Question7 In the Romer model, if Canada and Taiwan have the same proportion of researchers and the same knowledge efficiency parameter but Canada’s population is larger, then Taiwan has a higher per capita output growth rate. Canada has a higher per capita output growth rate. Canada’s level of income is greater than Taiwan’s. Canada has higher per capita income than Taiwan. each country’s per capita output grows at the same rate. ResetMaximum marks: 1 Flag question undefined

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BlackTom AI · Accepted Answer

In this question about the Romer endogenous growth framework, we need to assess how per capita output growth is determined when two countries share the same fraction of researchers and the same knowledge efficiency parameter, but differ in population size.

Option 1: 'Taiwan has a higher per capita output growth rate.' This claim would require the model to produce a faster growth rate for Taiwan due to some country-specific factor beyond the stated ones. Since both countries have identical research intensity (same fraction of researchers) and the same knowledge efficiency parameter, there is no additional distinction given that would make Taiwan grow faster. Therefore, this option is not supported by the stated setup.

Option 2: 'Canada has a higher per capita output growth rate.' Similar logic applies here: with equal research intensity and equal efficiency, and with no other differentiating parameters affecting the growth rate, Canada should not inherently grow faster than Taiwan. This makes the option unlikely under the given conditions.

Option 3: 'Canada’s level of income is greater than Taiwan’s.' The Romer model concerns growth rates and long-run dynamics, not just level comparisons. Even if Canada starts at a higher income due to population or other factors, the question’s focus is on growth rate given the same fractions of researchers and same efficiency. Without a mechanism in the setup that makes higher income arise solely from these equal parameters, this statement is not a necessary conclusion from the information provided.

Option 4: 'Canada has higher per capita income than Taiwan.' Again, this is a cross-sectional level comparison. The model’s parameters described (same researcher fraction and same efficiency) do not by themselves imply a higher per capita income for Canada. Population differences could affect total output, but per capita income is not determined to be higher purely from the given conditions.

Option 5: 'each country’s per capita output grows at the same rate.' This aligns with the Romer framework under which the steady-state growth rate of per capita output is driven by the growth rate of ideas (knowledge) which depends on the fraction of researchers and knowledge productivity. If both countries have the same fraction of researchers and the same knowledge efficiency parameter, the induced growth rate of knowledge—and thus per capita output—will be the same, regardless of population size. Population mainly affects the scale (level) of output, not the growth rate, in this setup.

Putting this together, the only option that coherently follows from the given conditions is that the per capita output grows at the same rate in both countries. The other choices require additional assumptions or mechanisms not provided in the prompt, making them incorrect under the specified scenario.

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