Microeconomics and Policy Analysis PUAF 640

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Microeconomics and Policy Analysis PUAF 640

• Professor Randi Hjalmarsson
• Fall 2008
• Lecture 7

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Class Outline Chapters 7.1, 7.2, 8

• The firm and its goals
• Total revenue and total cost
• Firms optimal output rule
• Should the firm shut down?
• Production functions

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From consumer to the firm

• Individuals goal maximize utility
• Firms goal?
• Maximize profits
• Profits ?
• Profits p Total Revenue Total Cost TR-TC
• Often called economic profits
• TC are economic costs total expenditure on
  inputs as measured in terms of opportunity costs
• Opportunity costs cost of a resource as
  measured by the value of the next best
  alternative use of that resource

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Opportunity Cost Examples

• Suppose you own a company and pay salaries to
  your employees of 20,000 per month and rent
  office space for 3,000 per month.
• What is the total economic cost per month?
• 20,000 3,000 23,000?
• This is just the accounting cost.
• Have not included the opportunity cost of your
  time.
• If you could earn 5,000 per month at another
  job, then 28,000/month is the economic cost.

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• The economic cost of going to college?
• Tuition, room and board, etc. (accounting costs)
• If could earn 15,000 from working instead of
  college, this should be included in economic
  cost.
• Opportunity cost of college includes the value of
  ones time in the next best alternative.
• Suppose a firm bought a building for headquarters
  that is bigger than needed.
• If the firm could rent out the extra space at
  5/sq.ft., then this is the opportunity cost of
  leaving the space idle.

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• What is the economic cost of going to the movies?
• Ticket price 10 (accounting cost)
• Popcorn, candy, etc.? (accounting cost)
• What else could you do with that 10?
  (opportunity cost)
• What else could you do with your time?
  (opportunity cost)
• The government owns a vast amount of wilderness.
  Is it worthwhile to convert some of that land
  into a national park?
• What is the economic cost of the park?
• Even though they own the land, is there still a
  cost?
• Land could be used for timber or grazing sheep
  what is the value of the land in its next best
  use?

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EN Opportunity Cost Example

• Suppose you won a free ticket to see an Eric
  Clapton concert tonight. You cant resell it. Bob
  Dylan is also performing tonight and his concert
  is the only other activity youd consider. A
  Dylan ticket costs 40 and on any given day you
  would be willing to pay as much as 50 to see him
  perform (more than 50, and you would pass).
  There is no other cost of seeing either
  performer.
• What is your opportunity cost of attending the
  Clapton concert?
• 0, 10, 40, or 50?

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• The only thing you must sacrifice to attend the
  Clapton concert is the Dylan concert.
• By skipping Dylan
• You miss out on a performance worth 50 to you
• Avoid having to spend 40 on the ticket
• The value of what you are giving up by skipping
  Dylan is worth 10 to you.
• This is the opportunity cost.
• If seeing Clapton is worth at least 10 to you,
  you should see Clapton otherwise, Dylan.

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The firms decision

• Given that the firm decides to maximize profits,
  it must also decide
• What to produce
• How to produce it
• What combination of inputs should the firm use?
• How much to sell at what price
• How to promote the good

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First Question How much should the firm produce?

• What level of output, Q, will maximize profits?
• Profits are a function of total revenue and total
  cost.
• So, we need to understand what total revenue and
  total cost look like.

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What is Total Revenue (TR)?

• TR amount of received from sale of output
• TR p(Q)Q
• Note price as a function of quantity
• Allows the price to depend on how much the firm
  sells.
• This does not assume price takers.
• If price takers, then
• TR pQ where p(Q) p (the market price).
• Q affects TR directly (by selling more) and
  indirectly (changing Q can change p)
• Firms total revenue curve, TR(Q), depends on the
  demand curve faced by the firm how much can the
  firm get per unit in the market?

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Scenario 1 Firm is a price taker

• Extra output doesnt affect the market price.
• Firm can sell all it wants at price p.
• What does TR curve look like?

TR
TR(Q)
Slope p
Q
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Scenario 2 Firm faces downward sloping demand
curve.

• To sell more Q, firm must charge a lower P.

TR
P
TR(Q) p(Q)Q
D
Q
Q
Revenue increases at a decreasing rate can sell
more, but at a lower price.
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Total Cost function For each Q, how much does it
cost the firm to produce it?

• Assume that the following are constant when
  calculating total cost
• Factor (or input) prices
• Technological possibilities
• Product characteristics

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Total Cost Curve
Why does it have this shape?
Slopes up costs more to produce more.
TC
Curve depends on returns to scale. At first, TC ?
at a ?ing rate. You dont need to double inputs
to double outputs (therefore, cost would less
than double). Then, TC ? at an ?ing rate need to
more than double inputs to double output
(therefore, costs would more than double).
TC
Q
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How much should the firm produce to maximize
profits?

• Choose Q to max p TR(Q) TC(Q)

Where is profit maximized?
TR, TC ()
Where the distance between TR and TC is greatest.
TC
TR(Q) p(Q)Q
p
Slopes of TC and TR are equal. That is, marginal
cost marginal revenue.
Firm chooses output such that MR MC
Q
Q
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Marginal Revenue (MR) and Marginal Cost (MC)

• MR additional amount of revenue from additional
  unit of output produced.
• MR dTR/dQ ?TR/ ?Q
• Slope of total revenue curve
• MC additional amount of cost from one more unit
  of good produced.
• MC dTC/dQ ?TC/ ?Q
• Slope of total cost curve

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MR and MC graphed

• What does marginal revenue (MR) look like (for
  firm with downward sloping demand curve)?
• What does marginal cost (MC) look like?

TC
MR, MC ()
TR, TC ()
MC
TR
p
Not necessarily straight line.
MR
Q
Q
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Why does MRMC imply max p?
What if MRMC? Then producing 1 more unit yields
more revenue than cost, so can increase profit.
MR, MC ()
MC
What if MRthan cost, so decreases profit. Should produce
less.
MR
Q
Q
Marginal Output Rule If firm does not shut down,
then should produce Q such that MR MC!
More generally, continue a project until MB MC!
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Optimal Output Decision for Price-Taking Firm?
How much should the firm produce?
What does MR look like?
Where is Q on MR, MC graph? Be careful!
TR
TC
MR, MC ()
TR, TC ()
MC
p
MR
Q
Q
Q
Q
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Second Question Shut Down Decision

• Would the firm be better off not producing at
  all?
• Compare p when open (pO) to p when shut (pS).
• Shut down if pS pO.
• If shut, TRS 0 and TCS 0 .
• Thus, pS TRS TCS 0.
• So, firm should shut down if pO
• Note that this is economic profits firms with
  positive accounting profits may close and those
  with negative accounting profits may stay open.

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Shut Down Rule Expressed with Averages

• Average p total p / Q
• Shut if p
• So, shut if average p
• (Divided second line by Q)
• Definitions
• Average Revenue AR TR/Q
• TR p(Q)Q (not a price taker)
• AR p(Q) demand
• TR pQ (price taker)
• AR p
• Average Cost AC TC/Q

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Shut Down Rule in terms of AR and AC

• Shut down if p TR - TC
• Divide through by Q.
• Shut down if Ap AR AC
• Can graph this but need to know shape of AC.

TC
AC ()
TC
AC
Slope (TC-0)/(Q-0)AC
Q
Q
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Graph of Shut Down Rule

• Both firms should shut down if AR

Price taking firm
Non-Price taking firm
()
()
AC
AC
ARp
ARD
Q
Q
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• If AR crossed AC, firm stays in business and
  produces Q according to marginal output rule.

Where are profits?
()
AC
Yellow rectangle TR
AR(Q)
Striped rectangle TC
AC(Q)
Red outlined rectangle Profit TR TC
ARD
Q
Q
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The firms production decision

• We want to know
• Whether to produce (shut down rule)
• How much to produce (marginal output rule)
• What combinations of inputs to use (third
  question).
• But need to understand production functions
  first.
• Assume that firms are price takers in all
  commodities.
• They cannot influence market prices for a good or
  input.

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Firms production function

• Firm produces single output, Q, using labor (L)
  and other inputs K1, , Kn.
• Production function Q f(L, K1, K2 ,, Kn)
• Schedule of the highest level of output the firm
  can produce from a given combination of inputs.
• Two inputs, K and L, for simplicity.
• Q f(K, L)
• Ex. f(K, L) 2L K.5 or f(K, L) ALaKß

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Responses of production to changing inputs

• Marginal Physical Product
• Extra amount of output that can be produced when
  the firm uses an additional unit of an input,
  holding other inputs constant.
• Marginal Physical Product of Labor (MPPL)
  holding K constant
• Marginal Physical Product of Capital (MPPK)
  holding L constant

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Average Physical Product
Marginal Physical Product Additional output per
additional unit of input, holding other inputs
constant. Average Physical Product Average
number of units of output produced per unit of
input.
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Assumptions Behind Production Functions(Think
Starbucks)

• MPPL 0 at low levels of L, with K fixed.
• Having one machine with no workers will yield
  positive MPP when first worker is added.
• MPPL may increase as labor is added, holding K
  fixed, at low levels of L.
• Adding a second worker to the machine may
  increase output even more if the 2 workers work
  well together or machine is difficult to operate.

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Assumptions Behind Production Functions(Think
Starbucks)

• MPPL will eventually decline as more labor is
  added, with K fixed.
• Only so much additional output can be obtained
  with many workers on one machine.
• At high enough levels of labor, MPPL may become
  negative, holding K fixed.
• Too many cooks in the kitchen.

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Use Assumptions to Graph TPPL

• Total Physical Product of Labor how output
  changes holding K constant
• MPPL 0 at low levels of L
• MPPL may increase as labor is added at low L
• MPPL will eventually decline as more labor is
  added
• At high enough L, MPPL may become negative

F(K,L)
4
TPPL
3
1,2
L
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Get MPP and APP from TPP
f(K,L)

• MPPL is slope of TPPL
• APPL is slope of line from origin to TPPL
• If MPPL APPL, then APPL is increasing.
• If MPPL
• MPPL APPLat max of APPL curve.

TPPL
APP MPP
L
MPPL, APPL
APPL
MPPL
L
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Typical TPP curve

• Most typical
• Increasing returns to L
• Then constant returns to L
• Then decreasing returns to L
• TPP curves do not have to display all of these
  properties.

f(K,L)
TPPL
L
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Increasing Marginal Returns

• As input increases, MPP increases.
• As more of the input is put in, output rises
  faster and faster.

TPPL
MPPL
Qf(K,L)
MPPL(Q)
L
L
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Constant Marginal Returns

• As input increases, MPP does not change.

TPPL
MPPL
Qf(K,L)
MPPL
MPPL(Q)
L
L
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Decreasing Marginal Returns

• As input increases, MPP decreases.
• As more of the input is put in, output rises but
  slower and slower.

TPPL
MPPL
Qf(K,L)
MPPL
MPPL(Q)
L
L
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Returns to Scale

• MPP shows how Q changes if one input is changed,
  holding all other inputs fixed.
• What if all inputs (K and L) change
  simultaneously?
• Assume a proportionate increase in K and L.
• Concept of returns to scale
• Decreasing returns to scale
• Constant returns to scale
• Increasing returns to scale

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Decreasing Returns to Scale (DRTS)

• A production function displays DRTS if increasing
  all inputs by the same proportion increases
  output by less than that proportion.
• Doubling inputs less than doubles outputs.
• Consider a scale factor a.
• Q0 f(K0, L0)
• Q1 f(a K0, a L0)
• DRTS if Q1

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Constant and Increasing Returns to Scale

• Constant Returns to Scale (CRTS)
• Increasing all inputs by the same proportion
  yields an exactly proportionate increase in
  output.
• CRTS if Q1 a Q0
• Increasing Returns to Scale (IRTS)
• Increasing all inputs by the same proportion
  yields a more than proportionate increase in
  output.
• IRTS if Q1 a Q0

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Characterize the following production functions
IRTS, CRTS, or DRTS?

• F(K,L) K2L
• IRTS
• Q0 (K0)2L0 Q1 (a K0)2 a L0 Q1 a3 (K0)2 L0
  Q1 a3 Q0
• F(K,L) 10K 5L
• CRTS
• Q0 10K0 5L0 Q1 a 10K0 a 5L0 Q1 a (10K0
  5L0) Q1 a Q0
• F(K,L) (KL).5
• CRTS
• Q0 (K0L0).5 Q1 (a K0 a L0).5 Q1 a(K0
  L0).5) Q1 a Q0