Suppose you recieve your entire yearly income of 3600 in the beginning of the ye

Question

Suppose you recieve your entire yearly income of 3600 in the beginning of the
year, and then spend it evenly over the year. Also suppose you have no other
assets.
Before the income is spent, it can either be kept in money or bonds. Money yields
no interest. Bonds yield a yearly interest of 4%, but a transaction fee of 18 has
to be payed each time bonds are sold.
(a) Use the Baumol-Tobin model of money demand to calculate the optimal
way to divide your assets between money and bonds. What is your optimal
money holdings (M), as an average over the year?
(b) What is your optimal average bond holdings (B)?
(c) Suppose the interest on bonds is 9% instead. Then what is your optimal
money holdings (M)?

Explanation / Answer

N = (Yi/2C)0.5

substituting y = 3600, i = 4,c =18

we get optimal N = (3600*4/36)0.5= 20

so average money holding = Y/2N

= 3600/40

= 90

similarily calculate for i = 9

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