There are six groups of people each with population n(i) where i=1,2...6. I want to solve for both individual and aggregate variables, including aggregate output and tax revenue. There are many circular arguments, but the one giving me the most problem is the assumption that subsidies to the poor lowers their work effort, and thus before tax income. However, because I assume that government budgets are balanced, tax revenues depend on before tax income, but the size of the subsidy depends on tax revenues, hence a circular dependency. Initially, Excel broke down until I put the workbook in iterative mode, but works for only 9-10 time periods.

Let BTY equal before tax income, ATY equal after tax income, C(t) equal current consumption, I(ht) equal current investment in human capital, I(kt) equal current investment in capital, h(t+1) current human capital expenditures, h(t) human capital expenditures of the last period then for each household:

ATY = C(t) + I(ht) + I(kt)

I assume that

C(t) = mpc*ATY

I(ht) = mph*ATY

I(kt) = mpk*ATY

where mpc + mph + mpk = 1 and are given. Also

I(ht) = h(t+1) - (1-dh)*h(t) where dh is greater than zero but less than one.

I(kt) = k(t+1) - (1-dk)*k(t) where dk is greater than zero but less than one.

also K is the capital stock which equals k(t+1) plus the sum of all non-depreciated capital.

Likewise H is human capital stock which equals h(t+1) plus the sum of all non-depreciated human capital.

BTY is given by potential earnings (W) (which is given) and is reduced by a factor e times the subsidy s. So

BTY = W - e*s

the subsidy for each lower income group is given by

Total Tax Revenue*population share of the revenue/population of the lower income group.

The model is further complicated by the assumptions that consumption has a minimum expenditures requirement and satiation point. Also, both h(t+1) and H have satiation points, this creates long strings of if and then statements, which I have been able to shorten by creating new unsatiated intermediate variables. There is also a capital tax which reduces capital stock formation. However, I get around this circular problem by assuming that the wealth tax does not reduce work effort and that the proportion of the tax avoided goes to increase consumption and human capital accumulation as long as those variables are not satiated. However, I pretty much have to set up a second round of calculations which adds a few more tables to my program.

My general setup is to have a long table that first calculates each households BTY, ATY and subsidies. I then make long tables of my human capital accumulation, consumption expenditures, then capital accumulation. Because a certain percentage of the capital expenditures is avoided by the household, a second round of tables consisting of final human capital calculations, final consumption calculations, and what's left over goes back into final capital expenditures.

Is there a more efficient program setup? I've heard about the matrix option on excel. Would that work and how would that work? Or does the description of my program makes you believe that Matlab or another program may be more appropriate?