Answer to Question #144601 in Macroeconomics for Zaman

Question

Consider an economy described by the equations of the
Solow-model (without technological or population growth), except that all labor income
is consumed and all other income is saved. The production function is Cobb-Douglas,
so f(k(t)) = k(t)α.
1. Write down the equation that governs capital accumulation!
2. Does this economy converge to a steady-state? If so, what is the steady state level
of k. How does that compare to the level derived in the lecture notes?
3. Is the saving rate in the economy constant? Increasing? Decreasing? What is the
intuition for that?

Answer 1

1. F(k(t)) = k(t)a

F = a

2. Yes the economy converges to a steady state because the population and capital are constant. The staedy state level is 0

3. The saving rate in the economy is constant. This is due to the onstage capital and population