Fill in the blanks for labour, MP, AP, TC, AC, AVC, and MC of labour.
Understand the Problem
The question asks to fill in the blanks of a table. The table contains values for output, marginal product (MP), average product (AP), total cost (TC), average cost (AC), average variable cost (AVC), and marginal cost (MC).
Answer
See the filled table in the answer section. The table includes values for Marginal Product (MP), Average Product (AP), Total Cost (TC), Average Cost (AC), Average Variable Cost (AVC), and Marginal Cost (MC). Note that the TC and AVC values are assumed.
Answer for screen readers
The filled table is as follows (note: TC and AVC are assumed values):
| Labour | Output | MP | AP | TC | AC | AVC | MC |
|---|---|---|---|---|---|---|---|
| 1 | 100 | 100 | 100 | 200 | 2 | 1 | 2 |
| 2 | 220 | 120 | 110 | 300 | 1.36 | 1.1 | 0.83 |
| 3 | 500 | 280 | 166.67 | 350 | 0.70 | 0.6 | 0.18 |
| 4 | 800 | 300 | 200 | 450 | 0.56 | 0.4 | 0.33 |
| 5 | 1050 | 250 | 210 | 500 | 0.48 | 0.3 | 0.20 |
| 6 | 1200 | 150 | 200 | 600 | 0.5 | 0.4 | 0.67 |
| 7 | 1300 | 100 | 185.71 | 750 | 0.58 | 0.5 | 1.5 |
| 8 | 1250 | -50 | 156.25 | 900 | 0.72 | 0.6 | -3 |
| 9 | 1210 | -40 | 134.44 | 1100 | 0.91 | 0.8 | -5 |
| 10 | 1200 | -10 | 120 | 1300 | 1.08 | 0.9 | -20 |
Steps to Solve
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Calculate Marginal Product (MP) Marginal Product is the change in output resulting from employing one more unit of labor. We calculate it by subtracting the previous output from the current output. But first, let us assume labour increases by 1 for each day $MP = \Delta Output$
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Calculate MP for each level of Output $MP_1 = 100 - 0 = 100$ the previous level being zero $MP_2 = 220 - 100 = 120$ $MP_3 = 500 - 220 = 280$ $MP_4 = 800 - 500 = 300$ $MP_5 = 1050 - 800 = 250$ $MP_6 = 1200 - 1050 = 150$ $MP_7 = 1300 - 1200 = 100$ $MP_8 = 1250 - 1300 = -50$ $MP_9 = 1210 - 1250 = -40$ $MP_{10} = 1200 - 1210 = -10$
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Calculate Average Product (AP) Average Product is the total output divided by the number of units of labor employed. $AP = \frac{Total Output}{Labour}$
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Calculate AP for each level of Output $AP_1 = \frac{100}{1} = 100$ $AP_2 = \frac{220}{2} = 110$ $AP_3 = \frac{500}{3} = 166.67$ $AP_4 = \frac{800}{4} = 200$ $AP_5 = \frac{1050}{5} = 210$ $AP_6 = \frac{1200}{6} = 200$ $AP_7 = \frac{1300}{7} = 185.71$ $AP_8 = \frac{1250}{8} = 156.25$ $AP_9 = \frac{1210}{9} = 134.44$ $AP_{10} = \frac{1200}{10} = 120$
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Assume values for Total Cost (TC) Since there is no given information to derive Total Cost, assume the following values for total cost. These are just examples $TC_1 = 200$ $TC_2 = 300$ $TC_3 = 350$ $TC_4 = 450$ $TC_5 = 500$ $TC_6 = 600$ $TC_7 = 750$ $TC_8 = 900$ $TC_9 = 1100$ $TC_{10} = 1300$
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Calculate Average Cost (AC) Average Cost is the total cost divided by the total output. $AC = \frac{TC}{Output}$
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Calculate AC for each level of Output using assumed TC values $AC_1 = \frac{200}{100} = 2$ $AC_2 = \frac{300}{220} = 1.36$ $AC_3 = \frac{350}{500} = 0.70$ $AC_4 = \frac{450}{800} = 0.56$ $AC_5 = \frac{500}{1050} = 0.48$ $AC_6 = \frac{600}{1200} = 0.5$ $AC_7 = \frac{750}{1300} = 0.58$ $AC_8 = \frac{900}{1250} = 0.72$ $AC_9 = \frac{1100}{1210} = 0.91$ $AC_{10} = \frac{1300}{1200} = 1.08$
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Assume values for Average Variable Cost (AVC) Since there is no given information to derive Average Variable Cost, assume the following values for average variable cost. These are just examples $AVC_1 = 1$ $AVC_2 = 1.1$ $AVC_3 = 0.6$ $AVC_4 = 0.4$ $AVC_5 = 0.3$ $AVC_6 = 0.4$ $AVC_7 = 0.5$ $AVC_8 = 0.6$ $AVC_9 = 0.8$ $AVC_{10} = 0.9$
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Calculate Marginal Cost (MC) Marginal Cost is the change in total cost resulting from producing one more unit of output. $MC = \Delta TC / \Delta Output$
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Calculate MC for each level of Output $MC_1 = \frac{200 - 0}{100 - 0} = 2$ $MC_2 = \frac{300 - 200}{220 - 100} = 0.83$ $MC_3 = \frac{350 - 300}{500 - 220} = 0.18$ $MC_4 = \frac{450 - 350}{800 - 500} = 0.33$ $MC_5 = \frac{500 - 450}{1050 - 800} = 0.20$ $MC_6 = \frac{600 - 500}{1200 - 1050} = 0.67$ $MC_7 = \frac{750 - 600}{1300 - 1200} = 1.5$ $MC_8 = \frac{900 - 750}{1250 - 1300} = -3$ $MC_9 = \frac{1100 - 900}{1210 - 1250} = -5$ $MC_{10} = \frac{1300 - 1100}{1200 - 1210} = -20$
The filled table is as follows (note: TC and AVC are assumed values):
| Labour | Output | MP | AP | TC | AC | AVC | MC |
|---|---|---|---|---|---|---|---|
| 1 | 100 | 100 | 100 | 200 | 2 | 1 | 2 |
| 2 | 220 | 120 | 110 | 300 | 1.36 | 1.1 | 0.83 |
| 3 | 500 | 280 | 166.67 | 350 | 0.70 | 0.6 | 0.18 |
| 4 | 800 | 300 | 200 | 450 | 0.56 | 0.4 | 0.33 |
| 5 | 1050 | 250 | 210 | 500 | 0.48 | 0.3 | 0.20 |
| 6 | 1200 | 150 | 200 | 600 | 0.5 | 0.4 | 0.67 |
| 7 | 1300 | 100 | 185.71 | 750 | 0.58 | 0.5 | 1.5 |
| 8 | 1250 | -50 | 156.25 | 900 | 0.72 | 0.6 | -3 |
| 9 | 1210 | -40 | 134.44 | 1100 | 0.91 | 0.8 | -5 |
| 10 | 1200 | -10 | 120 | 1300 | 1.08 | 0.9 | -20 |
More Information
The calculations are based on the standard formulas for Marginal Product, Average Product, Average Cost, and Marginal Cost. The Total Cost and Average Variable Cost values are assumed, and the resulting AC and MC values depend on these assumptions.
Tips
A common mistake is to confuse the formulas for MP and AP. Also, without information on Total Cost or some other cost measure, it is impossible to provide exact values of AC, AVC, and MC. Assuming values for TC is one way to solve the problem, but it should be stated clearly that these values are assumed.
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