A formulation of behavioral function fo human being in general by using Amartya Sen’s Capability and Agency Approach(CAA). 

KITANO, MASAKAZU (2016). 'A formulation of behavioral function fo human being in general by using Amartya Sen’s Capability and Agency Approach(CAA). ' Paper presented at the annual conference of the HDCA, Tokyo 2016.

§ Sen’s Behavioral function and formulation of 4 kind of market; goods and service, stock market, bond market and foreign assets market with exchange rate.
                                                201610、Masakazu Kitano.
I show the behavioral function of mankind which reflect A. Sen’ s capability and agency approach. I will show this at section 1 as equation [6].
Laborer’s life is heavily influenced by the market conditions such as worldwide depression caused by financial crisis and distribution of income and wealth today. The typical agency action is fight against these diseases. And so, I want to show the relation of humankind and other markets.
I offer the relations of good & service (GS) market with 3 kinds of asset markets; capital stock, national bond, and foreign assets intermediated by exchange rate (/$, etc.). To make such model, the time structure of transaction of each market is essential, but now little attention is paid for these markets.    
Section 2 define the time structure of 4 kinds of markets by using J. Hicks’s week which was offered by his “Value and Capital”(1939).
Section 3 treats capital stock market, and its speculative characteristics.
Section 4 treats money and bond market which is reformation of Hicks’ LM model.
Section 5 treats foreign asset market with foreign exchange rate.
As we already have short-term and long-term real GS market model such as Okishio’ “Accumulation”, we now have both real and monetary market model linked with A. Sen’s capability and agency approach.
1. Formulation of Sen’s CAA.
RCT(Rational Choice theoriy) formulate man’s behavior at the market as the following;
[1]  U(c1, …,cn,l)→max(c1, …, cn, l)、subject to Σpici=wl.
We will reformulate it in terms of functioning of man. Here, consumption good ci are reinterpreted from consumption goods to the time necessary to consume ci. A man’s one day is consisted by consumption hours, labor hour (l) and the other personal time such as sleep, summed up to 24 hours. Then we can reformulate [1] as [2].
[2]  U(c, l, o)→max(c, l, o)、subject to pc=wl, c+l+o=24,
where, c express the hour for consumption, and we treat it as a scalar.
Now, we define the behavior of Sen’s CAA. Sen defines a function of a man as his/her state of being and doing. We interpret the function vector b as the product of his/her activity using the entitled resources r. Then, a function b is produced by his activity of using the characteristics c of the resources r as the following:
[3]  b=f(r).
The capability set from which he can select is defined as the following.
[4]  C=C{fi(ri)}=C{F(R)}.
We specify the set of activity in a day which includes, as [2] of RCT, consumption, labor and others, and in addition Agent activity a as the following;
[5] B{C[F(R)];Info}=B(c,l,o,a; Info), subject to pc+wa=wl, c+l+o+a=24.
We furthermore specify the behavioral function of [5] as B=U(c,l,o)+γa, where γ denotes the weight of Agent action a in term of utility. Then, the optimal behavior under the concrete situation is determined as the following:
[6]  B(c,l,o,a; Info)=U(c,l,o)+γa→max(c, l, o, a), subject to pc+wa=wl, c+l+o+a=24.
    ∴ c*, l*, o*, a*.
The optimum values are depicted in Fig. 1, where the slide line shows time budget of 24 hours.
c+l+o(well being)
  24       budget constrained behavior
                 time constraint
   0         a*          24  a(Agency)
Fig. 1.  24 hours of a day are divided into time for Well-Being and for Agency.

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