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why does the growth rate of output and the output per worker approximately the same in...

why does the growth rate of output and the output per worker approximately the same in the simple variant of the solow model in the long run?

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The Solow growth model states that the increase in capital investment is proportional to the growth rate for only a short period, since the ratio of capital to labor rises. On the other hand, the marginal product of capital may decline (due to diminishing returns), causing the economy to decline in the long-term. Therefore, when output, capital and labor grow in the constant rate, a steady state growth in the economy will be reached, where output per worker and capital per worker are the same.

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