Introduction

The simple linear differential equation is a useful coefficient in any homogenous equation. The equation results individually lead into the population in funds allocation equation to be satisfied as the solution entails a function that ensures the mathematical satisfaction of the equation. The government budget is a good example where the simple linear equation is applied successfully.

The equation is used by the ministry of finance to effectively balance the expenditure of the government versus its income during any financial year. In the article International Journal of Trade, Economics, and Finance by(Aydin, Celil, and Ömer 170), the mathematical formulation of the simple lineardifferential equation is useful in the determination of the state of equilibrium in the preparation of government budget. The formulation examines the exports during a fiscal year, investments in the economy, the imports in the country. It is thus used to predict any deficits induring the financial year in the country when preparing the government budget.

However, in the mathematical formulationof the governmentbudget, the model is based on critical assumptions such as:

• The national economy has five sectors. This assumption involves areas such as savings, the taxes imposed, the investment levels, the expenditure of the government, imports, and the exports realized in the country.
• The government budget deals with a short period. This assumption primarily emphasizes on the deviation of the actual injections into the economy from the leakages realized. It also means that expected unemployment levels and depreciation traits are to be continuous during the durationsince the period is not enough to enable the automatic balancing of the injections and leakages expected gross domestic product into anequilibrium stateThe government controls and interferes with the economy. The assumption focuses on the point that the government spends its income on the provision of subsidies or investment to the public. The hypothesis also states that the government does impose taxes on the economy.
• However, the for the model to be considered being at a balance in the equation, the savings, taxes, and imports have to be equal to the summation of the investments in the economy, the government expenditure and exports(Guerrieri, Luca, and Matteo 26). The model when in equilibrium has to appear as follows.

S+T+M=I+G+X

However, regardless of the state of equilibrium is maintained, the sum of leakages which involve all the expenses such as investments, government spending and exports may not be equal to the summation of injections which include savings, imports, and taxes imposed by the government. A state of disequilibrium is capable of causing a recession in the general economy. Moreover, to solve the state of imbalance which may harm the economy of the country, it is essential to apply generalization models to ensure that the country’s economy is back to its initialstate.

A stochastic model is a vital tool in the estimation of the probability of potential results of the national economy with the injection of funds and leakages realized in the economy(Mesbah 30). The stochastic model is essential in allowing random variation of inputs and outputs to balance over some time. The model focuses on the variations of the funds injected into the economy and funds that are spent by the historical trends for the chosen fiscal year using the standard time-series techniques in mathematic formulations.

Conclusion

The stochastic model is one of the most useful financial models which appropriately applies the random variables with the essence of obtaining the state of equilibrium in the economy during the preparation of the government budget. The generalization estimates the expected results in the economy thus predicts and analyzes the conditions for various economic situations when finalizing on the government budget.

Works Cited

Aydin, Celil, and Ömer Yilmaz. “The Analysis of Visible Hand of Government: The Threshold Effect of Government Spending on Economic Growth.” International Journal of Trade, Economics, and Finance 7.5 (2016): 170.

Guerrieri, Luca, and Matteo Iacoviello: A toolkit for solving dynamic models with occasionally binding constraints efficiently.” Journal of Monetary Economics 70 (2015): 22-38.

Mesbah, Ali. “Stochastic model predictive control: An overview and perspectives for future research.” IEEE Control Systems36.6 (2016): 30-44.

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