The following table gives the total weekly output of bicycle

The following table gives the total weekly output of bicycles at Al’s Bicycle Town.

Table 1

Labor      Total Product (TP)   Average Product of labor (AP)   Marginal Product of labor (MP)

0               0                                  na                                                     na

1             100                              100                                                   100

2             300                             150                                                    50

3             450                             150                                                    0

4             1040                           260                                                   110

5             630                             126                                                  -134

6             660                            110                                                    -16

The cost of 1 worker is $2000 per month. Total fixed cost is $4000 per month.

Complete Table 2 using your answers from Table 1 and by computing total variable cost (TVC) and total cost(TC).

Table 2

Labor      Total Product (TP)   Total variable cost (TVC)   Total cost (TC)

0               0                                  na                                                  4000

1             100                              2000                                                6000

2             300                             4000                                               8000

3             450                             6000                                                 10000

4             1040                           8000                                                 12000

5             630                             10000                                               14000

6             660                             12000                                                16000

Draw the graphs of the TC and TVC curves. What is the relationship between these two curves?

Complete Table 3 by using your answers from the previous Tables and calculating the AVC, ATC, and MC.

Table 3

Total Product (TP) Average variable cost (AVC) Average total cost (ATC)   Marginal cost (MC)

               0          na                                na                     na

             100        20                                ___                    20

             300       ----                                 ___                 ___

             450       ___                               ___                ___

             1040      ___                               21.43              ___

             630        ___                                ___                ___

            660         ___                                ___              66.67

Draw the graphs of the ATC, AVC, and MC curves. What is the relationship between the ATC and AVC curves? Between the MC and AVC curves?

Suppose that Al discovers new technology that boosts the productivity of his workers, so that more bicycles can be produced than before.

Complete Table 4, which presents production data with the new technology.

Table 4

Labor      Total Product (TP)   Average Product of labor (AP)   Marginal Product of labor (MP)

0               0                                  na                                                     na

1             120                               120                                                   120

2             360                              -----                                                   ___

3             540                              ___                                                    ___

4             672                              ___                                                    ___

5             756                              ___                                                    ___

6             792                              ___                                                    ___

Al’s fixed cost remains at $4000, and he can continue to hire workers at the monthly rate of $2000.

Use the new technology data to complete Tables 5 and 6.

Table 5

Labor      Total Product (TP)   Total variable cost (TVC)   Total cost (TC)

0               0                                  na                                                    ___

1             120                              ___                                                    ___

2             360                              -----                                                   ___

3             540                              ___                                                    ___

4             672                              ___                                                    ___

5             756                              ___                                                    ___

6             792                              ___                                                    ___

Draw the ATC and MC curves you just entered in Table 5. How do the old and new ATC curves compare? The old and the new MC curves?

Table 6

Total Product (TP) Average variable cost (AVC) Average total cost (ATC)   Marginal cost (MC)

               0                na                                na                                           na

             120             ___                              ___                                        ___

             360            -----                              ___                                         ___

             540           ___                               ___                                         ___

             672            __                               ___                                         ___

             756           ___                                ___                                        ___

             792         ___                                ___                                         ___

Return to the old technology data. Suppose that the cost of Al’s fixed inputs remains the same at $4000, but the cost of labor rises. Specifically, suppose that a worker now receives $3000 per month.

Complete Table 7. For the two missing TP copy your answers from Table 1

Table 7

Labor      Total Product (TP)   Total variable cost (TVC)   Total cost (TC)

0               0                                  na                                                   4000

1             100                              3000                                                 ___

2             300                             -----                                                   ___

3             450                             ___                                                    ___

4             ___                             ___                                                    16000

5             630                             ___                                                    ___

6             ___                             18000                                                ___

In Table 8 compare the cost before and after the increase

Table 8

              Before the increase                                            After the increase

TP            ATC         MC                                                   ATC         MC

0               ___        ___                                                       ___        ___         

100            ___        ___                                                       ___        ___

300           ___        ___                                                       ___        ___

450           ___        ___                                                       ___        ___     

___           ___        ___                                                       ___        ___  

630           ___        ___                                                       ___        ___   

___          ___        ___                                                       ___        ___

Last question: how did the rise in variable costs affect the average total cost? The marginal cost?

Whenever appropriate, please use Excel to show supporting computations in an appendix, present economic information in tables, and use the data to answer follow-up questions.

Solution

Total variable cost(TVC) reflects the law of variable proportions. TVC is zero when amount of labour employed is zero but TC=TFC+TVC, so TC can not be zero even when TVC is zero as it includes TFC also.

Table 3

Total Product (TP) Average variable cost (AVC) Average total cost (ATC)   Marginal cost (MC)

               0          na                                na                     na

             100        20 60 20

             300 13.3 26.66 10

             450 13.3 22.22 13.33

             1040 7.69 11.53 3.38

             630 15.87 22.22 4.87

            660 18.181 24.24 66.67

The AVC is a part of ATC, given ATC=AFC+AVC. Both AVC and ATC are U-shaped, reflecting the law of variable proportions.

So lang as the MC lies below the AC curve, it pulls the latter downwards; when the MC rises above the AC, it pulls the latter upwards. The MC cuts the ATC and AVC at their lowest points.

Table 4

Labor      Total Product (TP)   Average Product of labor (AP)   Marginal Product of labor (MP)

0               0                                  na                                                     na

1             120                               120                                                   120

2             360 180 240

3             540 180 180

4             672                              168 132

5             756                              151.2 84

6             792                              132 36

Table 5

Labor      Total Product (TP)   Total variable cost (TVC)   Total cost (TC)

0               0                                  na                                                  4000

1             120                              2000 6000

2             360                              4000 8000

3             540                            6000 10000

4             672                           8000 12000

5             756                           10000 14000

6             792                          12000 16000

Table 6

Total Product (TP) Average variable cost (AVC) Average total cost (ATC)   Marginal cost (MC)

               0                                na                                na                                           na

             120                         16.66 50

             360                          11.11 22.22 ___

             540                        11.11 18.51 ___

             672                         11.90 17.85 ___

             756                         13.22 18.51 ___

             792                        15.15 20.20 ___