Problem Set for Friday 3/11
Dear all,
please try to solve exercises 1-4, chapter 5 of Gregor Smith's notes. The solutions should be handed in with Simon by 11am on Friday 3/11. ( See also Jeremy's announcements on his G02 homepage. )
Andreas
posted by authe @ 8:37 AM
5 Comments:
Hi Andreas. We have quite a few questions:
Regarding question (2)-(c), what does the author means by "the relative supply of labour in period 1"? Is it n1/n2 or n2/n1? And, is a "temporary increase in wages" just an increase in w1 (but not in w2)? Then, is a"permanent increase in wages" a joint increase in w1 and w2?
Finally, regarding (3)-(b), how can we derive the elasticity of intertemporal substitution. And, what is the implication of assuming "acyclical wages" in part (d). Are they supposed to be constant or move against the direction of shocks?
Thanks a lot for your help,
Ana
Hi Andreas,
Jeremy has set us Q.14 and 15 from Smith Ch.5 to hand in this Friday. In the lecture Jeremy went through a simple example of dynamic programming, but Q.14 has both capital and labour in the utility function.
Would you be able to give us a hint on how to solve this type of problem? Do we need to treat both captial and labour as state variables?
Thanks,
Emma
a state variable is something which is predetermined at the time of the decision problem ( e.g. current capital stock, or an exogenous shock ). it describes the state of the system. the control variables are something you chose in time t to optimally move the system to it's next state. so now ask yourself: is labour in period t something which is predetermined or something which you have to chose optimally in t ? if it's something you have to chose in t it's a control variable like consumption. in this case you will have to maximize the value function with respect to both labour and consumption.
Hi Andreas,
I am finding questions 14 and 15 (due this Friday)very hard. Is there any reading you can suggest to me that would be useful for these topics apart from the notes we have been given?
Thanks
For Dynamic Programming most textbook treatments are at a 1st year PhD level. Maybe you can have a look at chapter 3 of Ljungqvist and Sargent's Recursive Macroeconomic Theory textbook.
Ex. 14 and 15 are very similar to the examples solved in chapter 5 of the script. The only difference is that now you have a second control variable, labour supply. But that does not complicate things too much. It's really just an additional first order condition, which gives you a labour supply equation just like in last week's tutorial session.
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