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Lecture 12

Lecture 12-Production and Cost Schedules

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Department
Economics
Course Code
ECO101H1
Professor
Jack Carr

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Tuesday, October 27th, 2009.
Production and Cost Schedules
Production Function
Production function: Relates output to quantity of inputs (capital, labour)
Short-run: One input (capital) is fixed, while one input (labour) can vary
Long-run: All inputs (capital, labour) can vary
Example: General Motors
Short-run: GM can vary amount of labour (overtime, lay-offs)
GM cannot vary number of plants (capital)
Long-run: GM can vary number of plants and amount of labour
Product Schedules (Short-Run)
(TP) Total Product: total output, given labour input
(MP) Marginal Product*: increase in total output divided by increase in labour input
(AP) Average Product: total output divided by labour input
Law of Diminishing Returns:
The marginal product of a variable input, in the presence of a fixed input,
eventually diminished
Example:
Labour Output Marginal Product Average Product
(Total Product)
0 0
1 4 4 4.00
2 10 6 5.00
3 13 3 4.33
4 15 2 3.75
5 16 1 3.20
Note: if MP is above AP, AP is rising: if MP is less than AP, AP is falling
www.notesolution.com
L=1 AP = 4
MP = 6 (exceeds AP)
L = 2 AP = 5
L = 3 AP = 4.33
MP = 2 (is less than AP)
L = 4 AP = 3.75
Law of Diminishing Returns: Intuition
Number of chefs in restaurant kitchen:
1. First chef: must make all meals, attend all ovens, no specialization
2. An additional chef: chefs can specialize, help one another
Æ marginal product rises
3. Additional chefs are added: eventually, kitchen becomes too crowded, chefs must
wait to use ovens, etc.
Æ marginal product declines
0HDVXUHVRID)LUP¶V&RVWRI3URGXFWLRQ
Total Cost (TC): Total of all costs
Total Fixed Cost (TFC): Total Cost of fixed input
Total Variable Cost (TVC): Total Cost of variable input
TC = TFC + TVC
**Marginal Cost (MC): Increases in total cost / increase in output
Note: TFC "Sunk Costs"
Example: Total Cost ($) Marginal Cost
($ per unit)
(1) (2) (3) (4) (5) (6)
Labour (L) Output (Q) Fixed (TFC) Variable (TVC) Total (TC) (MC)
0 0 100 0 100
1 15 100 10 110 0.67
2 34 100 20 120 0.53
3 48 100 30 130 0.71
4 60 100 40 140 0.83
5 62 100 50 150 5.00
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Description
Tuesday, October 27th, 2009. Production and Cost Schedules Production Function Production function: Relates output to quantity of inputs (capital, labour) Short-run: One input (capital) is fixed, while one input (labour) can vary Long-run: All inputs (capital, labour) can vary Example: General Motors Short-run: GM can vary amount of labour (overtime, lay-offs) GM cannot vary number of plants (capital) Long-run: GM can vary number of plants and amount of labour Product Schedules (Short-Run) (TP) Total Product: total output, given labour input (MP) Marginal Product*: increase in total output divided by increase in labour input (AP) Average Product: total output divided by labour input Law of Diminishing Returns: The marginal product of a variable input, in the presence of a fixed input, eventually diminished Example: Labour Output Marginal Product Average Product (Total Product) 0 0 1 4 4 4.00 2 10 6 5.00 3 13 3 4.33 4 15 2 3.75 5 16 1 3.20 Note: if MP is above AP, AP is rising: if MP is less than AP, AP is falling www.notesolution.com L=1 AP = 4 MP = 6 (exceeds AP) L = 2 AP = 5 L = 3 AP = 4.33 MP = 2 (is less than AP) L = 4 AP = 3.75 Law of Diminishing Returns: Intuition Number of chefs in restaurant kitchen: 1. First chef: must make all meals, attend all ovens, no specialization 2. An additional chef: chefs can specialize, help one another Æ marginal product rises 3. Additional chefs are added: eventually, kitchen becomes too crowded, chefs must wait to use ovens, etc. Æ marginal product declines 0HDVXUHVRID)LUP¶V&RVWRI3URGXFWLRQ Total Cost (TC): Total of all costs Total Fixed Cost (TFC): Total Cost of fixed input Total Variable Cost (TVC): Total Cost of variable input TC = TFC + TVC **Marginal Cost (MC): Increases in total cost / increase in output Note: TFC "Sunk Costs" Example: Total Cost ($) Marginal Cost ($ per unit) (1) (2) (3) (4) (5) (6) Labour (L) Output (Q) Fixed (TFC) Variable (TVC) Total (TC) (MC) 0 0 100 0 100 1 15 100 10 110 0.67 2 34 100 20 120 0.53 3 48 100 30 130 0.71 4 60 100 40 140 0.83 5 62 100 50 150 5.00 www.notesolution.com L 0 to1 MP = 15 MC = $10/15 = $0.67 L 1 to 2 MP = 19 MC = $10/19 = $0.53 L 2 to 3 MP = 14 MC = $10/14 = $0.71 Observations: 1) /DZRI'LPLQLVKLQJ5HWXUQVVKRUWUXQ03HYHQWXDOO\; 2) MP 9 => MC ; MP ; => MC 9 **Average Total Cost (ATC): Average cost per unit of output ATC = TC/Q Average Variable Cost (AVC): Average variable cost per unit of output TVC/Q Average Fixed Cost (AFC): Average fixed cost per unit of output (TFC/Q) Example: Total Cost ($) Marginal Cost Average Cost ($ per unit) ($ per unit) (1) (2) (3) (4) (5) (6) (7) (8) (9) Labour Output Fixed Variable Total (MC) Fixed Variable Total (L) (Q) (TFC) (TVC) (TC) (AFC) (AVC) (ATC) 0 0 100 0 100 -- -- -- 1 15 100 10 110 0.67 6.67 0.67 7.33 2 34 100 20 120 0.53 2.94 0.59 3.53 3 48 100 30 130 0.71 2.08 0.62 2.71 4 60 100 40 140 0.83 1.67 0.67 2.33 5 62 100 50 150 5.00 1.61 0.81 2.42 Wage rate: 10 0& ¨7&¨4 AFC = TFC / Q AVC = TVC / Q ATC = TC / Q = AFC + AVC www.notesolution.com 3URSHUWLHVRID)LUP¶V&RVW&XUYHV 1. MC curve eventually rises (to reflect the diminishing marginal product of the variable input) 2. When MP is rising, MC is falling. When MP is at a maximum, MC is at a minimum. When MP of labour is at its maximum, MC is at its minimum 3. ATC curve is U-shaped (ATC = AFC + AVC) $)&DOZD\VGHFOLQHVDVRXWSXWLQFUHDVHVDVIL[HGFRVWVDUH³VSUHDG´RYHUDlarger output) AVC eventually increases due to diminishing MP 4. MC curve intersects ATC curve at its minimum point (when MC is less than ATC, then ATC is decreasing. When MC is greater than ATC, ATC is rising). Output MP Cost Labour MC Q Law of Diminishing Returns www.notesolution.com Cost MC Q ATC MC intersects ATC at minimum of ATC www.notesolution.comth Tuesday, October 27 , 2009. Production and Cost Schedules Production Function Production function: Relates output to quantity of inputs (capital, labour) Short-run: One input (capital) is fixed, while one input (labour) can vary Long-run: All inputs (capital, labour) can vary Example: General Motors Short-run: GM can vary amount of labour (overtime, lay-offs) GM cannot vary number of plants (capital) Long-run: GM can vary number of plants and amount of labour Product Schedules (Short-Run) (TP) Total Product: total output, given labour input (MP) Marginal Product*: increase in total output divided by increase in labour input (AP) Average Product: total output divided by labour input Law of Diminishing Returns: The marginal product of a variable input, in the presence of a fixed input, eventually diminished Example: Labour Output Marginal Product Average Product (Total Product) 0 0 1 4 4 4.00 2 10 6 5.00 3 13 3 4.33 4 15 2 3.75 5 16 1 3.20 Note: if MP is above AP, AP is rising: if MP is less than AP, AP is falling www.notesolution.com
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