Consider the economies of Hermes and Gribinez, both of which produce glops of gloop using only tools and workers. Suppose that, during the course of 50 years, the level of physical capital per worker rises by 4 tools per worker in each economy, but the size of each labor force remains the same. Complete the following tables by entering productivity (in terms of output per worker) for each economy in 2016 and 2036.Year HermesPhysical Capital Labor Force Output Productivity(Tools per worker) (Workers) (Glops of gloop) (Glops per worker)2016 7 30 3,000 2036 11 30 3,600 Year GribinezPhysical Capital Labor Force Output Productivity(Tools per worker) (Workers) (Glops of gloop) (Glops per worker)2016 4 30 2,400 2036 8 30 3,600 Initially, the number of tools per worker was higher in Hermes than in Gribinez. From 2016 to 2036, capital per worker rises by 4 units in each country. The 4-unit change in capital per worker causes productivity in Hermes to rise by a amount than productivity in Gribinez. This illustrates the effect.

The productivity growth rate for Hermes is 20%.

The productivity growth rate for Gribinez is 40%.

There is higher productivity growth rate in the poorer economies  as compared to the wealthier or more robust economies. As a result,, their productivity converge with richer economies after a certain time period.

Explanation:

From the question the economies of Hermes and Gribinez are given. Both the economies are producing glops of gloop using only workers and tools. Over the period of 50 years the number of tools per worker rises by 4 units, although the number of workers employed remain same.

The table given below shows the amount of workers and tools employed and the output produced for the economy Hermes:

Year     Physical capital   Labor force (workers)   Output (glops of gloop)

              (tools per worker)

2016                 7                            30                                3000

2036               11                             30                                3600

Productivity (2016) = Output / labour force

                               = 3000 / 30

                              = 100

In 2016 productivity per worker 100 units

Productivity (2036) = Output / labour force

                               = 3600 / 30

                              = 120

In 2036 productivity per worker 120 units

Year        Physical capital        Labor force       Output                  Productivity

            (tools per worker)    (workers)    (glops of gloop)     (output per worker)

2016                 7                            30                       3000                      100

2036               11                             30                      3600                       120

Now, if we see the the amount of workers and tools employed and the output produced for the economy Gribinez, the number of tools was initially lower as compared to Hermes. But the output generated in the year 2036 is same for both the economies.

Year     Physical capital   Labor force (workers)   Output (glops of gloop)

              (tools per worker)

2016                 4                           30                                2400

2036               8                             30                                3600

Productivity (2016) = Output / labour force

                               = 2400 / 30

                              = 80

In 2016 productivity per worker 80 units

Productivity (2036) = Output / labour force

                               = 3600 / 30

                              = 120

In 2036 productivity per worker 120 units

Year        Physical capital        Labor force       Output                  Productivity

            (tools per worker)    (workers)    (glops of gloop)     (output per worker)

2016                 4                           30                       2400                      80

2036               8                            30                      3600                       120

Both Hermes and Gribinez have same productivity level in the year 2036, even though tools per worker was higher in Hermes. This shows the catch up effect or the idea of convergence. Because of the diminishing marginal returns on input involved in production, the poorer economies are able to catch up with the wealthier economies.

Calculating productivity growth rate for both the economies.

Productivity growth rate for Hermes = Change in productivity/initial productivity level*100

= 120 - 100 / 100 x 100

=20 /100 x 100

= 20%

Productivity growth rate for Gribinez = Change in productivity/initial productivity level*100

= 120 - 80 / 100 x 100

=40 /100 x 100

= 40%