Solow-Swan Model

The Solow-Swan model, also called the exogenous growth model, is an economics model of national production.


Formulation

Assume that production is a Cobb-Douglas function of capital investment, labor, and technology: Y = f(K,L,A), specifically Y = Kα(AL)(1-α).

Some important notes about that formulation:

The interest of the model lies in growth of production, so re-phrase as a time-dependent function: Y(t) = K(t)α(A(t)L(t))(1-α).

Capital grows as under the Harrod-Domar model: dK(t)/dt = sY(t) - δK(t).

Further assume though that labor and technology are exogenous. This is not a dynamic system for these inputs. Labor is a function of time and a growth rate n: L(t) = L(0)etn; technology is a function of time and a growth rate r: A(t) = A(0)etr.

Some important notes about that formulation:

The model can usefully be re-stated in terms of effective labor units:

model1.svg

model2.svg

That inner term of capital per effective labor units (or capital intensity) is typically written as k(t), therefore y(t) = k(t)α.

Some important notes about that formulation:

The interpretation is that capital investment will grow to a 'break-even point', and then cease growth. Therefore the key to long-term growth lies in the other productive factors, labor and technology. Since growth of the labor supply inherently has diminishing returns on production per effective labor unit (i.e., GDP per capita), the key to long-term growth per capita lies solely in technology.


History


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Economics/SolowSwanModel (last edited 2024-07-23 03:16:33 by DominicRicottone)