Answer:
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%
