What is the Solow model in continuous time?
-So far, time was divided into discrete periods
-It is often more convenient to shrink the length of periods to 0
-Difference equations then become differential equations
Law of motion for capital
Any time period:
Discrete time:
Change in stock = flow x duration
Continuous time:
Growth rate in continuous time
What are Differential equations?
What happens to capital per worker? What computations do we need to do?
This is equal to asking: What is the derivative of k relative to time. Taking the derivative with respect to time can be hard
-> Instead, taking the derivative of the log could be much easier
Take logs
Take derivatives
How does the Solow Equation look like in Continous time?
Logarithmic derivative
Last changeda year ago
