1 short run costs. production processes x-box production ktm factory
TRANSCRIPT
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Short Run Costs
Production Processes
X-Box Production
http://www.youtube.com/watch?v=dzJUSFr5EvQ&feature=related
KTM Factory
http://www.youtube.com/watch?v=jihqmdX0jkM
1939 River Rouge Plant
http://www.youtube.com/watch?v=TcXfk0op6JA
Scorpion Factory
http://www.youtube.com/watch?v=hMCyqyyh5MA
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3
What would you need to start a Panera?
http://www.franchisechatter.com/2014/01/26/franchise-costs-detailed-estimates-of-panera-bread-franchise-costs-2013-fdd/
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Short Run versus Long Run?
short run - a period of time where some inputs are fixed (capital = building, equipment, etc.)
long run - a period of time in which all inputs can be varied (no inputs are fixed)
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Short Run Cost Function
Definition: A function that defines the minimum
possible cost of producing each output level when variable factors are employed in the cost-minimizing fashion. (Based on the inability to change the fixed factors)
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In this case, what is your total product/output (Q)? Number of Paninis (for simplicity assume
that Panera only produces a single product).
In general a firm uses capital, labor and materials to produce the product/output where capital is often fixed in the short run.
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In Short Run, how does the number of Paninis produced change as you change the number of workers?
# of workers # of paninis
0 0
1 5
2 12
3 20
4 25
5 28
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How does output change if you hire one more person? Depends on how many workers you
currently have. Output increases by 5 paninis when you hire the 1st worker, increases by 7 paninis when you hire the 2nd worker, …., and increases 3 paninis when you hire the 5th worker.
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What happens to “productivity” as the first few employees are hired?
Specialize and marginal product increases.
Marginal Product is the change in total output attributable to the last unit of an input.
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What would happen to “productivity” if you continued to hire more and more workers?
Marginal product would start to fall because some inputs are fixed in the short run.
Law of diminishing marginal returns OR Law of diminishing marginal product.
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What costs would you have to pay even if you didn’t produce a single panini?
Fixed Costs, FC (or Total Fixed Costs, TFC)
(often involves building and equipment)
Fixed Costs = Costs that do not change with changes in output
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What costs would you have to pay only if you produced paninis?
Variable Costs, VC (or Total Variable Costs, TVC)
(often assumed to be labor and material)
Variable Costs = Costs that change with changes in output
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What costs would increase if we wanted to produce one more panini?Variable Costs (such as labor
and materials)
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If you hired more and more employees and the store became more and more
crowded until the marginal product of a worker started to fall, what would happen to the cost of producing one more panini (marginal cost)?
Marginal cost = cost of producing an additional unit of output
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CostsQ FC VC TC AFC AVC ATC MC
0 100 0 100 - - - 50
1 100 50 150 100 50 150
30
2 100 80 180 50 40 90
20
3 100 100 200 33.3 33.33 66.7
10
4 100 110 210 25 27.5 52.5
20
5 100 130 230 20 26 46
(150-100)/1=Fixed costs do not vary with output
Variable costs increase by 50 from 0 to 1 unit of output and increases by 30 from 1 to 2 units.
Average Fixed Costs (AFC) = Fixed Costs/Q so at an output of 2, AFC=100/2=50.
Average Variable Costs (AVC) = Variable Costs/Q so at an output of 2, AVC=80/2=40.
Average Total Costs (ATC) = Total Costs/Q so at an output of 2, ATC=180/2=90 or AFC+ATC.
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Costs Q FC VC TC AFC AVC ATC MC
5 100 130 230 20 26 46
30
6 100 160 260 16.7 26.67 43.3
40
7 100 200 300 14.3 28.57 42.9
50
8 100 250 350 12.5 31.25 43.8
60
9 100 310 410 11.1 34.44 45.6
70
10 100 380 480 10 38 48
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Q AFC AVC ATC MC 0 - - - 50
1 100.00 50.00 150.00 30
2 50.00 40.00 90.00 20
3 33.33 33.33 66.67 10
4 25.00 27.50 52.50 20
5 20.00 26.00 46.00 30
6 16.67 26.67 43.33 40
7 14.29 28.57 42.86 50
8 12.50 31.25 43.75 60
9 11.11 34.44 45.56 70
10 10.00 38.00 48.00
0
10
20
30
40
50
60
70
80
90
100
0 1 2 3 4 5 6 7 8 9 10
Q
$/Q
MC
ATC
AVC
AFC
What is happening to TC as Q increases?TC= ATC*Q
150180
480
Increases!
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Q AFC AVC ATC MC0 - - -
501 100.00 50.00 150.00
302 50.00 40.00 90.00
203 33.33 33.33 66.67
104 25.00 27.50 52.50
205 20.00 26.00 46.00
306 16.67 26.67 43.33
407 14.29 28.57 42.86
508 12.50 31.25 43.75
609 11.11 34.44 45.56
7010 10.00 38.00 48.00
0
10
20
30
40
50
60
70
80
90
100
0 1 2 3 4 5 6 7 8 9 10
Q
$/Q
MC
ATC
AVC
AFC
What are total fixed costs in this example? AFC*Q
100*1=100
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Q AFC AVC ATC MC0 - - -
501 100.00 50.00 150.00
302 50.00 40.00 90.00
203 33.33 33.33 66.67
104 25.00 27.50 52.50
205 20.00 26.00 46.00
306 16.67 26.67 43.33
407 14.29 28.57 42.86
508 12.50 31.25 43.75
609 11.11 34.44 45.56
7010 10.00 38.00 48.00
0
10
20
30
40
50
60
70
80
90
100
0 1 2 3 4 5 6 7 8 9 10
Q
$/Q
MC
ATC
AVC
AFC
Why are AFC diminishing? Spreading a fixed number out over a larger and larger Q
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Q AFC AVC ATC MC0 - - -
501 100.00 50.00 150.00
302 50.00 40.00 90.00
203 33.33 33.33 66.67
104 25.00 27.50 52.50
205 20.00 26.00 46.00
306 16.67 26.67 43.33
407 14.29 28.57 42.86
508 12.50 31.25 43.75
609 11.11 34.44 45.56
7010 10.00 38.00 48.00
0
10
20
30
40
50
60
70
80
90
100
0 1 2 3 4 5 6 7 8 9 10
Q
$/Q
MC
ATC
AVC
AFC
Why is AVC getting closer to ATC?
Because ATC = AVC+AFCand AFC is getting close to 0
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Q AFC AVC ATC MC0 - - -
501 100.00 50.00 150.00
302 50.00 40.00 90.00
203 33.33 33.33 66.67
104 25.00 27.50 52.50
205 20.00 26.00 46.00
306 16.67 26.67 43.33
407 14.29 28.57 42.86
508 12.50 31.25 43.75
609 11.11 34.44 45.56
7010 10.00 38.00 48.00
0
10
20
30
40
50
60
70
80
90
100
0 1 2 3 4 5 6 7 8 9 10
Q
$/Q
MC
ATC
AVC
AFC
Where does the law of diminishing marginal product set in and how do you know? Where MC starts increasing!
Why does this happen?An input is fixed in the short run!
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Where does MC cross ATC?Where does MC cross AVC?
0
10
20
30
40
50
60
70
80
90
1000 1 2 3 4 5 6 7 8 9 10
Q
$/Q
MC
ATC
AVC
AFC
At their minimums
What is the relationship between MC and ATC? MC and AVC?
If MC<ATC, ATC is decreasingIf MC>ATC, ATC is increasingSame for AVC
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Q AFC AVC ATC MC0 - - -
501 100.00 50.00 150.00
302 50.00 40.00 90.00
203 33.33 33.33 66.67
104 25.00 27.50 52.50
205 20.00 26.00 46.00
306 16.67 26.67 43.33
407 14.29 28.57 42.86
508 12.50 31.25 43.75
609 11.11 34.44 45.56
7010 10.00 38.00 48.00
0
10
20
30
40
50
60
70
80
90
100
0 1 2 3 4 5 6 7 8 9 10
Q
$/Q
MC
ATC
AVC
AFC
How do you know this is the short run?
There are fixed costs
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Fixed Cost versus Sunk CostFixed Cost = costs that do not change with changes in
outputSunk Cost= a cost that is forever lost after it has been paid
Does profit maximizing output depend on whether cost if fixed or sunk given that you produce paninis?
Does the decision whether to produce any paninis depend on whether cost is fixed or sunk?
No
Yes
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Short Run versus Long Run? short run - a period of time where some
inputs are fixed (capital = building, equipment, etc.)
long run - a period of time in which all inputs can be varied (no inputs are fixed)
UQM Technologies
http://www.youtube.com/watch?v=UvnHQz6lDQ8&feature=related
Profit Maximization
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Profit Maximization assuming:
1. Firm must charge every consumer the same price (i.e., no price discrimination)
2. No Strategic Interaction among Firms
We will consider three industry structures: Price taking Firms Monopoly Monopolistic Competition
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Price Taking Firm’s Short Run CostsQ FC VC TC AFC AVC ATC MC
0 100 0 100 - - - 50
1 100 50 150 100 50 150
30
2 100 80 180 50 40 90
20
3 100 100 200 33.3 33.33 66.7
10
4 100 110 210 25 27.5 52.5
20
5 100 130 230 20 26 4628
Price Taking Firm’s Short Run CostsQ FC VC TC AFC AVC ATC MC
5 100 130 230 20 26 46
30
6 100 160 260 16.7 26.67 43.3
40
7 100 200 300 14.3 28.57 42.9
50
8 100 250 350 12.5 31.25 43.8
60
9 100 310 410 11.1 34.44 45.6
70
10 100 380 480 10 38 48 29
Q AFC AVC ATC MC 0 - - - 50
1 100.00 50.00 150.00 30
2 50.00 40.00 90.00 20
3 33.33 33.33 66.67 10
4 25.00 27.50 52.50 20
5 20.00 26.00 46.00 30
6 16.67 26.67 43.33 40
7 14.29 28.57 42.86 50
8 12.50 31.25 43.75 60
9 11.11 34.44 45.56 70
10 10.00 38.00 48.00
0
10
20
30
40
50
60
70
80
90
100
0 1 2 3 4 5 6 7 8 9 10
Q
$/Q
MC
ATC
AVC
AFC
What output maximizes profits if the marginal revenue (MR) for each unit the firm sells is $55? What are these profits?
8 55*8-43.75*8=90
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Q AFC AVC ATC MC 0 - - - 50
1 100.00 50.00 150.00 30
2 50.00 40.00 90.00 20
3 33.33 33.33 66.67 10
4 25.00 27.50 52.50 20
5 20.00 26.00 46.00 30
6 16.67 26.67 43.33 40
7 14.29 28.57 42.86 50
8 12.50 31.25 43.75 60
9 11.11 34.44 45.56 70
10 10.00 38.00 48.00
0
10
20
30
40
50
60
70
80
90
100
0 1 2 3 4 5 6 7 8 9 10
Q
$/Q
MC
ATC
AVC
AFC
What output maximizes profits if the marginal revenue for each unit the firm sells is $35? What are these profits?
6 35*6-43.33*6=-50
Produce an output of 6 in short-run if fixed costs are sunk.
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Q AFC AVC ATC MC 0 - - - 50
1 100.00 50.00 150.00 30
2 50.00 40.00 90.00 20
3 33.33 33.33 66.67 10
4 25.00 27.50 52.50 20
5 20.00 26.00 46.00 30
6 16.67 26.67 43.33 40
7 14.29 28.57 42.86 50
8 12.50 31.25 43.75 60
9 11.11 34.44 45.56 70
10 10.00 38.00 48.00
0
10
20
30
40
50
60
70
80
90
100
0 1 2 3 4 5 6 7 8 9 10
Q
$/Q
MC
ATC
AVC
AFC
What output maximizes profits if the marginal revenue for each unit the firm sells is $25? What are these profits?
5? 25*5-46*5=-105
Better off producing 0 so profits=-FC=-100 32
Short-Run Profit Maximizing Rule
Produce at an Output where
Marginal Revenue = Marginal Cost
(MR) (MC)
if Total Revenue > Variable Cost
[When the firm cannot price discriminate, this is the same thing as saying as long as
Price > AVC (from P*Q > AVC*Q) ]
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Monopoly Characteristics
1. There is a single seller
2. There are no close substitutes for the good
3. There are extremely high barriers to entry
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Monopolist Marginal Revenue (with no price discrimination)
P Q TR MR
10 0 0
9 1 9
8 2 16
7 3 21
6 4 24
5 5 25
4 6 24
3 7 21
2 8 16
1 9 9
0 10 0
+7+5+3
+1-1-3-5-7-9
Q
TRMR
0
1
2
3
4
5
6
7
8
9
10
0 1 2 3 4 5 6 7 8 9 10 11 12
D
+9
MR
Q
Note that Marginal Revenue for a given unit is plotted at the midpoint of that unit.35
Use Calculus to Obtain MR curve for Linear
Demand Curve Demand Curve:
P=a-bQ TR = (a-bQ)Q =aQ-bQ2
MR =ΔTR/ ΔQ =∂TR/ ∂Q
=a-2bQ[In prior graph, a=10 and b=1]
Slope of D
Slope of MR
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Monopoly If the firm’s goal were to
maximize total revenue, where would it produce?
P=$5; TR=$25
Will a monopolist ever charge a price less than $5?
What price will the monopolist charge?
0
1
2
3
4
5
6
7
8
9
10
0 1 2 3 4 5 6 7 8 9 10 11 12
D
Q
MR
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Monopoly Maximizing Profits
If the monopolist maximizes profits, where would it produce?
At an output where MR=MC as long as P>AVC.
This is at an output of Q=4 so a price of P=6.
0
1
2
3
4
5
6
7
8
9
10
0 1 2 3 4 5 6 7 8 9 10 11 12
AVC
MC
ATC
D
Q
MR
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MATH BEHIND: Maximizing Profits being where MR=MC
MaxQ Profits = MaxQ TR(Q)-TC(Q)
so profits are maximized where
Or where,
Applies when Q>0
0
MCMRQ
TC
Q
TR
MCMR
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Monopoly Maximizing Profits At Q=4 and P=6, what
is Total Revenue?TR=P*Q=6*4=24 At Q=4, what are Total
Costs?TC=ATC*Q=4.5*4=18 At Q=4 and P=6, what
are Profits?Profits=TR-TC=24-18=6OrProfits=P*Q-ATC*Q
=(P-ATC)*Q=(6-4.5)*4=6
0
1
2
3
4
5
6
7
8
9
10
0 1 2 3 4 5 6 7 8 9 10 11 12
AVC
MC
ATC
D
Q
MR
TR
TC
Profits
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Monopolist in Long Run What should this
monopolist do in the Long Run assuming that the monopolist thinks his costs will not change and neither will demand?
Keep producing Q=4 or change plant size depending if there is a plant size that would result in greater profits.
0
1
2
3
4
5
6
7
8
9
10
0 1 2 3 4 5 6 7 8 9 10 11 12
AVC
MC
ATC
D
Q
MR
Profits
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Monopolist in Long Run
What should this monopolist do in the Long Run assuming that the monopolist thinks his costs will not change and neither will demand?
Exit the industry or change plant size depending if there is a plant size that would result in positive profits given demand curve.
0
1
2
3
4
5
6
7
8
9
10
0 1 2 3 4 5 6 7 8 9 10 11 12
AVC
MC
ATC
D
MR
Profits
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Monopolistic Competition Characteristics1. There are many buyers and seller
2. Each firm in the industry produces a differentiated product
3. There is free entry into and exit from the industry
[Think bakery or coffee shop in big city.]
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Bakery in a Monopolistically Competitive Industry Maximizing Profits in the Short Run
If bakery maximizes profits, where would it produce?
Where MR=MC which is at an output of Q=3.5 so a price of P=8.
What are the bakery’s profits?
TR-TC=P*Q-ATC*Q=8*3.5 - 6.25*3.5 = 6.12
0123456789
10111213
0 1 2 3 4 5 6 7 8 9
10Q
MC
ATC
AVC
D
MR44
Bakery in a Monopolistically Competitive Industry Maximizing Profits in the Long Run
In long-run if the bakery is making positive economic profits, we would expect other bakeries to enter causing a reduction in demand.
What are maximum profits when demand is D’?
Q=3 so a price of P=6.67.Profits=P*Q-ATC*Q
=6.67*3-6.67*3=00123456789
101112
0 1 2 3 4 5 6 7 8 9
10 Q
MC
ATC
AVC
MR
D’
45
Review of Profit Maximization (when setting a single price)
46
Marginal Revenue from 5th Unit is just the shaded area below. This area is $11.
0
2
4
6
8
10
12
14
16
18
20
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Q
$/u
nit
MC
ATC
AVC
D
MR
When the MR curve is linear, the area under the MR curve can be obtained by just taking the MR at the midpoint of the quantities – in this case at 4.5.
The orange area is the same as the purple area. 47
Marginal Cost of 5th Unit is just the shaded area below. This area is $9.
0
2
4
6
8
10
12
14
16
18
20
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Q
$/u
nit
MC
ATC
AVC
D
MRThe purple area is the same as the red area
When the MC curve is linear, the area under the MC curve can be obtained by taking the MC at the midpoint of the quantities – in this case at 4.5.
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Change in Profits associated with producing 5 Units rather than 4 units.
0
2
4
6
8
10
12
14
16
18
20
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Q
$/u
nit
MC
ATC
AVC
D
MR
Yellow area is change in profits associated with producing 5 units rather than 4 units. This area is $2.
Subtract MC of 5th unit from MR of 5th unit– brown area from purple. 49
Review of Profit Maximization (when setting a single price)
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PROFIT MAXIMIZATION
0
2
4
6
8
10
12
14
16
18
20
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Q
$/u
nit
MC
ATC
AVC
D
MR
11.2
15
Profits are maximized at an output where MR=MC which is Q=5. Price is 15 and ATC is 11.2 at Q=5.
Profits are then 15*5-11.2*5=19
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