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Consider the hypothetical economies of Thalassa and Svarta

4. The catch-up effect

Consider the hypothetical economies of Thalassa and Svarta, both of which produce cases of argo using only workers and tools. Suppose that, during the course of 35 years, the level of physical capital per worker rises by 5 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 2022 and 2057.

YearThalassa
Physical CapitalLabor ForceOutputProductivity
(Tools per worker)(Workers)(Cases of argo)(Cases per worker)
202216603,60060
205721604,32072
YearSvarta
Physical CapitalLabor ForceOutputProductivity
(Tools per worker)(Workers)(Cases of argo)(Cases per worker)
202213601,80030
205718603,24054
Explanation:
In 2022, there are 16 tools for each worker in Thalassa. You can compute productivity in the following way:
Output per Worker
 = Output with 16 Tools per Worker / Number of Workers
                               = 3,600 cases of argo / 60 = 60 Cases per worker
In 2057, capital per worker rises to 21 tools per worker, and output per worker rises to 72 cases per worker (4,320 cases of argo / 60). In Thalassa, a 5-unit change in capital per worker causes output per worker to rise by 12 cases per worker.
Similarly, in 2022, there are 13 tools for each worker in Svarta, and output per worker is 30 cases of argo per worker (1,800 cases of argo / 60). In 2057, capital per worker rises to 18 tools per worker, and Svarta's output per worker rises to 54 cases per worker (3,240 cases of argo / 60). In Svarta, a 5-unit change in capital per worker causes output per worker to rise by 24 cases per worker.

Initially, the number of tools per worker was higher in Thalassa than in Svarta. From 2022 to 2057, capital per worker rises by 5 units in each country. The 5-unit change in capital per worker causes productivity in Thalassa to rise by a smaller   amount than productivity in Svarta. This illustrates the  catch-up   effect.

Explanation:
The disparity in the growth of productivity reflects the fact that capital is subject to diminishing returns (that is, the increase in output generated by an increase in capital is less than the increase in output generated by previous increases in capital). In Svarta, where workers have relatively few tools to work with, additional tools substantially increase productivity. In Thalassa, workers already have a relatively large quantity of tools to work with, so adding more tools results in more modest productivity growth.
This hypothetical example illustrates a real-world phenomenon known as the catch-up effect. The catch-up effect is when higher productivity growth in countries with less capital per person helps those countries grow faster and catch up to the per-capita incomes of countries with more capital per person.

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