This is a draft cheat sheet. It is a work in progress and is not finished yet.
Basic Cobb-Douglas Production Function
Key Properties |
Marginal Product of Capital |
Marginal Product of Labor |
-Constant Returns to Scale |
MPK=Partial derivate of F(K,N) |
MPN=Partial derivate of F(K,N) |
-If inputs are 0 outputs will be 0 |
MPK= Aα(K/N)^α-1 |
MPK= A(1-α)(K/N)^α |
-The production function is increaseing in each of the inputs |
α(Y/K) > 0 |
(1-α)(Y/K) > 0 |
-The production function exhibits diminishing returns |
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Neg Impact of Aging LAbor Force
-Rapid retirement decreases the firms overall knowledge, decreasing productivity. |
-Productivity peaks at age 50 |
Growth Rate of GDP
Y= (Y/N) * N |
then take logs |
lnY = ln[Y/N] +lnN |
Differentiate for time |
Y◦/Y = (Y◦/N)/(Y/N) +N◦/N |
Growth rate of GDP equals the growth rate of labor productivity and the growth rate of labor stock
Solow Growth Model Basics
Aggregate Production Function |
Y=AKαN1-α |
Per Worker Production Function |
y= Akα |
Capital Stock Accumulation |
K◦= I-δK |
Capital Per Worker Accumulation |
k◦ =sf(k)-(n+δ)k |
Steady-State Equilibrium |
k◦= 0 -> sf(k)=(n+δ)k |
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