Question on wage rate in Ayiagari model

1

Author: s121...@sms.ed.ac.uk

Hi

I hope this is the right place to ask this maybe a little stupid question.

In the quantecon notes on the Aiyagari model I do not see how equation 3.31 is derived

(3.31) w(r) = A * (1-alpha) * (alpha/(1+r))**(alpha/(1-alpha))

No matter how I twist the algebra I arrive at

w(r) = A * (1-alpha) * ((A*alpha)/r)**(alpha/(1-alpha))

This is how I get there. From 3.30

(3.30) r = A *alpha * (N/K)**(1-alpha)

I solve for K/N as a function of r

(2) (1) K/N = ((A*alpha)/r)**(1/(1-alpha))

I substitute (1) into my FOC for wages, which is

(2) w = A * (1-alpha) * (K/N)**alpha

To get

(3) w(r) = A * (1-alpha) * ((A*alpha)/r)**(alpha/(1-alpha))

Could somebody please help me find where I go off track.

Thank you!

2

Hi Ben and apologies for the slow reply.

We are racing to finish a grant application that will help us extend the lectures and the code libraries. It’s due in very soon.

As I said in private communication, it seems you are 100% right and this needs to be fixed.

Actually I would like to combine our continuous state and discrete state work on the income fluctuation problem and then tie both in to the Aiyagari model. At the same time I’ll fix this error. These tasks are high on my to-do list and I hope to get to it very soon.

Thanks once again for your feedback. It’s most appreciated.

John.

3

Hi Ben,

We finally go around to fixing this! Thanks again for the heads up.

At the same time we added depreciation of capital, as well as a Julia version of the lecture, which you can see here:

http://quant-econ.net/jl/aiyagari.html

The fix won’t show up in the Python lecture for up to 24 hours, but the correct equations are already visible on the Julia side.

Regards, John