EconDev Midterm - Classic Theories

Y

national output/income - variable

K

capital stock - variable

S

savings - variable

I

investment (into capital) - variable

c

capital-output ratio - parameter

δ

capital depreciation rate - parameter

s

saving rate - variable

Y= 1/c*K

output depends linearly on capital alone, c>0 (assumption)

S=I

All investment is from savings and all savings are invested (assumption).

S = sY

Total savings are a fixed share of national income (assumption)

∆K = I − δK

amount of new capital is investment minus depreciation

Harrod-Domar growth equation

∆Y/Y = s/c − δ

Y_t

national output/income - variable

K_t

capital stock -variable

L_t

labor - variable

S_t

savings - variable

I_t

Investment (into capital) -variable

F (.,,)

technology - parameter

δ

capital depreciation rate - parameter

n

population growth rate - parameter

s

savings rate - parameter

Y_t = F_t(K_t , L_t)

Output depends on labor and capital - assumption

F(γK, γL) = γF(K, L)

Production exhibits constant returns to scale - assumption

d² F (K,L) /dK² < 0 and d² F (K,L) /dL² < 0

Diminishing returns to each input - assumption

I_t = S_t

All investment is from savings and all savings are invested - assumption

S_t = sY_t

Total savings are a fixed share of output - assumption

K_t+1 = I_t + (1- δ) K_t

in the next period, capital is investment and remaining capital - assumption

L_t+1 = (1+n)L_t

population of workers grows at a fixed rate - assumption

Solow equation

∆k_t = sf(k_t) − (n + δ)k_t

Solow equation for steady state

sf(k_t) = (n + δ)k_t