Econ 410 Test 2 Equations

Money supply

M = 1 / v (p)(y)

Change in capital stock

△k = (s)f(k)-𝛿k

production (Graph)

f(k)

Investment (Graph)

sf(k)

C* = Y* - i*

C* = f(k*) - 𝛿k

Golden Rule 

Max Consumption

Steady-state consumption per worker (c*) as a function of output per worker and investment per worker

c* = k* - 𝛿f(k)*

Quantity theory of money

π (inflation) = u (growth rate of money supply) - g (growth rate of real GDP)

Inflation (π) with changing money velocity =

△m + △v - △y

Growth Accounting equation

gY​=gA​+αgK​+(1−α)gL​

Law of motion

kt+1​=(1−δ)kt​+sf(kt​)

steady-state level of income per worker

Y* = f(k*)

Steady state level of saving/investment per worker

S = (savings rate)(y*)

Steady state level of consumption per worker

c* = (1 - savings rate) (y* which means income per worker)

Steady state capital stock per worker

δk* = (s)f(k)