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Production SR 2
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You are managing a single-product firm. You have leased some equipment (economists call this the fixed factor, because you cannot change it for the period of the lease. Assume you need 5 units of capital (left column below). You then employ units of labour (the variable input) to use the leased equipment to produce the product. Assume each unit of labour has equal knowledge and skills.
Production in the short run
Assume all figures are on a ‘per-hour’ basis. i.e. 2 people, using the fixed units could produce 25 units of output per hour.Fixed cost = $20 per unit per hour Variable costs = $30 per unit per hour.
1 2 3 4 5 6 7 8 9 10 11
Fixed units
TFCVariable units
OutputMarginal Product (MP)
Average product (AP)
Total variable
cost
Total cost
Average variable
cost
Marginal cost
AverageTotal cost
5 100 0 0 0 0 $0 $100 - - -
5 100 1 10 10 10 $30 $130 $6.00 $3.50 $8.00
5 100 2 25 15 12.5 $60 $160 $3.80 $2.33 $4.40
5 100 3 42 17 14 $90 $190 $3.10 $2.06 $3.33
5 100 4 57 15 14.25 $120 $220 $2.89 $2.33 $2.98
5 100 5 67 10 13.4 $150 $250 $2.99 $3.50 $2.99
5 100 6 75 8 12.5 $180 $280 $3.13 $4.38 $3.07
5 100 7 77 2 11 $210 $310 $3.51 $17.50 $3.38
Our aim is to find the lowest-cost combination of variable and fixed factors in the short run.
Total product
Buttons
MP and AP
Total costs
Average and marginal costs
Conclusion
1
Data
1Tuesday, 13 August 13
Assume all figures are on a ‘per-hour’ basis. i.e. 2 people, using the fixed units could produce 25 units of output per hour.
1 2 3 4 5 6 7 8 9 10 11
Fixed units
TFCVariable units
OutputMarginal Product (MP)
Average product (AP)
Total variable
cost
Total cost
Average variable
cost
Marginal cost
AverageTotal cost
5 100 0 0 0 0 $0 $100 - - -
5 100 1 10 10 10 $30 $130 $6.00 $3.50 $8.00
5 100 2 25 15 12.5 $60 $160 $3.80 $2.33 $4.40
5 100 3 42 17 14 $90 $190 $3.10 $2.06 $3.33
5 100 4 57 15 14.25 $120 $220 $2.89 $2.33 $2.98
5 100 5 67 10 13.4 $150 $250 $2.99 $3.50 $2.99
5 100 6 75 8 12.5 $180 $280 $3.13 $4.38 $3.07
5 100 7 77 2 11 $210 $310 $3.51 $17.50 $3.38
0
20
40
60
80
0 1 2 3 4 5 6 70
10
25
42
57
67
75 77
Qua
ntity
Units of labour
a
Total product
The graph illustrates the production function. The total product curve is s-shaped. Quantity produced rises at an increasing rate as the first units of the variable factor (labour) are added to the fixed factors; then rises at a decreasing rate. Point a describes the point where diminishing returns to labour sets in (after 3 units of labour).
2
Total product
MP and AP
Total costs
Average and marginal costs
Conclusion
Data
2Tuesday, 13 August 13
Assume all figures are on a ‘per-hour’ basis. i.e. 2 people, using the fixed units could produce 25 units of output per hour.
1 2 3 4 5 6 7 8 9 10 11
Fixed units
TFCVariable units
OutputMarginal Product (MP)
Average product (AP)
Total variable
cost
Total cost
Average variable
cost
Marginal cost
AverageTotal cost
5 100 0 0 0 0 $0 $100 - - -
5 100 1 10 10 10 $30 $130 $6.00 $3.50 $8.00
5 100 2 25 15 12.5 $60 $160 $3.80 $2.33 $4.40
5 100 3 42 17 14 $90 $190 $3.10 $2.06 $3.33
5 100 4 57 15 14.25 $120 $220 $2.89 $2.33 $2.98
5 100 5 67 10 13.4 $150 $250 $2.99 $3.50 $2.99
5 100 6 75 8 12.5 $180 $280 $3.13 $4.38 $3.07
5 100 7 77 2 11 $210 $310 $3.51 $17.50 $3.38
Marginal product (MP) and average product (AP)
0
5
10
15
20
1 2 3 4 5 6 7
Qua
ntity
Units of labour
The MP and AP curves have inverted U-shapes. Diminishing Returns sets in after the third unit of labour, after which the MP curve falls.
3
Total product
MP and AP
Total costs
Average and marginal costs
Conclusion
Data
3Tuesday, 13 August 13
Assume all figures are on a ‘per-hour’ basis. i.e. 2 people, using the fixed units could produce 25 units of output per hour.
1 2 3 4 5 6 7 8 9 10 11
Fixed units
TFCVariable units
OutputMarginal Product (MP)
Average product (AP)
Total variable
cost
Total cost
Average variable
cost
Marginal cost
AverageTotal cost
5 100 0 0 0 0 $0 $100 - - -
5 100 1 10 10 10 $30 $130 $6.00 $3.50 $8.00
5 100 2 25 15 12.5 $60 $160 $3.80 $2.33 $4.40
5 100 3 42 17 14 $90 $190 $3.10 $2.06 $3.33
5 100 4 57 15 14.25 $120 $220 $2.89 $2.33 $2.98
5 100 5 67 10 13.4 $150 $250 $2.99 $3.50 $2.99
5 100 6 75 8 12.5 $180 $280 $3.13 $4.38 $3.07
5 100 7 77 2 11 $210 $310 $3.51 $17.50 $3.38
Total costs, total variable costs, total costs
TFC is horizontal because some costs are fixed in the short run. TVC increases at a decreasing rate as marginal product per unit of labour rises, then starts to fall after the point of diminishing returns. Likewise for TFC. Note TC = TVC + TFC
350
300
250
200
150
100
0 20 40 60 80
TC
TVC
TFC
Fixed cost = $20 per unit per hour Variable costs = $30 per unit per hour.
4
Total product
MP and AP
Total costs
Average and marginal costs
Conclusion
Data
4Tuesday, 13 August 13
Assume all figures are on a ‘per-hour’ basis. i.e. 2 people, using the fixed units could produce 25 units of output per hour.
1 2 3 4 5 6 7 8 9 10 11
Fixed units
TFCVariable units
OutputMarginal Product (MP)
Average product (AP)
Total variable
cost
Total cost
Average variable
cost
Marginal cost
AverageTotal cost
5 100 0 0 0 0 $0 $100 - - -
5 100 1 10 10 10 $30 $130 $6.00 $3.50 $8.00
5 100 2 25 15 12.5 $60 $160 $3.80 $2.33 $4.40
5 100 3 42 17 14 $90 $190 $3.10 $2.06 $3.33
5 100 4 57 15 14.25 $120 $220 $2.89 $2.33 $2.98
5 100 5 67 10 13.4 $150 $250 $2.99 $3.50 $2.99
5 100 6 75 8 12.5 $180 $280 $3.13 $4.38 $3.07
5 100 7 77 2 11 $210 $310 $3.51 $17.50 $3.38
Average total costs, average variable costs, marginal costsFixed cost = $20 per unit per hour Variable costs = $30 per unit per hour.
6.00
5.00
4.00
3.00
2.00
1.00
ATC
AVC
AFC
MC
0 20 40 60 80
AFC falls as fixed costs are shared between higher output. ATC, AVC and MC are all ‘u-shaped’ because MC starts to rise after diminishing returns, forcing AVC and ATC to rise.
5
Total product
MP and AP
Total costs
Average and marginal costs
Conclusion
Data
5Tuesday, 13 August 13
Assume all figures are on a ‘per-hour’ basis. i.e. 2 people, using the fixed units could produce 25 units of output per hour.
1 2 3 4 5 6 7 8 9 10 11
Fixed units
TFCVariable units
OutputMarginal Product (MP)
Average product (AP)
Total variable
cost
Total cost
Average variable
cost
Marginal cost
AverageTotal cost
5 100 0 0 0 0 $0 $100 - - -
5 100 1 10 10 10 $30 $130 $6.00 $3.50 $8.00
5 100 2 25 15 12.5 $60 $160 $3.80 $2.33 $4.40
5 100 3 42 17 14 $90 $190 $3.10 $2.06 $3.33
5 100 4 57 15 14.25 $120 $220 $2.89 $2.33 $2.98
5 100 5 67 10 13.4 $150 $250 $2.99 $3.50 $2.99
5 100 6 75 8 12.5 $180 $280 $3.13 $4.38 $3.07
5 100 7 77 2 11 $210 $310 $3.51 $17.50 $3.38
In the short run, it is not wise to keep adding units of variable factor to the fixed factor, because marginal product falls after diminishing returns set in (i.e. at 3 units of labour). This is also the point where marginal costs per unit of output are lowest ($2.33 per unit). Irrespective of the price of output, this will be the most profitable combination of fixed and variable inputs.This principle applies to all production everywhere.
Conclusion
6
Total product
MP and AP
Total costs
Average and marginal costs
Conclusion
Data
6Tuesday, 13 August 13
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