According to the Solow Growth Model, at the steady state:

a) Capital per worker, output per worker, and consumption per worker are constant, and so are aggregate capital (K), output (Y), and consumption (C) constant.

b) Capital per worker, output per worker, and consumption per worker are constant, and aggregate capital (K), output (Y), and consumption (C) grow at the positive rate of n.

c) Capital per worker, output per worker, and consumption per worker all grow at the rate of n, as do aggregate capital (K), output (Y), and consumption (C) grow at the rate of n.

d) Capital per worker, output per worker, and consumption per worker all grow at the rate of n, and aggregate capital (K), output (Y), and consumption (C) are constant.

According to the Solow Growth Model, if two countries are fairly similar, which country's economy will grow more quickly to reach the steady state?

a) Both countries will grow at the same rate.

b) The country with the lower capital-labor ratio.

c) The country with the higher capital-labor ratio.

d) Not enough information to answer the question.

Problem:

1. Use the model of chapter 6 to illustrate and discuss the impact of a fall in the population growth rate on the steady state level of capital per worker. Discuss intuitively the impact on $k^$, $c^$, and $y^*$. Then discuss what impact this shock has on K, C, and Y at the steady state.

According to the Solow Growth Model, at the steady state, option (a) is correct. Capital per worker, output per worker, and consumption per worker remain constant, and so do aggregate capital (K), output (Y), and consumption (C). This means that there is no further growth in these variables once the steady state is reached.

In the Solow Growth Model, if two countries are fairly similar, the country with the lower capital-labor ratio (option b) will grow more quickly to reach the steady state. This is because a lower capital-labor ratio indicates a higher potential for capital accumulation and productivity growth, leading to faster economic growth. The country with the higher capital-labor ratio is already relatively closer to its steady state, so its growth rate will be slower as it approaches the steady state equilibrium.

A fall in the population growth rate has several impacts on the steady state level of capital per worker (k∗), consumption per worker (c∗), and output per worker (y∗). Intuitively, a decrease in population growth rate leads to a decrease in the labor force growth rate. As a result, the capital-labor ratio (k) increases in the long run, leading to higher levels of capital per worker (k∗). This increase in capital per worker boosts productivity and output per worker (y∗), contributing to higher standards of living and consumption per worker (c∗) at the steady state.

The impact of this shock on aggregate capital (K), consumption (C), and output (Y) at the steady state is as follows: Since the steady state values of capital per worker, consumption per worker, and output per worker increase, the aggregate capital (K) will also increase to support the higher level of output. However, the steady state values of aggregate consumption (C) and output (Y) remain constant as they are determined by the steady state values of consumption per worker and output per worker, respectively. Therefore, the fall in population growth rate has a positive impact on the steady state levels of capital per worker, consumption per worker, and output per worker, while keeping aggregate consumption and output constant.

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