Question

5. (15%) Consider an economy at the long-run steady state. Population grows at rate gy and the technology grows at the rate ga. Explain how each of the flowing would affect the steady state growth rates of K/AN, Y/AN, K/N, Y/N, K, and Y Illustrate your answers with appropriate graphs. a. The government reduces the tax rate on earnings from savings. b. Technological growth declines.

Answer 1

At first derive the steady state equilibrium in long run.

with Technology Y = F(k, L times E) \\ Y/LE = F(K/LE > 1) \\ y = f(k) \\ L rightarrow labour obmented E rightarrow Efficiency \\where, y = Y/LE\\ k = k/le \\k = dk/dt = I-delta k\\ = sy-deelta k\\k/LE = s.Y/LE-delta k/LE = sy-delta k\\k/LE = sf(k) -delta k\\ Therefore k = delta k/dt\\k = 6f(k) -delta k -nk-gk\\k = dk/dt = sf(k) -(n + delta + g) k\\At study state = dk/dt = 0\\sf(k) = (n + delta + g) k
the solow growth model saving rate is the key determinant of steady state capital stock.If the saving rate is high the economy will have a large capital stock and a high level of output.If the saving rate is low the economy will have a small capital stock and a low level of output.Govt. reduces tax rate that means k rises. Now technological growth declines.The effect is shown in the diagramme.