*Businesstopia*, January 12, 2018, https://www.businesstopia.net/economics/macro/second-fiscal-model-and-equilibrium-level-income-output.

The second fiscal model differs from the first model in that it takes into consideration the transfer payments made by the government to individuals. Although the second model assumes that government makes transfer payments, they are assumed to be autonomous, which means they are not affected by the individual’s level of income.

Thus, the assumption of government transfer payments in the second fiscal model can be expressed as

R= R_{0}

Where, R= Transfer payments

R_{0}= Fixed or given value of R

The assumptions made in the first fiscal model are followed in the second fiscal model as well. This means that the second fiscal model also assumes government purchases expenditure is autonomous (G= G_{0}), taxes are autonomous (T=T_{0}), and business investment is autonomous (I= I_{0}). The consumption of household depends on their level of disposable income.

### Equilibrium Level of Income/Output: Equations

Considering the assumptions of the model, the equilibrium level of income can be derived with aggregate expenditure and actual output/income. Symbolically,

Y= AE

Substituting AE with the components,

Y= C + I + G

Or, Y= C_{a} + λY_{D} + I_{a} + G_{a}

Or, Y= C_{a} + λ (Y – T_{n}) + I_{a} + G_{a} [T_{n} is the net tax]

Or, Y= C_{a} + λ [Y – (T – R) + I_{a} + G_{a}] [T is the gross tax]

Or, Y= C_{a} + λ [Y – (T_{a} – R_{a}) + I_{a} + G_{a}] [Taxes and Transfer payments are autonomous]

Or, Y= C_{a} + λY – λT_{a} + λR_{a} + I_{a} + G_{a}

Or, Y – λY= C_{a} – λT_{a} + λR_{a} + I_{a} + G_{a}

Or, Y (1-λ) = C_{a} – λT_{a} + λR_{a} + G_{a}

So, the final equilibrium income is

*Businesstopia*, January 12, 2018, https://www.businesstopia.net/economics/macro/second-fiscal-model-and-equilibrium-level-income-output.

Thus, the transfer payments made by the government have a positive effect on the equilibrium income through its impact on marginal propensity to consume.

Equilibrium Income with Leakages-Injections in the Second Fiscal Model

The leakages-injections expression under the second fiscal model can be explained as

S + T_{n }= I_{a} + G_{a} [T_{n} is the net tax]

Or, Y_{D} – C + (T –R) = I_{a} + G_{a} [From the definition of saving and net tax T_{n}]

Or, (Y – T_{n}) – (C_{a} + λY_{D}) + T_{a} – R_{a} = I_{a} + G_{a}

Or, Y – (T_{a} – R_{a}) – C_{a} – λ (Y – T_{n}) + T_{a} – R_{a} = I_{a} + G_{a}

Or, Y – T_{a} + R_{a} – C_{a} – λY + λ (T_{a} – R_{a}) + T_{a} – R_{a} = I_{a} + G_{a}

After cancelling out the common terms and rearranging,

Y – λY = C_{a} – λT_{a} + λR_{a} + I_{a} + G_{a}

So, the final equilibrium equation is,