A financial analyst is comparing two countries, 'Agraria' and 'Industria,' using the Solow Growth Model without technological progress. Both countries have the same aggregate production function, savings rate, and depreciation rate. Agraria has a lower capital-to-labor ratio than Industria. Which of the following is the most accurate prediction regarding their steady states and growth rates according to this model?
- ABoth countries will converge to the same steady-state capital-to-labor ratio, but Agraria will have a higher growth rate of output per capita in the short run.
- BAgraria will have a higher steady-state capital-to-labor ratio and a higher growth rate of output per capita than Industria.
- CIndustria will have a higher steady-state capital-to-labor ratio, and both countries will eventually have the same growth rate of output per capita.
- DBoth countries will converge to different steady-state capital-to-labor ratios, and Agraria will have a lower growth rate of output per capita in the short run.
Show answer & explanationAnswer & explanation
Correct answer: A. Both countries will converge to the same steady-state capital-to-labor ratio, but Agraria will have a higher growth rate of output per capita in the short run.
In the basic Solow model without technological progress, countries with the same production function, savings rate, and depreciation rate will converge to the same steady-state capital-to-labor ratio. Since Agraria starts with a lower capital-to-labor ratio, it is further from the steady state and will thus experience a higher growth rate of output per capita in the short run as it accumulates capital faster to catch up to the steady state.
Why the other options are wrong
- B. Agraria will not have a higher steady-state capital-to-labor ratio; they converge to the same one. It will have a higher *short-run* growth rate.
- C. Industria will not have a higher steady-state capital-to-labor ratio; they converge to the same one. While both eventually have zero growth *at* steady state in this basic model, Agraria will grow faster *towards* it.
- D. They converge to the same steady state. Agraria, starting from a lower capital base, will have a higher marginal product of capital and thus a higher growth rate in the short run.
Solow Model (Convergence)
The basic Solow Growth Model predicts that economies with similar parameters (production function, savings, depreciation) will converge to the same steady-state capital-to-labor ratio, with poorer countries (lower capital-to-labor ratio) growing faster in the short run.
- Assumes exogenous technological progress (or none, as in this question).
- Predicts conditional convergence: countries with similar fundamentals converge.
- Poorer countries grow faster if they are further below their steady state.
- Steady state is where investment equals depreciation.
- Long-run growth rate of output per capita is zero without technological progress.
Memory trick: Same rules, same end; starting low means faster ascend.