The Green Solow Model

Environmental Kuznets curve (EKC)

Hypothesized inverted U-shaped relationship between missions and per capita income

The Production Function

Y = F(K, BL)

• B represents labor augmenting technological progress

• Assumptions

  1. Constant returns to scale

  2. Diminishing returns to individual inputs

• Analyze all variables relative to the effective # of workers, BL. Dividie both siders of the production function by BL

y = f(k)

Pollution Abatement

• The production of each unit of output generates pollution

• A constant fraction of output, θ, is devoted to abatement.

  • Technological progress in abatement is represented by g_A

• (1-θ) represents the fraction of output left over for consuming & saving

• Incorporating thid into the production function, in per effctive wokers terms (dividing by BL), and using the Cobb-Douglas functional form

  • Get y = (1-θ)k^⍺

θ

A constant fraction of output is devoted to abatement

g_A

Technological progress in abatement

(1-θ)

The fraction of output left ovr for consuming & saving

Abatement Production Function

y = (1 - θ)k^⍺

Capital accumulation

∆k = sy − δk

∆k

Represents the change in capital per effective worker over time

s

A fixed savings rate

δ

Capital depreciation rate

Factors that Impact capital accumulation

1. Population growth (n)

2. Technological progress (g_B)

3. Pollution Abatement (θ)

Population growth —> n

Growth in the labor force leads to less capital pr effective worker. Th capital stock is spread more thinly over a larger population.

Technological progress —> g_B

Leads to less capital per effctive worker because workers are now more efficient

Pollution abatement —> θ

The higher the fraction of output devoted to abatement, the less output is left over for saving & investment.

Capital accumulation equation (final)

∆k = s(1-θ)k^⍺ - (𝛿 + n + g_B)k

Steady State

∆k = 0

Capital accumulation stops due to diminishing returns

B

Represents labor augmenting technological progress in the production function