Optimal Control Dynamic Relationships and Fiscal Policies in Indonesia’s Economy

Abstract

Purpose: This study aims to estimate optimal control in the Keynesian macroeconomic model for the Indonesian economy. Approach/Methodology/Design: Researchers use optimal control in retrieval in connection with macro-econometric models' problems. One way is used to influence macroeconomic variables, which include national income and expenditure. In this study, optimal control is used on the expenditure side, namely, to influence changes in the budget deficit. The data used is secondary data in the form of time series, in the period 1990-2018. Simulation is used to obtain the optimal value, with a simulation period starting from 2019-2023-optimal control theory through fiscal policy on the budget deficit. Findings: The results showed that the optimal value of macroeconomic variables has a deviation from the target value for all macroeconomic variables, consumption, investment, exports, imports, GDP, and budget deficits. So, it can be seen that optimal growth, through macroeconomic variables that influence it, including GDP, consumption, investment, exports, and imports with the budget deficit as a control variable. In the scientific concept, optimal control theory is used as a tool to determine an optimal policy. Practical Implication: The research provides a solution to the budget deficit problem. The government needs to control the deficit so that optimal economic growth will be obtained. The largest deviation from the average during the simulation period occurred in GDP, followed by investment, exports, and fiscal policy deficits. Meanwhile, the lowest average deviation is found in imports. Original/Value: This research contributes and provides solutions to fiscal Policy. They are mostly related to the budget deficit.

Classical Continuous Boundary Optimal Control Vector Problem for Triple Nonlinear Parabolic System

“…,for 𝑙 = 1,2,3, and 2 (Ω), then there exists {𝑣 𝑙𝑛 0 }, with 𝑣 𝑙𝑛 0 ∈ 𝑉 𝑛 , such that 𝑣 𝑙𝑛 0 → 𝑦 𝑙 0 strongly (ST) in 𝐿 2 (Ω) , and since 3 and 𝑦 𝑛 ∈ (𝐿 2 (𝐼, 𝑉)) 3 in the 1 𝑠𝑡 term of the L.H.S. of (21), hence for this term we can use Lemma 1.2 in [16] and since the 2 𝑛𝑑 term is positive, taking 𝑇 = 𝑡 ∈ [0, 𝑇], finally using Assum.…”

“…Optimal control problems (OCPs) play an important role in many practical applications, such as in medicine [1], aircraft [2], economics [3], robotics [4], weather conditions [5] and many other scientific fields. They are two types of OCPs; the classical and the relax type, each one of these two types is dominated either by nonlinear ODEs [6] or by nonlinear PDEs (NLPDEs) [7].…”

Quaternary Continuous Classical Boundary Optimal Control Problem Dominating by Parabolic System

“…Optimal control problems play an important role in many practical applications, such as in medicine [1], aircraft [2], economics [3], robotics [4], weather conditions [5] and many other scientific fields. They are two types of optimal control problems; the classical and the relax type, each one of these two types is dominated either by ODEqs [6] or PDEqs [7].…”

Quaternary Boundary Optimal Control Problem Dominating by Quaternary Nonlinear Parabolic System

“…Optimal control problems (OCPs) play an important role in many practical applications, such as in medicine [1], aircraft [2], economics [3], robotics [4], weather conditions [5] and many other scientific fields. There are two types of OCPs; the classical and the relax type, each one of these two types is dominated either by ODEqs [6] or by PDEqs [7].…”

“…𝑡, 𝑦 3 , 𝑣 3 ) + (𝑏 3 (𝑡)𝑦 3 , 𝑣 3 ) Ω + (𝑏 9 (𝑡)𝑦 2 , 𝑣 3 ) 𝛺 − (𝑏 6 (𝑡)𝑦 1 , 𝑣 3 ) Ω + (𝑏 15 (𝑡)𝑦 4 , 𝑣3 ) Ω ]𝜑 3 (𝑡)𝑑𝑡 = ∫ (𝑓 3 (𝑥, 𝑡, 𝑦 3 ), 𝑣 3 ) 𝛺 𝜑 3 (4 (𝑡, 𝑦 4 , 𝑣 4 ) + (𝑏 4 (𝑡)𝑦 4 , 𝑣 4 ) Ω − (𝑏 7 (𝑡)𝑦1 , 𝑣 4 ) 𝛺 + (𝑏 11 (𝑡)𝑦 2 , 𝑣 4 ) Ω − (𝑏 15 (𝑡)𝑦 3 , 𝑣 4 ) Ω ]𝜑 4 (𝑡)𝑑𝑡 = (84) ∫ (𝑓 4 (𝑥, 𝑡, 𝑦 4 ), 𝑣 4 ) 𝛺 𝜑 4 (𝑡)𝑑𝑡 𝑇 0 + ∫ (𝑢 4 , 𝑣 4 ) Г 𝜑 4 (𝑡)𝑑𝑡 𝑇 0 + (𝑦 4 (0), 𝑣 4 ) Ω 𝜑 4 (0)Now, one has the following two cases: Case1: Choose 𝜑 𝑟 ∈ 𝐷[0, 𝑇], i.e., 𝜑 𝑟 (𝑇) = 𝜑 𝑟 (0) = 0 ,∀𝑟 = 1,2,3,4, Now, by using integrating both sides for the first terms in the L.H.S. of ((80) -(83)), to get:∫ (𝑦 1𝑡 , 𝑣 1 ) 𝜑 1 (𝑡, 𝑦 1 , 𝑣 1 ) + (𝑏 1 (𝑡)𝑦 1 , 𝑣 1 ) Ω − (𝑏 5 (𝑡)𝑦 2 , 𝑣 1 ) Ω + (𝑏 6 (𝑡)𝑦 3 , 𝑣 1 ) Ω + (𝑏 7 (𝑡)𝑦 4 , 𝑣 1 ) Ω ]𝜑 1 (𝑡)𝑑𝑡 = ∫ (𝑓 1 (𝑥, 𝑡, 𝑦 1 ), 𝑣 1 ) Ω 𝜑 1 (𝑡)𝑑𝑡 𝑇 0 + ∫ (𝑢 1 , 𝑣 1 ) Γ 𝜑 1 (𝑡)𝑑𝑡 𝑇 0 𝑡, 𝑦 2 , 𝑣 2 ) + (𝑏 2 (𝑡)𝑦 2 , 𝑣 2 ) Ω + (𝑏 5 (𝑡)𝑦 1 , 𝑣 2 ) Ω − (𝑏 9 (𝑡)𝑦 3 , 𝑣 2 ) Ω − (𝑏 11 (𝑡)𝑦 4 , 𝑣 2 ) Ω ]𝜑 2 (𝑡)𝑑𝑡 = ∫ (𝑓 2 (𝑥, 𝑡, 𝑦 2 ), 𝑣 2 ) Ω 𝜑 2 (𝑡, 𝑦 3 , 𝑣 3 ) + (𝑏 3 (𝑡)𝑦 3 , 𝑣 3 ) Ω + (𝑏 9 (𝑡)𝑦 2 , 𝑣 3 ) Ω − (𝑏 6 (𝑡)𝑦 1 , 𝑣 3 ) Ω + (𝑏 15 (𝑡)𝑦 4 , 𝑣 3 ) Ω ]𝜑 3 (𝑡)𝑑𝑡 = ∫ (𝑓 3 (𝑥, 𝑡, 𝑦 3 ), 𝑣 3 ) Ω 𝜑 3 (𝑡)𝑡, 𝑦 4 , 𝑣 4 ) + (𝑏 4 (𝑡)𝑦 4 , 𝑣 4 ) Ω − (𝑏 7 (𝑡)𝑦 1 , 𝑣 4 ) Ω + (𝑏 11 (𝑡)𝑦 2 , 𝑣 4 ) Ω − (𝑏 15 (𝑡)𝑦 3 , 𝑣 4 ) Ω ]𝜑 4 (𝑡)𝑑𝑡 = ∫ (𝑓 4 (𝑥, 𝑡, 𝑦 4 ), 𝑣 4 ) Ω 𝜑 4 (the QSVS 𝑦 ⃗ = 𝑦 ⃗ 𝑢 ⃗ ⃗⃗ satisfy the WF ((8a)-(11a)).…”