If country X has a higher capital per person than country Y, then ________.

Question

BlackTom AI · Accepted Answer

When comparing per-person income across countries, a higher capital stock per person can support more output, but long-run prosperity is fundamentally tied to productivity, particularly total factor productivity (TFP).
Option 1: 'country X is richer than country Y' This ignores the given premise (X has higher capital per person) and makes a claim about overall wealth without addressing productivity or realized income differences. Capital per person alone does not guarantee X is richer; Y could be more productive and thus catch up or exceed X in income.
Option 2: 'the only way for country X to be richer than country Y is if X is just as productive (has the same TFP) as Y' This statement is too restrictive. If X already has more capital per person, X could be richer even with higher TFP in Y, or even with higher or lower TFP, depending on how capital and productivity interact in output; equality of TFP is not a necessary condition for X to be richer.
Option 3: 'the only way for country Y to be richer than country X is if Y is more productive (has a higher TFP) than X' This aligns with the idea that, holding capital per person constant, a country with higher productivity will produce more output per worker, potentially making Y richer than X despite differences in capital; higher TFP can offset or amplify capital differences and determine relative per-capita income.
Option 4: 'the only way for country X to be richer than country Y is if X is less productive (has a lower TFP) than Y' This is inconsistent with standard growth accounting: being richer would, if anything, require equal or higher productivity, not lower, given capital per person is already higher in X. It suggests a contradiction between higher capital and lower productivity.
Option 5: 'none of the above' This would be selected only if none of the previous statements captured the plausible link between capital per person and relative wealth via productivity, but option 3 presents a coherent and commonly understood mechanism linking higher per-capita output to relative wealth through TFP.
In summary, the statements hinge on the relationship between capital per person, productivity, and relative wealth. The option describing that a country Y could be richer only if Y has higher TFP than X properly reflects how productivity differences drive per-capita income when capital per person differs across countries. The other options either misstate the relationship, rely on overly strict conditions, or contradict core growth accounting intuitions.

If country X has a higher capital per person than country Y, then ________.单项选择题

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