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Econ Exam 2 Cheat Sheet (DRAFT) by

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

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
Per Worker Production Function
y= Akα
Capital Stock Accumu­lation
K= I-δK
Capital Per Worker Accumu­lation
Steady­-State Equili­brium
k= 0 -> sf(k)=(n+δ)k