ECON 3133: Chapter 6

Long-Run Economic Growth

basline assumption Solow growth model

y = f(k) because the labor force L is assumed to be constant. therefore, k changes because the capital stock K changes

saving per worker formula

sy

investment per worker formula

i = sy or i = sf(k)

consumption per worker formula

c = (1-s)y

depreciation rate

d, the rate at which capital stock declines by wearing out through use or becoming obsolete

depreciation in capital per worker

dk

steady-state equation

Δk = i - dk = 0, or sf(k*) = dk*, i.e., investments increase capital per worker and depreciation decrease capital per worker, offsetting each other. assumes k = k*, y = f(k*) = y*, K is constant and Y is constant

stock variable

measured at a specific point in time and represents an accumulated amount. capital per worker k is an example

flow variable

measured over a period of time and represents changes during that period. investment per worker i and depreciation dk are examples

law of motion for capital per worker

Δk = sf(k) - dk

capital worker increases

sf(k) > dk, Δk > 0

capital worker decreases

sf(k) < dk, Δk < 0

capital per worker is constant at k*

sf(k) = dk, Δk = 0

what the Solow growth model predicts

a higher saving rate is associated with a higher steady-state level of 𝑦 and thereof RGDP per capita.

break-even investment

amt of investment required to exactly offset depreciation and dilution

break-even investment formula

$$\left(d+n\right)k$$

law of motion for k with labor-force growth formula

∆k = i - (d+n)k = sf(k) - (d+n)k

steady-state of k with labor-force growth formula

actual investment equals break-even investment; sf(k*) = (d+n)k*