Reference no: EM131086474

ECON 448: Week 5-

1. The Solow Growth Model with Technical Progress

Solow model (a simple version):

y_t = Y_t/P_t = F(K_t, P_t)/P_t = F(K_t/P_t, P_t/P_t) = F(k_t, 1) = f(k_t)

(1 + n)k_t+1 = (1 - δ)k_t + sy_t

In the steady state,

k^∗/y^∗ = s/n + δ

Solow model (with technical progress):

yˆ_t = Y_t/E_tP_t = F(K_t, E_tP_t)/E_tP_t = F(K_t/E_tP_t, E_tP_t/E_tP_t) = F(k^{^}_t, 1) = f(k^_t)

(1 + n)(1 + π)k^{^}_t+1 = (1 - δ)k^_t + syˆ_t

In the steady state,

K^{^∗}/yˆ^∗ = s/n + π + δ

1. The simple Solow model and the Solow model with technical progress share the same assumption about the production function-the production function is CRS in all inputs and shows diminishing returns when one of the factors is fixed.

2. As a result, both models predict the existence of the steady state; in other words, convergence.

3. The key difference between the two is that while the former predicts the convergence of per capita income and capital, the latter predicts the convergence of per effective-labor income and capital.

4. In the Solow model with technical progress, the per capita variables grow at the rate of technical progress.

5. Hence, in the Solow model with technical progress, per capital income grow at the rate of technical progress, which is exogenously given.

6. (Growth rates) If X grows at the annual growth rate of a% and Y grows at the annual growth rate of b%, what is the annual growth rate of Z = X × Y? What about U = X/Y?

2. New Growth Theories: Human Capital and Endogenous Technical Progress

1. Define human capital. What are the similarities and differences between physical capital and human capital?

A simple growth model with human capital (n=δ=0):

y_t = k_t^α h_t^1-α

k_t+1 = k_t + sy_t

h_t+1 = h_t + qy_t

The growth rate of per capita capital:

k_t+1 - k_t/kt  = s^αq^1-α

2. Observation 1: Although there are strong diminishing returns to physical capital alone, there may be broadly constant returns to physical and human capital combined.

3. Observation 2: Complementarity between physical and human capital can matter.

4. "Endogeneity" of Technical Progress: Human capital may be deliberately invested in production of knowledge which causes future technical progress.

5. "Externalities" of Technical Progress: Investments in R&D (and in physical capital) generate positive externalities for other individuals and businesses.