Question 1: In each state, how many stable steady states are there?. Question 2: In each state, which points are stable steady states? : Question 3: Explain each state. State (a): Two stable steady-states State (b): Fragile economic booms followed by stagnation trap Even in this case, economy may fluctuate forever. kM k ke k k State (c): Economy can bounce around infinitely between k' and k" without converging. State (d): Animal spirits play an important role when economic activity is stagnant. K+14 k+14 State (c): Economy can bounce around infinitely between k' and k" without converging. State (d): Animal spirits play an important role when economic activity is stagnant. kM. k k k Question 4: Consider the function N(k+1) = "*1, where s, = s(r:+1) = s(r(k+1)). St Differentiate the function N(k+1) with respect with k+1, and express the result using dlog(st) dlog(1+rt+1) -and dlog(1+rt+1) dlog(kt+1)

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Steady State: It represents the long-run equilibrium in the economy. According to the steady-state, the level variables such as capital and output grow at constant rates and the ratios among these key variables are stable. Steady-state is the point that shows that regardless of the level of capital an economy starts off with, it always converges to its steady-state of capital.

Stable Steady State:  A stable steady state is one where:

• if the economy is not at the steady-state, it will return to it
• if the economy is at the steady-state, it will remain there.

In all 4 cases:

• The dotted line represents the break-even investment line. The break-even investment line shows how much flow of new capital per unit of effective labour is required to keep the existing capital stock to an efficient labour ratio constant. it is a linear curve.
• The Blue coloured curve shows the actual investments per worker.

For a stable steady-state:

• Whenever the amount of new investment per effective worker (on BLUE curve) exceeds the amount required for breakeven (on the dotted line), k increases till k=k*
• Whenever the amount of new investment per effective worker falls short of the amount required for breakeven, k decreases till k=k*
• At k* the amount of new investment per effect worker exactly balances the required amount for breakeven investment, so k is stable.