# 6. Appendix¶

## 6.1. NTA Variables in MicroWELT:¶

```- Private Consumption Education (CFE)
- Private Consumption Health (CFH)
- Private Consumption other than Education and Health (CFX)
- Public Consumption Education (CGE)
- Public Consumption Health (CGH)
- Public Consumption other than Education and Health (CGX)
- Public Transfers Pensions, Inflows (TGSOAI)
- Public Transfers Other Cash Inflows (TGXCI)
- Public Transfers Other In-Kind Inflows (TGXII)
- Public Transfers Education Inflows (TGEI)
- Public Transfers Health Inflows (TGHI)
- Public Transfers Outflows (TGO)
- Net Interhousehold Transfers (TFB)
- Net Intrahousehold Transfers (TFW)
- Private Saving (SF)
- Public Saving (SG)
- Labor Income (LY)
- Private Asset Income (YAF)
- Public Asset Income (YAG)
```

## 6.2. Calculation of the Support Ratio and the Impact Index for a closed economy:¶

```Variables:

- yl(x)    Average labor income age x
- yk(x)    Average capital income age x
- P(x)     Population age x
- i(x)     Average savings age x
- s(x)     Saving rate age x - constant
- c(x)     Average Consumption age x (reference values for calculation of N) - reference
- L        Labor
- K        Capital
- I        Saving
- S        Saving rate
- C        Consumption
- r        Interest rate
- w        Wage
- Yl       Labor Income
- YK       Capital Income
- Y        Total Income Yl+Yk
- α        Alpha – constant
- N        Effective Consumers (population-weighted base-year consumption)
- l(x)     Average labor age x – constant
- k(x)     Average capital age x – constant

Cobb Douglas production function:

- Y = L^α K^(1- α)
- Y = wL + rK
- w = αY / L
- r = (1- α) Y / K
- Yl = wL = αY
- Yk = rK = (1- α)Y

Known:

- yl(x)    NTA data of reference year
- yk(x)    NTA data of reference year
- i(x)     NTA data of reference year
- c(x)     NTA data of reference year
- P(x)     NTA data of reference year
- r        parameter for reference year (used also to estimate stock from capital income flow)

Calculated for initial year:

- Yl   = ∑ yl(x) * P(x)
- Yk   = ∑ yk(x) * P(x)
- Y    = Yl + Yk
- α    = Yl / Y
- K    = Yk / r
- L    = ( Y / K^(1- α))^(1/α)
- w    = Yl / L
- s(x) = i(x) / (yl(x) + ykx))
- l(x) = yl (x) / w
- k(x) = yk (x) / r
- N    = ∑ cl(x) * P(x)

Simulation: calculate for an updated population by age P(x)

- L     = ∑ l(x)* P(x)
- K     = ∑ k(x)* P(x)
- Y     = L^α K^(1- α)
- Yl    = αY
- YK    = (1- α)Y
- w     = αY / L
- r     = (1- α) Y / K
- N     = ∑ c(x) * P(x)
- yl(x) = w * l(x)
- yk(x) = r * k(x)
- C     = ∑ (1-s(x)) * (yl(x) + yk(x) ) * P(x)

Indices

- SR    = L / N  	Support Ratio
- IMP   = C / N  	Impact Index
```