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2. Consider the Solow model with a production function Y(t) = AKL¹, where A is a fixed technological parameter (hint: cutting-edge growth). Draw a well-labeled graph to show how the steady-state value of the per capita capital stock and per capita income changes in response to a rise in (20 Marks) (a) the population growth rate (n) (b) the rate of saving (s), (c) 6, the depreciation rate, (d) the technological parameter A?

Question

  1. Consider the Solow model with a production function Y(t) = AKL¹, where A is a fixed technological parameter (hint: cutting-edge growth). Draw a well-labeled graph to show how the steady-state value of the per capita capital stock and per capita income changes in response to a rise in (20 Marks)

(a) the population growth rate (n)

(b) the rate of saving (s),

(c) 6, the depreciation rate,

(d) the technological parameter A?

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Solution

The Solow model is a neoclassical growth model where long-term economic growth is determined by capital, labor, and technology. In this model, Y(t) = AKL¹ represents the production function, where Y is the total output, A is the technology level, K is the capital stock, and L is the labor force.

(a) Population growth rate (n): An increase in the population growth rate would increase the labor force (L), which would lead to an increase in total output (Y). However, on a per capita basis, both the capital stock and income would decrease because the same amount of capital and income is now being spread over a larger population. This can be represented by a downward shift in the per capita capital stock and income curves on the graph.

(b) Rate of saving (s): An increase in the rate of saving would lead to an increase in the capital stock (K), as more of the income is being saved and invested. This would lead to an increase in both the per capita capital stock and income, represented by an upward shift in their respective curves on the graph.

(c) Depreciation rate (δ): An increase in the depreciation rate would decrease the capital stock (K), as more capital is being depreciated. This would lead to a decrease in both the per capita capital stock and income, represented by a downward shift in their respective curves on the graph.

(d) Technological parameter (A): An increase in the technological parameter would increase the total output (Y), as the same amount of capital and labor can now produce more output due to improved technology. This would lead to an increase in both the per capita capital stock and income, represented by an upward shift in their respective curves on the graph.

Please note that these are general effects and the actual impact may vary depending on the specific values of the parameters and the elasticity of substitution between capital and labor.

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