Final answer:
In the Solow model with constant productivity, the economy is destined to reach a steady state where the capital-labor ratio stabilizes, and economic growth halts without technological improvements.
Step-by-step explanation:
In the Solow model, if productivity does not change, then the economy must eventually reach a steady state. This is characterized by a stable capital-labor ratio where all investment is just enough to cover depreciation, and the economy essentially stops growing. In the long run, as productivity, which measures how much output can be produced with a given quantity of labor, remains constant, the continuous investment of savings leads to a point where the amount of capital per worker becomes constant, and so does the output per worker. Thus, the correct answer is option c., 'the economy must eventually reach a steady state.'
It's important to note that this conclusion is drawn from the assumption that there are no continual improvements in technology, which would otherwise shift the production function upward and could potentially lead to capital deepening or other changes in the long run. In practice, technological advances play a key role in continuous economic growth by offsetting the effects of diminishing returns to capital investment.