Taro On Dynamic Optimization

I said that my resolution of this year was to write as many topics related to my research field as possible.

My intellectual research is (1) the technique of dynamic optimization and (2) the search models applied in the field of macroeconomics. Of course, I will continue to report my everyday life in this blog, too.

If you have never heard of these above topics, please let me talk about my idea on dynamic optimization briefly (The search model will be raised as a topic later in this blog):

The technique of dynamic optimization is used to get the optimal choices in the problems of intertemporal choice. What is the optimal choice? What is the meaning of the term," intertemporal choice"?

Before talking about what it means, please allow me to talk about the problems of intratemporal choices. If you reflected on your everyday life, you could encounter many problems of intratemporal choice, say, how much beef and bread you should buy in the nearest store, how long you should work today at your office and enjoy your time with your girlfriend after your work, and how many times you should kiss her and....... (Some readers may say that the number of times you kiss her is not the problem of optimization, but I don't think so. Let me think a little: The more times you kiss her, the less happier you(and she) will be than the first time you kissed her. Considering that, there must be the unique point where your satisfaction from kiss is maximal as long as your utility is strictly concave.)

Anyway, these could be the problems of optimal choice at the same point in time, that is, the problems of optimal intratemporal choice. Note that these optimal choices should be made for you to get the maximum satisfaction from these choices. We call it the maximum utility in economics. In these cases, we face some contraints on time and money available to us. So, we usually seek for the optimal choices subject to money and time constraints we face.

However, these are not the problems of "dynamic" optimal choice(but they could be made such problems like the below examples). To put it another, these are not the problems of optimal choice at the different points in time. The problems of dynamic optimal choice are how we can get the optimal intertemporal choice.

The problems of dynamic optimization is not hard to imagine in our life. You could see many problems of that choice, say, how much money you should spend on today's and on tomorrow's meal, how long you should work at your office in your life and enjoy the time with your wife(or another woman?) after your retire, and how many children you should have and so on.

Anyway, these could be the important problems of optimal intertemporal choice at the different points in time. Note that these optimal choices should also be made for you to get the maximum satisfactions from these choices at different points in time. These cases are not the same as those raised before in terms of what point in time you make an optimal choice. Of course, we face some contraints on our lifespan and the income earned in our whole life. So, we usually seek for the optimal intertemporal choices by considering our lifetime and income constraints.

In sum, the problem of intertemporal optimal choice is the extension of that of intratemporal optimal choice. In the problem of dynamic optimization, we can see different goods as goods at different points of time we enjoy.