Macro - Topic D : The long run

SR vs MR vs LR

SR - business cycles

MR - Revert to norm

• These are dominated by shocks & policy

LR - K accumulates + tech change dominates

Very LR - tech change dominates even more

Neoclassical growth model (with tech progress)

Assume L augmenting tech progress - As tech improves it makes L more productive

Constant RtS

Diminishing returns to inputs (K / AN)

State of technology

A

Output per unit of effective L

Y / AN = F (1/AN * K , 1) → y_AN = f(K_AN)

Assume closed economy

Ignore G & T

Savings and MPC

S = 1 - MPC

I, S and Output

I = S = sY

I / AN = sY/AN

I / AN = sy_AN

i_AN = sf(K_AN)

Inflow of K per effective L (+∆k_AN)

i_AN = sf(K_AN)

Output per effective L graph

K, AN increase over time

A, N growth exogenous - but consta

K growth endogenous

Effective L

AN

Growth rate of effective Labour

Investment needed to maintain a constant level of K per unit of effective worker

(δ + g_N + g_A) k_AN

Every time period some tech wears out (at a constant rate)

Outflow of capital per effective worker (-∆k_AN)

d_AN = (δ + g_N + g_A) k_AN

Dynamics of capital

Blue line = inflows & Green line = outflows

In equilibrium K/AN ratio constant → If not at equilibrium it will converge

Model shows us countries have different per capita incomes due to varying savings rates