econ death kill me i hate kushal

(R) output production model

Yt = A_t^g * (1- l ) (N_t)

(R) flow of new ideas

change in A_t+1 = (z)(l)(N_t)

(R) population N_t

Nt = Lyt + Lat

Lyt 

Lyt = (1 - l)(Nt)

Lat

Lat= (l)(Nt)

(R) population growth n

n = change in Nt + 1 / Nt

(R) output per person yt

yt = (At^g)(1 - l )

(R) gAt : stock of knowledge

change of At + 1/ At

• in the long run, this is proportional to the growth rate of population (n)

• gA = n in the BGP

(R) income per person

y = Nt^g

(R) long run growth rate of income per person

gy = g * n

(R) growth rate of output per capita ( change in yt +1 / yt)

change in yt +1 / yt = g * (change in At + 1 / At)

(S) output production function

Yt = AKt^a Lt^1-a

(S) output in terms of investment and (S) consumption (resource constraint)

Ct + It = Yt

(S) investment (It)

It = s * Yt

(S) consumption (Ct)

Ct = (1-s) * Yt

Kt + 1 (capital stock of next year/ capital accumulation equation)

Kt + 1 = Kt + It - dKt

change in Kt + 1 (change in capital stock between today and next year

• change in Kt + 1 = Kt + 1 - Kt

• change in Kt + 1 = sYt  - dKt

ratio of steady state gdp per worker comparing countries

y*1/y*2 = (A1/A2)^1/1-a (s1/s2)^a/1-a

investment and depreciation at steady state

sy* = dk* (investment = depreciation)

sAk*^a = dk*

(R) growth accounting equation Yt

Yt = (AKt)^g (Lyt)^1-g

(R) growth accounting for Y/L

growth rate of Y/L

Y/L = A (K/L)^a (Ly/L)^1-a

g(Y/L) = c + (alpha)(a) + (1- alpha)(b)

• use growth rate rules

(S)

finding population of the next year from the original year when there is population growth every year

N1 = N0 (1+n)

(S)

k* equation (no population growth)

k* equation (with pop growth)

k* (no pop growth) = (sA/d)^1/1-a

k* (pop growth) = (sA/n+d)^1/1-a

(S) steady state level of output (Y*)

Y* = A(k*)^a (L)^1-a

Y* = A (sA/d)^a/1-a (L)^1-a

(S) population growth n equation

Lt + 1/Lt

(S) change in capital adjusted for change in workers

change nt + 1/ nt = alpha (change in kt + 1 / kt)

(S) (growth rate of output per capita) change in yt +1/yt

alpha * change in kt + 1/kt

(S) change in the capital labor ratio

change in k = (SAkt^a -(n+d)kt)/1+n

growth rate of capital per person (kt)

change in kt +1 /kt = (sAkt^a-1 - (n+d)kt)/1 + n

(S) income per person

y* = Ak^a