Sem 1 Modern Approach to Economic Growth

Production Function

Defines the technoplgy that translates inputs into outputs.

Y = F(K,N)

If you have CRS then doubling your inputs will double your outputs.

zY = F(zK,zN). So if K and N increase by 5% z = 1.05, therefore output Y increases by 1.05.

Production function when z = 1/N

starting with: Y = F(K,N)

1/N Y = 1/N K, 1/N N =

Y/N = F(K/N, 1)

• this means that output per worker is a positive function of capital per worker.

• Can be easily written as y= f(k)

Marginal product of capital (MPK)

With each additional unit of capital, for a constant labour force, the MPK will decline.

Savings in the solow model

As savings are S = sY. If we convert to per worker:

• S/N = s(Y/N) → sy = sf(k)

• where y = f(k) and Y/N

Investment equation

I = ΔK+𝛿K

• where, Δ𝐾 = addition of investment, 𝛿K = depreciation of capital

investment needed to sustain capital per worker

(𝛿+n)k

• where, 𝛿 = rate of depreciation, n = rate of growth of labour, k = capital per worker

Savings and investment growth equation

sf(k) = (𝛿+n)

• the equation tells us that output, capital and labour grow at rate n