production. costs problem 6 on p.194.
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Production. Costs Problem 6 on p.194. . Production. Costs Problem 6 on p.194. . Production. Costs Problem 6 on p.194. . Production. Costs Problem 6 on p.194. . Production. Costs Problem 6 on p.194. . Production. Costs Problem 6 on p.194. . Production. Costs Problem 6 on p.194. . - PowerPoint PPT PresentationTRANSCRIPT
Production. Costs Problem 6 on p.194.
Output FC VC TC AFC AVC ATC MC
0 10,000 ---
100 200
200 125
300 133.3
400 150
500 200
600 250
Production. Costs Problem 6 on p.194.
Output FC VC TC AFC AVC ATC MC
0 10,000 ---
100 10,000 200
200 10,000 125
300 10,000 133.3
400 10,000 150
500 10,000 200
600 10,000 250
Production. Costs Problem 6 on p.194.
Output FC VC TC AFC AVC ATC MC
0 10,000 ---
100 10,000 20,000 200
200 10,000 125
300 10,000 133.3
400 10,000 150
500 10,000 200
600 10,000 250
Production. Costs Problem 6 on p.194.
Output FC VC TC AFC AVC ATC MC
0 10,000 ---
100 10,000 20,000 200
200 10,000 25,000 125
300 10,000 40,000 133.3
400 10,000 60,000 150
500 10,000 100,000 200
600 10,000 150,000 250
Production. Costs Problem 6 on p.194.
Output FC VC TC AFC AVC ATC MC
0 10,000 ---
100 10,000 10,000 20,000 200
200 10,000 15,000 25,000 125
300 10,000 30,000 40,000 133.3
400 10,000 50,000 60,000 150
500 10,000 90,000 100,000 200
600 10,000 140,000 150,000 250
Production. Costs Problem 6 on p.194.
Output FC VC TC AFC AVC ATC MC
0 10,000 0 ---
100 10,000 10,000 20,000 200
200 10,000 15,000 25,000 125
300 10,000 30,000 40,000 133.3
400 10,000 50,000 60,000 150
500 10,000 90,000 100,000 200
600 10,000 140,000 150,000 250
Production. Costs Problem 6 on p.194.
Output FC VC TC AFC AVC ATC MC
0 10,000 0 10,000 ---
100 10,000 10,000 20,000 200
200 10,000 15,000 25,000 125
300 10,000 30,000 40,000 133.3
400 10,000 50,000 60,000 150
500 10,000 90,000 100,000 200
600 10,000 140,000 150,000 250
Production. Costs Problem 6 on p.194.
Output FC VC TC AFC AVC ATC MC
0 10,000 0 10,000 --- --- ---
100 10,000 10,000 20,000 100 200
200 10,000 15,000 25,000 50 125
300 10,000 30,000 40,000 33.3 133.3
400 10,000 50,000 60,000 25 150
500 10,000 90,000 100,000 20 200
600 10,000 140,000 150,000 16.7 250
Production. Costs Problem 6 on p.194.
Output FC VC TC AFC AVC ATC MC
0 10,000 0 10,000 --- --- ---
100 10,000 10,000 20,000 100 100 200
200 10,000 15,000 25,000 50 75 125
300 10,000 30,000 40,000 33.3 100 133.3
400 10,000 50,000 60,000 25 125 150
500 10,000 90,000 100,000 20 180 200
600 10,000 140,000 150,000 16.7 233.3 250
Production. Costs Problem 6 on p.194.
Output FC VC TC AFC AVC ATC MC
0 10,000 0 10,000 --- --- ---
100 10,000 10,000 20,000 100 100 200
200 10,000 15,000 25,000 50 75 125
300 10,000 30,000 40,000 33.3 100 133.3
400 10,000 50,000 60,000 25 125 150
500 10,000 90,000 100,000 20 180 200
600 10,000 140,000 150,000 16.7 233.3 250
MC = cost of making an extra unit
Production. Costs Problem 6 on p.194.
Output FC VC TC AFC AVC ATC MC
0 10,000 0 10,000 --- --- ---
100 10,000 10,000 20,000 100 100 200
200 10,000 15,000 25,000 50 75 125
300 10,000 30,000 40,000 33.3 100 133.3
400 10,000 50,000 60,000 25 125 150
500 10,000 90,000 100,000 20 180 200
600 10,000 140,000 150,000 16.7 233.3 250
Q
TCMC
Production. Costs Problem 6 on p.194.
Output FC VC TC AFC AVC ATC MC
0 10,000 0 10,000 --- --- ---
100 10,000 10,000 20,000 100 100 200
200 10,000 15,000 25,000 50 75 125
300 10,000 30,000 40,000 33.3 100 133.3
400 10,000 50,000 60,000 25 125 150
500 10,000 90,000 100,000 20 180 200
600 10,000 140,000 150,000 16.7 233.3 250
Q
VC
Q
TCMC
Production. Costs Problem 6 on p.194.
Output FC VC TC AFC AVC ATC MC
0 10,000 0 10,000 --- --- ---
100 10,000 10,000 20,000 100 100 200 100
200 10,000 15,000 25,000 50 75 125
300 10,000 30,000 40,000 33.3 100 133.3
400 10,000 50,000 60,000 25 125 150
500 10,000 90,000 100,000 20 180 200
600 10,000 140,000 150,000 16.7 233.3 250
Q
VC
Q
TCMC
Production. Costs Problem 6 on p.194.
Output FC VC TC AFC AVC ATC MC
0 10,000 0 10,000 --- --- ---
100 10,000 10,000 20,000 100 100 200 100
200 10,000 15,000 25,000 50 75 125 50
300 10,000 30,000 40,000 33.3 100 133.3
400 10,000 50,000 60,000 25 125 150
500 10,000 90,000 100,000 20 180 200
600 10,000 140,000 150,000 16.7 233.3 250
Q
VC
Q
TCMC
Production. Costs Problem 6 on p.194.
Output FC VC TC AFC AVC ATC MC
0 10,000 0 10,000 --- --- --- ---
100 10,000 10,000 20,000 100 100 200 100
200 10,000 15,000 25,000 50 75 125 50
300 10,000 30,000 40,000 33.3 100 133.3 150
400 10,000 50,000 60,000 25 125 150 200
500 10,000 90,000 100,000 20 180 200 400
600 10,000 140,000 150,000 16.7 233.3 250 500
Q
VC
Q
TCMC
If cost is given as a function of Q, then For example:
TC = 10,000 + 200 Q + 150 Q2
MC = ?
dQ
TCdMC
)(
Profit is believed to be the ultimate goal of any firm. If the production unit described in the problem above can sell as many units as it wants for P=$360, what is the best quantity to produce (and sell)?
Output FC VC TC AFC AVC ATC MC
0 10,000 0 10,000 --- --- --- ---
100 10,000 10,000 20,000 100 100 200 100
200 10,000 15,000 25,000 50 75 125 50
300 10,000 30,000 40,000 33.3 100 133.3 150
400 10,000 50,000 60,000 25 125 150 200
500 10,000 90,000 100,000 20 180 200 400
600 10,000 140,000 150,000 16.7 233.3 250 500
Profit is believed to be the ultimate goal of any firm. If the production unit described in the problem above can sell as many units as it wants for P=$360, what is the best quantity to produce (and sell)?
Output FC VC TC
0 10,000 0 10,000
100 10,000 10,000 20,000
200 10,000 15,000 25,000
300 10,000 30,000 40,000
400 10,000 50,000 60,000
500 10,000 90,000 100,000
600 10,000 140,000 150,000
Doing it the “aggregate” way,by actually calculating the profit:
Output FC VC TC TR
0 10,000 0 10,000
100 10,000 10,000 20,000
200 10,000 15,000 25,000
300 10,000 30,000 40,000
400 10,000 50,000 60,000
500 10,000 90,000 100,000
600 10,000 140,000 150,000
Doing it the “aggregate” way,by actually calculating the profit:
P=$360
Output FC VC TC TR
0 10,000 0 10,000 0
100 10,000 10,000 20,000 36,000
200 10,000 15,000 25,000 72,000
300 10,000 30,000 40,000 108,000
400 10,000 50,000 60,000 144,000
500 10,000 90,000 100,000 180,000
600 10,000 140,000 150,000 216,000
Doing it the “aggregate” way,by actually calculating the profit:
P=$360
Output FC VC TC TR Profit
0 10,000 0 10,000 0
100 10,000 10,000 20,000 36,000
200 10,000 15,000 25,000 72,000
300 10,000 30,000 40,000 108,000
400 10,000 50,000 60,000 144,000
500 10,000 90,000 100,000 180,000
600 10,000 140,000 150,000 216,000
Doing it the “aggregate” way,by actually calculating the profit:
P=$360
Output FC VC TC TR Profit
0 10,000 0 10,000 0 –10,000
100 10,000 10,000 20,000 36,000 16,000
200 10,000 15,000 25,000 72,000 47,000
300 10,000 30,000 40,000 108,000 68,000
400 10,000 50,000 60,000 144,000 84,000
500 10,000 90,000 100,000 180,000 80,000
600 10,000 140,000 150,000 216,000 66,000
Doing it the “aggregate” way,by actually calculating the profit:
P=$360
Output FC VC TC TR Profit
0 10,000 0 10,000 0 –10,000
100 10,000 10,000 20,000 36,000 16,000
200 10,000 15,000 25,000 72,000 47,000
300 10,000 30,000 40,000 108,000 68,000
400 10,000 50,000 60,000 144,000 84,000
500 10,000 90,000 100,000 180,000 80,000
600 10,000 140,000 150,000 216,000 66,000
Doing it the “aggregate” way,by actually calculating the profit:
P=$360
Alternative: The Marginal ApproachThe firm should produce only units that are worth producing, that is, those for which the selling price exceeds the cost of making them.
Output FC VC TC AFC AVC ATC MC
0 10,000 0 10,000 --- --- --- ---
100 10,000 10,000 20,000 100 100 200 100
200 10,000 15,000 25,000 50 75 125 50
300 10,000 30,000 40,000 33.3 100 133.3 150
400 10,000 50,000 60,000 25 125 150 200
500 10,000 90,000 100,000 20 180 200 400
600 10,000 140,000 150,000 16.7 233.3 250 500
< 360
> 360
Principle (Marginal approach to profit maximization): If data is provided in discrete (tabular) form, then profit is maximized by producing all the units for which and stopping right before the unit for which
Principle (Marginal approach to profit maximization): If data is provided in discrete (tabular) form, then profit is maximized by producing all the units for which MR > MCand stopping right before the unit for which MR < MC In our case, price of output stays constant throughout therefore MR = P (an extra unit increases TR by the amount it sells for)
If costs are continuous functions of QOUTPUT, then profit
is maximized where
Principle (Marginal approach to profit maximization): If data is provided in discrete (tabular) form, then profit is maximized by producing all the units for which MR > MCand stopping right before the unit for which MR < MC In our case, price of output stays constant throughout therefore MR = P (an extra unit increases TR by the amount it sells for)
If costs are continuous functions of QOUTPUT, then profit
is maximized where MR=MC
What if FC is $100,000 instead of $10,000? How does the profit maximization point change?
Output FC VC TC TR Profit
0 10,000 0 10,000 0 –10,000
100 10,000 10,000 20,000 36,000 16,000
200 10,000 15,000 25,000 72,000 47,000
300 10,000 30,000 40,000 108,000 68,000
400 10,000 50,000 60,000 144,000 84,000
500 10,000 90,000 100,000 180,000 80,000
600 10,000 140,000 150,000 216,000 66,000
What if FC is $100,000 instead of $10,000? How does the profit maximization point change?
Output FC VC TC TR Profit
0 100,000 0 10,000 0 –10,000
100 100,000 10,000 20,000 36,000 16,000
200 100,000 15,000 25,000 72,000 47,000
300 100,000 30,000 40,000 108,000 68,000
400 100,000 50,000 60,000 144,000 84,000
500 100,000 90,000 100,000 180,000 80,000
600 100,000 140,000 150,000 216,000 66,000
What if FC is $100,000 instead of $10,000? How does the profit maximization point change?
Output FC VC TC TR Profit
0 100,000 0 100,000 0 –10,000
100 100,000 10,000 110,000 36,000 16,000
200 100,000 15,000 115,000 72,000 47,000
300 100,000 30,000 130,000 108,000 68,000
400 100,000 50,000 150,000 144,000 84,000
500 100,000 90,000 190,000 180,000 80,000
600 100,000 140,000 240,000 216,000 66,000
What if FC is $100,000 instead of $10,000? How does the profit maximization point change?
Output FC VC TC TR Profit
0 100,000 0 100,000 0–100,000
100 100,000 10,000 110,000 36,000 –74,000
200 100,000 15,000 115,000 72,000 –43,000
300 100,000 30,000 130,000 108,000 –22,000
400 100,000 50,000 150,000 144,000 –6,000
500 100,000 90,000 190,000 180,000 –10,000
600 100,000 140,000 240,000 216,000 –24,000
What if FC is $100,000 instead of $10,000? How does the profit maximization point change?
Output FC VC TC TR Profit
0 100,000 0 100,000 0–100,000
100 100,000 10,000 110,000 36,000 –74,000
200 100,000 15,000 115,000 72,000 –43,000
300 100,000 30,000 130,000 108,000 –22,000
400 100,000 50,000 150,000 144,000 –6,000
500 100,000 90,000 190,000 180,000 –10,000
600 100,000 140,000 240,000 216,000 –24,000
Fixed cost does not affect the firm’s optimal short-term output decision and can be ignored while deciding how much to produce today.
Principle:
Consistently low profits may induce the firm to close down eventually (in the long run) but not any sooner than your fixed inputs become variable ( your building lease expires, your equipment wears out and new equipment needs to be purchased,
you are facing the decision of whether or not to take out a new loan, etc.)
Sometimes, it is more convenient to formulate a problem not through costs as a function of output but through output (product) as a function of inputs used.
Problem 2 on p.194.
“Diminishing returns” – what are they?
In the short run, every company has some inputs fixed and some variable. As the variable input is added, every extra unit of that input increases the total output by a certain amount; this additional amount is called “marginal product”. The term, diminishing returns, refers to the situation when the marginal product of the variable input starts to decrease (even though the total output may still keep going up!)
Total output, or Total Product, TP
Amount of input used
Amount of input used
Marginal product, MPRange of diminishing returns
K L Q MPK
0 20 01 20 502 20 1503 20 3004 20 4005 20 4506 20 475
Calculating the marginal product (of capital) for the data in Problem 2:
K L Q MPK
0 20 0 ---1 20 50 502 20 1503 20 3004 20 4005 20 4506 20 475
Calculating the marginal product (of capital) for the data in Problem 2:
K L Q MPK
0 20 0 ---1 20 50 502 20 150 1003 20 300 1504 20 400 1005 20 450 506 20 475 25
Calculating the marginal product (of capital) for the data in Problem 2:
In other words, we know we are in the range of diminishing returns when the marginal product of the variable input starts falling, or, the rate of increase in total output slows down.(Ex: An extra worker is not as useful as the one before him)
Implications for the marginal cost relationship:
Worker #10 costs $8/hr, makes 10 units. MCunit =
In other words, we know we are in the range of diminishing returns when the marginal product of the variable input starts falling, or, the rate of increase in total output slows down.(Ex: An extra worker is not as useful as the one before him)
Implications for the marginal cost relationship:
Worker #10 costs $8/hr, makes 10 units. MCunit = $0.80
Worker #11 costs $8/hr, makes …
In other words, we know we are in the range of diminishing returns when the marginal product of the variable input starts falling, or, the rate of increase in total output slows down.(Ex: An extra worker is not as useful as the one before him)
Implications for the marginal cost relationship:
Worker #10 costs $8/hr, makes 10 units. MCunit = $0.80
Worker #11 costs $8/hr, makes 8 units. MCunit =
In other words, we know we are in the range of diminishing returns when the marginal product of the variable input starts falling, or, the rate of increase in total output slows down.(Ex: An extra worker is not as useful as the one before him)
Implications for the marginal cost relationship:
Worker #10 costs $8/hr, makes 10 units. MCunit = $0.80
Worker #11 costs $8/hr, makes 8 units. MCunit = $1
In the range of diminishing returns, MP of input is falling and MC of output is increasing
Marginal cost, MC
Amount of output
Amount of input used
Marginal product, MPThis amount of output corresponds to this amount of input
When MP of input is decreasing, MC of output is increasing and vice versa.
Therefore the range of diminishing returns can be identified by looking at either of the two graphs.(Diminishing marginal returns set in at the max of the MP graph, or at the min of the MC graph)
Back to problem 2, p.194.To find the profit maximizing amount of input (part d), we will once again use the marginal approach, which compares the marginal benefit from a change to the marginal cost of than change.More specifically, we compare VMPK, the value of marginal product of capital, to the price of capital, or the “rental rate”, r.
K L Q MPK VMPK r0 20 0 ---1 20 50 502 20 150 1003 20 300 1504 20 400 1005 20 450 506 20 475 25
Back to problem 2, p.194.To find the profit maximizing amount of input (part d), we will once again use the marginal approach, which compares the marginal benefit from a change to the marginal cost of than change.More specifically, we compare VMPK, the value of marginal product of capital, to the price of capital, or the “rental rate”, r.
K L Q MPK VMPK r0 20 0 --- ---1 20 50 50 1002 20 150 100 2003 20 300 150 3004 20 400 100 2005 20 450 50 1006 20 475 25 50
Back to problem 2, p.194.To find the profit maximizing amount of input (part d), we will once again use the marginal approach, which compares the marginal benefit from a change to the marginal cost of than change.More specifically, we compare VMPK, the value of marginal product of capital, to the price of capital, or the “rental rate”, r.
K L Q MPK VMPK r0 20 0 --- ---1 20 50 50 100 752 20 150 100 200 753 20 300 150 300 754 20 400 100 200 755 20 450 50 100 756 20 475 25 50 75
>>>>>< STOP
Back to problem 2, p.194.To find the profit maximizing amount of input (part d), we will once again use the marginal approach, which compares the marginal benefit from a change to the marginal cost of than change.More specifically, we compare VMPK, the value of marginal product of capital, to the price of capital, or the “rental rate”, r.
K L Q MPK VMPK r0 20 0 --- ---1 20 50 50 100 752 20 150 100 200 753 20 300 150 300 754 20 400 100 200 755 20 450 50 100 756 20 475 25 50 75
>>>>>< STOP
Why would we ever want to be in the range of diminishing returns?
Consider the simplest case when the price of output doesn’t depend on how much we produce. Until we get to the DMR range, every next worker is more valuable than the previous one, therefore we should keep hiring them. Only after we get to the DMR range and the MP starts falling, we should consider stopping.Therefore, the profit maximizing point is always in the diminishing marginal returns range!
Surprised?