Suppose that a country has no growth in technology and that capital and labor hours are growing at the same rate. The capital in the country continues to grow at its previous rate while technology growth is still zero, but growth in labor hours falls to half its previous rate. What happens to growth in real GDP per hour of work?Growth rate of real GDP per hour of work = %

The question seems to be referring to the Solow growth model, which is a standard model in economics to understand growth in an economy. The model suggests that in the long run, growth in real GDP per hour of work (or labor productivity) is driven by technological progress.

In the scenario you've described, there is no growth in technology, so that factor is not contributing to growth in real GDP per hour of work.

The growth in capital is continuing at its previous rate, but the growth in labor hours is falling to half its previous rate. This means that the amount of capital per worker (capital intensity) is increasing, which should increase labor productivity, all else being equal.

However, the Solow model also suggests that as capital intensity increases, the additional amount of output produced by each additional unit of capital decreases (this is known as diminishing returns to capital). So, while the increase in capital intensity should increase labor productivity, the effect will be less and less the more capital intensive the economy becomes.

In conclusion, the growth in real GDP per hour of work should increase due to the increase in capital intensity, but the rate of increase will likely be less than the rate of increase in capital because of diminishing returns to capital. The exact percentage increase in the growth rate of real GDP per hour of work would depend on the specific numbers involved.

The growth rate of real GDP per hour of work in this scenario would likely decrease. This is because while the amount of capital is still increasing, the growth in labor hours is now only half of what it was before.

Here's a step-by-step breakdown:

1. Initially, both capital and labor hours are growing at the same rate. This means that the ratio of capital to labor is constant, and so is the output per hour of work (real GDP per hour of work).

2. When the growth in labor hours falls to half its previous rate, but the capital continues to grow at its previous rate, the ratio of capital to labor increases. This means that there is more capital per worker.

3. However, because there is no growth in technology, the extra capital per worker does not lead to a proportionate increase in output per worker. This is due to the law of diminishing returns, which states that after a certain point, adding more of one factor of production, while holding all others constant, will result in smaller and smaller additions to output.

4. Therefore, even though there is more capital per worker, the growth rate of real GDP per hour of work will decrease.

The exact percentage change in the growth rate of real GDP per hour of work would depend on the specific rates of growth in capital and labor hours, as well as the production function of the economy.