EU countries struggle with debt

I received an article from which I quote:

„Seventeen of the 27 member states of the European Union (EU)exceededlast year, limits for budget deficits and public debt. This follows from data published on Tuesday by the European statistical office Eurostat. TASR reports on this based on the DPA report and Eurostat data.According to these figures in the euro area, the ratio of the public finance deficit to gross domestic product (GDP) fell to 3.1% in 2024 from 3.5% in 2023. Across the EU it also fell to 3.1% from 3.4%. But at the same time, the ratio of public debt to GDP last yearslightlyincreased, and that in the eurozonewhich is 87,1% from 87% at the end of 2023 and in the EU to 80.7% from 80.5%."

So, the economic situation of the EU countries is really baddisconsolate, bad. They aremenacinglyindebted. Didn't EC economists know in advance that it would end like this?

I will try to show that itthey should have known, however, they needed to do thattool. Economies develop dynamically and fluctuatingly, and economic science will determine their course with differential and differential equations. It is their application that also requires itconstruction of models investigations expensiveeconomic indicatorshare of government debt to GDP(which is the valuefinalsof products and services produced in the country per year).

Something has gone wrong systemically, as this indicator is required by the EU, which set its limit at 60%.the firstMaastricht criterion. It is flawed, a demonstration of equalization, leveling and impropriety. A natural question is whether this share can exceed the value1? He can.

There are a lot of changes in an economic system at a particular timetand the development of macroeconomic aggregates is not, unfortunately, onlyto estimate.

Definitely a factythey predict and determine and profile the wholespecific paths of economic quantitiesin time. Economic theory knows several such models. In this discussion, I will outline the construction of two models, and their essence will be differential equations.

Between government debt (D) and national income (HDP,Y) is a relation; there are several of them. Let's consider these basic relationships between the variables of the economic system (economy), model1:

where Ddenotes debt,Y stands for GDP, or national income. In this modelnational incomeis growingconstantby a rate equal toßper unit of time (equation 4.53) anational debt growth rateisfixed ratiozHDP, national incomeY(equation 4.52). The third and fourth equations statestarting conditionspreYaD. We assume that at all times tis a concrete value in the economyY(t), i.e. j. the first valueY(0)in the base year and the specific value of the debt in the base year –D(0). The relation (4.52) is a causal nexus. However, equation (4.52) is a differential equation. Let's differentiate the first equation with respect to time and after substitution from equation (4.53) we get:

Technically, the expression (4.56) isinhomogeneous differential equationsecond order with a constant coefficient. We got a really simple equation that we will solve to find out the unknownfunctional relationship of debt from parameters and variables, which appear in the model. We solve the relation (4.56) by double integration. Let us first integrate (4.56). We get:

This is itgeneral debt behavior equation. It is very importanteconomic insight, based on specific mathematical knowledge. Let's build into the model (4.59) the initial condition that in time0the national debt reached a value ofD(0):

The reader can find the rest of the steps in my bookMacroeconomic analysis. After a finite number of steps, we get the solution:

I meandebt growth D(t)is a quadratic function. We can calculate the path from equation (4.53) of the modelHDP,Y. The final solution for the quantityY we obtain by directly integrating (4.53) and inserting the initial condition (4.54). We get:

This is a functional relationshipexpensivenational incomeY(t). But we are interested in more, Frdebt to GDP ratio. What is its trajectory? Let's compare the obtainedD(t)aY(t):

respectively

The answer is clear, what (4.69) is talking about.The Delors Committee should have known this!

We can analyze it. Ift grows to infinity, the first fraction approaches zero, the second fraction approaches a constant, and the third fraction grows without bound (goes to plus infinity). Important knowledge. To give the reader a more concrete form, let's construct a graph for the selected values ​​of the model parameters. Let them be

alphabetY(0)D(0)0,2301429,8285,96

We get this graph:

Model-based analysis of the economic relationship between the share of government debt and GDP1logically led us to the conclusion that the trajectories of these two quantitiesthey can intersect. Debt can exceed the level of GDP (under certain conditions), that isD >Y.

They are not known in the Maastricht criteriastarting pointthe authors' assumptions and whydeterminedthe value of 0.60?

Let's construct another type of model (model2). Let's decide to modify the second equation of the model1. Our assumption will be that national income grows byconstant percentage,equation (4.71).

So the equations of the model are

Getting a solution to this model is a bit more difficult.  After examining equation (4.71), it turns out (on the basis of knowledge from differential calculus) that we consider the functionY(t) =aebt, that is

Let us substitute these values ​​into (4.71) and we will find that

that is

Now, using (4.72), we can write

We have the equation of the trajectoryY(t). This is the solution, the sought-after development path forY(t). Now we still need the path of the macroeconomic variableD(t). Dosaďme (4.78) to (4.70).

We will get

The reader can find the rest of the steps in my book mentioned above. And so

Given the importance of the share of government debt to GDP, let's express this relationship mathematically in a different way. We will get

Analyzing (4.85), we find that ift grows to infinity, the first fraction approaches zero and the second fraction approaches the limit a/b.Let the starting parameters be like this

alphabetaD(0)0.10.041429.8

The development of the relationship between GDP and national debt isanother, slower. It reaches a value of more than 60% in the 6th year. In addition, the share of debt to GDP does not grow untilinfinity(model1), but will approach the value of 2.5. However, these conclusions logically followed from the theory, which is based on the dynamic models proposed by us.

Model1a2they aremathematical imagefunctioning of the economy,driving force of the economy. In both models, we have shown how serious it isknowledgeeconomic theory in describing the behavior of the economic system.

We have shown that the facts about how tomessageeconomic system.

We saw completely on the chartsdifferentlythe behavior of the paths of basic macroeconomic variables. We also deduced that the proportion of debt aGDP canexceed value1, which also happened often in the practice of developed countries. After all, even the household gets into debt, takes out a mortgage when building a family home.

The restriction of the economy by the Maastricht criterion canslow downeconomic growth andit doesn't solve the problem.

Calculation of the value of the Maastricht criterion of the share of government debt to GDPrequires differential equations. But mainly the parametersa,ßaD(0) haseach one EU country other.

That fact Delors committee completelyignoredor they didn't know him.

Conclusion

The Delors Committee was tasked with investigating the problem in 1988economic and monetary union,he should have determined as wellthe way of their implementation.She expectedmonetary and fiscal convergence. The Delors report defined the Maastricht criteria, which became operational in 1993. The first is thatthe government's debt must not exceed 60 percentGDP. The number was unscientifically determined, as it follows from consideration, and similarly the other criteria.

In my reasoning, I showed two dynamic models that havespecific relationshipsbetween the variables and from them we can find out how the share of debt in GDP behaves. One says that the share can grow indefinitely, and the other states limits. Both models displayrelationships of the driving force of the economy, production and behavior, i.e. j. growthYaD and their share.

With its criteria, the EU directly documented thatignoreseconomic scienceand relies on guesswork. Is he not responsible? Especially the Delors committee? 2 graphs clearly document this.

The Delors committee was to constructdynamic modelsforeachEU country,a nobad criteria.

The parameters of the model cannot be the same for France, Germany, the Czech Republic or Slovakia. They playdecisivetask for the shape of the path of quantities. Economy-destroying effectsshare of debt to GDPwe have to leave.

Just as man turns a barren desert into fertile land, so must he todayto changethe functioning of the economy and notto fightwith a share of the debt.

Politicians must also know how the economy should work.

Prof. J. Hussar

Rohovce, 12/6/2026