1. Many endogenous growth models feature so called scale effects: per capita growth rises when population growth rises. Some economists have criticized these models for this reason, since countries with faster population growth do not in general appear to also experience faster per capita income growth. Consider an economy that has access to a production technology Y = AKª L¹-a where Y is output, A is the level of technology, K is capital and L is the amount of labor in the economy. Capital evolves according to K = SY (thus, the depreciation rate 6 = 0). The population growth rate is n. (Throughout, gx, where x can be any of the variables in the model). i. Assume that technology is determined by A =BK What sort of endogenous growth model is this? Find gk in terms of the K, L, and other parameters of the model. ii. Write an expression for gy in terms of gk and g₁. What must be true for a balanced growth path to exist in this model? Solve for the balanced growth path value of gy and gy, where y = Y/L. What must we assume about a + in this model for there to be a positive (finite) rate of per capita income growth? How does gy vary with the rate of population growth? iii. Now assume instead that technology is determined by A = B(+). Now, what causes technology to increase? Write down an expression for *. What must be true about a + in order for K to grow continuously at a constant rate? What is the constant rate?
1. Many endogenous growth models feature so called scale effects: per capita growth rises when population growth rises. Some economists have criticized these models for this reason, since countries with faster population growth do not in general appear to also experience faster per capita income growth. Consider an economy that has access to a production technology Y = AKª L¹-a where Y is output, A is the level of technology, K is capital and L is the amount of labor in the economy. Capital evolves according to K = SY (thus, the depreciation rate 6 = 0). The population growth rate is n. (Throughout, gx, where x can be any of the variables in the model). i. Assume that technology is determined by A =BK What sort of endogenous growth model is this? Find gk in terms of the K, L, and other parameters of the model. ii. Write an expression for gy in terms of gk and g₁. What must be true for a balanced growth path to exist in this model? Solve for the balanced growth path value of gy and gy, where y = Y/L. What must we assume about a + in this model for there to be a positive (finite) rate of per capita income growth? How does gy vary with the rate of population growth? iii. Now assume instead that technology is determined by A = B(+). Now, what causes technology to increase? Write down an expression for *. What must be true about a + in order for K to grow continuously at a constant rate? What is the constant rate?
Chapter3: Scarcity, Trade-offs, And Production Possibilities
Section: Chapter Questions
Problem 11P
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Transcribed Image Text:1. Many endogenous growth models feature so called scale effects: per capita growth
rises when population growth rises. Some economists have criticized these models
for this reason, since countries with faster population growth do not in general
appear to also experience faster per capita income growth.
Consider an economy that has access to a production technology
Y = AKª L¹-a
where Y is output, A is the level of technology, K is capital and L is the amount of labor
in the economy. Capital evolves according to K = SY (thus, the depreciation rate 6 = 0).
The population growth rate is n. (Throughout, gx, where x can be any of the variables
in the model).
i. Assume that technology is determined by
A =BK
What sort of endogenous growth model is this? Find gk in terms of the K, L, and other
parameters of the model.
ii. Write an expression for gy in terms of gk and g₁. What must be true for a
balanced growth path to exist in this model? Solve for the balanced growth
path value of gy and gy, where y = Y/L. What must we assume about a + in
this model for there to be a positive (finite) rate of per capita income growth?
How does gy vary with the rate of population growth?
iii.
Now assume instead that technology is determined by A = B(+). Now, what
causes technology to increase? Write down an expression for *. What must be
true about a + in order for K to grow continuously at a constant rate? What
is the constant rate?
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