Wrapping up supply

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Wrapping up supply

• Today More on profit maximization, determinants
  of supply, and surplus

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Today

• We make this graph make intuitive sense
• We will see that
• Profits are positive at price P1
• Profits are negative at prices P2 and P3
• Firms will shut down when price is P3

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Profit maximization

• Remember that this is our goal
• For the most part, we will implement MB/MC
  analysis again
• Exception Shutdown condition
• If a firm can lose less by closing than opening,
  it will close

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Costs

• Cost to hire an employee is 100/day
• Assume 1000 in fixed costs for a phone
  manufacturer per day
• Note average fixed cost (AFC) decreases as the
  number of phones increases

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Our output example for today
of employees hired per day Number of phones produced
0 0

1 20

2 45

3 55

4 63

5 67
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Increasing returns?

• Notice that the marginal productivity for the 1st
  worker is 20 2nd worker, 25
• Why?
• Specialization
• Assembly line can help increase marginal
  productivity up to a certain point
• Marginal productivity eventually decreases

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Cost table
of empl./day Phones per day Fixed cost (/day) Var. cost (/day) Total cost (/day) MC (/phone)
0 0 1000 0 1000

1 20 1000 100 1100

2 45 1000 200 1200

3 55 1000 300 1300

4 63 1000 400 1400

5 67 1000 500 1500
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How to calculate MC

• Marginal cost (MC) is how much additional cost is
  necessary to produce an additional phone
• For example, each additional phone from the 1st
  worker is
• cost to hire worker / of phones produced
• (100/day) / (20 phones/day) 5/phone

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Cost table
of empl./day Phones per day Fixed cost (/day) Var. cost (/day) Total cost (/day) MC (/phone)
0 0 1000 0 1000
5.00
1 20 1000 100 1100
4.00
2 45 1000 200 1200
10.00
3 55 1000 300 1300
12.50
4 63 1000 400 1400
25.00
5 67 1000 500 1500
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Suppose that phones sell for 18 each

• How many people should be hired?
• Hire the next worker if the MB of the next phone
  produced is at least as much as the MC
• This is the same as finding the number of workers
  that maximizes profits

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Marginal analysis Hire 4 employees/day
of empl./day Phones per day MB (/phone) MC (/phone)
0 0
18.00 5.00
1 20
18.00 4.00
2 45
18.00 10.00
3 55
18.00 12.50
4 63
18.00 25.00
5 67
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How much profit? 266
of empl./day Phones per day Total rev. (/day) Total cost (/day) Profit (/day)
0 0 0 1000 1000

1 20 360 1100 740

2 45 810 1200 390

3 55 990 1300 310

4 63 1134 1400 266

5 67 1206 1500 294
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Shutdown condition

• Finally, we must check to see if the firm is
  better off shutting down when profits are
  negative
• If total revenue is less than total variable cost
  for all levels of output (Q), then the firm
  should shut down
• This is equivalent to the firm making worse
  profits for all Q gt 0 than for Q 0

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Shutdown condition check
of empl./day Total cost (/day) Profit (/day)
0 1000 1000

1 1100 740

2 1200 390

3 1300 310

4 1400 266

5 1500 294

• Profits are better when 4 employees are hired
  (266) than when the firm shuts down
  (1000)
• This firm stays in business

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Back to our graph

• We have finished a discrete example
• Now, we will see how we get the marginal cost
  (MC), average total cost (ATC), and average
  variable cost (AVC) curves

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Marginal cost
of empl./day MC (/phone)
0
5.00
1
4.00
2
10.00
3
12.50
4
25.00
5

• MC starts by decreasing, then increases sharply

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Average total cost
of empl./day Phones per day Total cost (/day) ATC (/phone)
0 0 1000 N/A

1 20 1100 55

2 45 1200 26.67

3 55 1300 23.64

4 63 1400 22.22

5 67 1500 22.39

• ATC falls initially, then eventually increases

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Average variable cost
of empl./day Phones per day VC (/day) AVC (/phone)
0 0 0 N/A

1 20 100 5.00

2 45 200 4.44

3 55 300 5.45

4 63 400 6.35

5 67 500 7.46

• AVC falls initially, then eventually increases

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ATC and AVC costs converge

• Note ATC AVC AFC
• Since AFC is decreasing as Q increases, the
  difference between ATC and AVC gets smaller as Q
  increases
• Thus, ATC and AVC curves get closer as Q increases

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MC curve

• Remember Marginal means for an additional unit
  produced
• If marginal is below average, this brings the
  average down
• If marginal is above average, this brings the
  average up

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MC curve

• Marginal cost curve tells us how average cost
  curves (ATC and AVC) move
• MC curve is below average cost curve when average
  cost curve is decreasing
• MC curve is above average cost curve when average
  cost curve is increasing

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Back to the graph

• All curves decrease initially, but eventually
  increase
• MC curve tells us which direction ATC and AVC
  curves are going

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Back to the graph

• At P1 ? positive profits, since TR gt TC
  (P ? Q gt ATC ? Q)
• At P2 ? negative profits
• At P3 ? firm shuts down (TR is less than VC for
  all Q)

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Warning!

• Look at red circle
• This is a point where P3 and MC curves intersect
• Ignore these points on the MC curve that are
  downward-sloping, since profit is minimized here

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Determinants of supply

• Technology
• Input prices
• The number of suppliers
• Expectations of future prices
• Changes in the price of other relevant products

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Some examples

• If technology improves or input prices decrease,
  production becomes less costly
• If the number of suppliers increases, we can
  horizontally add the additional supply to the
  market
• If the price of calculators increases, some phone
  suppliers may devote more of its capital to
  producing calculators

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Producer surplus

• Producer surplus is similar conceptually to
  consumer surplus
• For a unit or service sold, producer surplus is
  the difference between the price paid and the
  minimum payment the seller is willing to accept
  for it

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Example of producer surplus

• When P 25 per unit, shaded area is approximate
  producer surplus
• Area is a triangle, one-half times length times
  height 0.5 ? 10 ? 25 125

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Why are CS and PS important?

• Consumer surplus (CS) and producer surplus (PS)
  are important since these measures give us a
  crude measure of the total benefits to society
• Next week, we will see situations in which total
  surplus can be reduced

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This concludes supply

• Important things to remember with supply
• Individual and market supply
• Steps to profit maximization
• Useful to know individual firm supply, production
  function, FC, VC, TC, MC, AFC, AVC, ATC, shutdown
  condition
• Determinants of supply
• Producer surplus