
• The levels of cost curves are determined by
  factor market prices along with technology.

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Jonathans Input Prices

• Each of the entries in this table represents a
  price that Jonathan must pay for an input.
• Notice that he pays for his managerial time
  because his next best alternative is to earn
  12/hour.
• He must pay rent for his land.
• Jonathan is a wage taker as well as
  price-taker.

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Jonathans Cost Curves

• When Jonathan faces the technology and input
  prices shown previously, the table shows his cost
  structure.

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Graph of Jonathans Cost Curves

• The marginal cost of each ton of apples is shown
  as the red line.
• The average total cost curve is shown as the blue
  line.
• Notice that the marginal cost average cost at
  minimum average cost.

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Long Run Cost Curves

• Describing the long run cost curves requires a
  description of all of the technological
  possibilities for operating in the industry.
• Now both labor and capital are considered
  variable.
• There are three long run cost curves for the
  firm
• long run total cost lrtc PLL(x) PKK(x)
• long run average total cost lratc lrtc/x
• long run marginal cost lrmc ?lrtc/?x
• The most important one for us is the lratc curve.
• Choosing L(x) and K(x) will depend on the
  prices of capital and labor relative to the
  marginal products of capital and labor and what
  x you expect to produce. The bang/buck
  condition would have to be met. That is, at L
  and K, the (mpL/PL ) (mpK/PK)

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Example 3 Potential Technologies

• Suppose there are three different ways for a
  company, System-fixer, to do business.
• Firm sizes A, B and C illustrate the
  possibilities.
• Firm A is small, using only 80 in fixed costs.
• Firm B uses twice the capital.
• Firm C uses three times the capital.

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Question

• What is the best technology for our system-fixer
  firm?

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Answer

• It depends on how much System-fixer expects to
  produce and sell in the market.

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The Firms Long Run Average Total Cost Curve

• The firms long run average total cost curve
  consists of the minimum of the three curves
  illustrated on the right.
• System-fixers long run average total cost curve
  is size As (blue) until 6 units, size Bs (red)
  from 6 to 10 units and size Cs (brown) from 11
  units onward.
• The shape of the firms lratc curve will be
  determined by how the technology behaves.
• The lratc is the outer envelope of the possible
  sratc curves.

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The Firms Long Run Average Total Cost Curve and
MES

• MES minimum efficient scale
• MES the level of output at the minimum of the
  firms lratc curve.
• When there are economies of scale, the lratc is
  declining.
• When there are diseconomies of scale, the lratc
  is increasing.
• At MES all the economies of scale are exhausted.
• In real world empirical analysis, economists
  often observe a more L-shaped lratc curve.

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Profit Maximization

• Profit (?) total revenue(tr) - total cost(tc).
• Profit depends on the firms output level (x).
• So ? (x) tr(x) - tc(x)
• Define
• marginal revenue (mr) ?tr/?x
• marginal cost (mc) ?tc/?x

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Profit Maximization

• General rules for profit maximization
• If x maximizes ? , then
• mr mc at x
• x is a profit max and not a profit min
• at x its worth operating
• If using a short-run perspective use short run
  cost curves.
• If using a long-run perspective uselong run cost
  curves.

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Running at a Profit

• When the market price exceeds the firms average
  total cost at x, the firm is running at a
  profit.
• Great.

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Running at a Loss

• When the market price is less than the firms
  average total cost at x, the business is running
  at a loss.
• What should the firm do in the short run?
• produce x if the firm takes in enough in revenue
  to cover its variable costs.
• shut down and play dead if its revenues at x
  dont even cover variable costs.

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Running at a Loss

• What should the firm do in the long run?
• It should plan to go out of business if it does
  not expect either the market price to rise or its
  costs to fall or both.

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Sunk Costs and Avoidable Fixed Costs

• In the real world the shut down rule is slightly
  different.
• When the firm actually operates, xgt0, it makes
  sense to only talk about fixed and variable
  costs.
• However, when the firm considers shutting down in
  the short run (when profits are negative at the
  profit maximizing output level) then they have to
  take another look at their fixed costs.
• Fixed costssunk costs avoidable fixed costs
• Now change the shutdown rule to be
• produce x if the firm takes in enough in revenue
  to cover its variable costs avoidable fixed
  costs, otherwise shut down.