scholarly journals An Elementary Mathematical Model for MMT (Modern Monetary Theory)

2021 ◽  
Vol 13 (3) ◽  
pp. 1
Author(s):  
Yasuhito Tanaka
Keyword(s):  
Technological Progress ◽  
Utility Maximization ◽  
Budget Deficit ◽  
Monopolistic Competition ◽  
Full Employment ◽  
Supply And Demand ◽  
Profit Maximization ◽  
Static Model ◽  
Monetary Theory ◽  
Necessary And Sufficient

In recent years, a school of economics called MMT (Modern Monetary Theory) has been attracting attention, but it has not been analyzed theoretically or mathematically. This study aims to provide a theoretical basis for the skeleton of the MMT argument, while maintaining the basics of the neoclassical microeconomic framework, such as utility maximization of consumers by means of utility functions and budget constraint, profit maximization of firms in monopolistic competition, and equilibrium of supply and demand of goods. Using a simple static model that includes economic growth due to technological progress, we will argue that: 1) a continuous budget deficit is necessary to maintain full employment when the economy is growing, and that this deficit does not have to be covered by future surpluses; 2) Inflation is caused when the actual budget deficit exceeds the level necessary and sufficient to maintain full employment. In order to avoid further inflation, it is necessary to maintain a certain level of budget deficit; 3) A shortfall in the budget deficit leads to recession and involuntary unemployment. To recover from this, a budget deficit that exceeds the level necessary to maintain full employment is required. However, since a continuous budget deficit is necessary after full employment is restored, the deficit created to overcome the recession does not need to be covered by future budget surpluses, nor should it be.

scholarly journals Very Simple Mathematical Model of MMT (Modern Monetary Theory)

2021 ◽  
Vol 11 (3) ◽  
pp. 78
Author(s):  
Yasuhito Tanaka
Keyword(s):  
Technological Progress ◽  
Budget Deficit ◽  
Full Employment ◽  
Returns To Scale ◽  
Perfect Competition ◽  
Monetary Theory ◽  
Budget Deficits ◽  
Growing Economy ◽  
The One ◽  
Constant Returns To Scale

The purpose of this paper is to provide a concise theoretical and mathematical foundation for the major parts of the debate in the recently discussed school of economics called Modern Monetary Theory (MMT), while maintaining the basics of the neoclassical microeconomic framework, such as utility maximization of consumers using budget constraints and utility functions, and equilibrium of demand and supply of goods under perfect competition with constant returns to scale technology. By a two-periods overlapping generations (OLG) model in which the economy grows by technological progress, we will show that: 1) We need a budget deficit to achieve full employment with constant price when the economy grows by technological progress. This budget deficit should not be offset by future surplus; 2) A budget deficit that exceeds the level necessary to maintain full employment in a growing economy with constant price will cause inflation. A stable budget deficit is required to prevent further inflation; 3) A budget deficit that is insufficient to maintain full employment will cause a recession with involuntary unemployment. A budget deficit larger than the one necessary and sufficient to maintain full employment without a recession can overcome a recession caused by insufficient budget deficit and restore full employment. The deficit created to overcome the recession should not be offset by subsequent surpluses, since full employment can then be maintained through constant budget deficits.

scholarly journals On Budget Deficit under Economic Growth: Towards a Mathematical Model of MMT

2021 ◽  
Vol 10 (1) ◽  
pp. 36
Author(s):  
Yasuhito Tanaka
Keyword(s):  
Economic Growth ◽  
Mathematical Model ◽  
Population Growth ◽  
Mathematical Analysis ◽  
Technological Progress ◽  
Budget Deficit ◽  
Overlapping Generations ◽  
Full Employment ◽  
Monetary Theory ◽  
Olg Model

Recently, a school of thought called Modern Monetary Theory (MMT) has been attracting attention, but it has not received much theoretical or mathematical analysis. In this paper, we examine the theoretical validity of the MMT argument using an overlapping generations (OLG) model that includes economic growth due to population growth, and give a generally positive evaluation of MMT. The basic idea is that a certain level of continuous budget deficit is necessary to maintain full employment when the economy is growing, that inflation occurs when the budget deficit exceeds that level, that a recession occurs when the budget deficit falls below that level, and involuntary unemployment occurs. In order to recover from a recession, a budget deficit in excess of that level is required, and that deficit need not be covered by a future budget surplus. The same can be said for growth resulting from technological progress.

scholarly journals A Brief Rationale for MMT Arguments

2021 ◽  
Vol 9 (2) ◽  
pp. 1
Author(s):  
Yasuhito Tanaka
Keyword(s):  
Economic Growth ◽  
Budget Deficit ◽  
Full Employment ◽  
National Income ◽  
Monetary Theory ◽  
Macroeconomic Model ◽  
Necessary And Sufficient

In this note we examine MMT (Modern Monetary Theory) arguments by a simple macroeconomic model without microeconomic foundation. Mainly we will show the following results. 1) In the underemployment case the national income is determined by the budget deficit. 2) In the full employment case we can define the budget deficit which is necessary and sufficient to achieve full employment. 3) The excessive budget deficit causes inflation. 4) We need budget deficit to achieve and maintain full employment under economic growth. 5) We can recover recession by the budget deficit which is larger than that when full employment is maintained. Also, we show that the budget deficit equals the increase in the savings between generations.

scholarly journals Mathematical Model of MMT with Profit Return under Monopolistic Competition

2021 ◽  
Vol 8 (2) ◽  
pp. 65
Author(s):  
Yasuhito Tanaka
Keyword(s):  
Budget Deficit ◽  
Monopolistic Competition ◽  
Full Employment ◽  
Returns To Scale ◽  
Budget Deficits ◽  
Price Inflation ◽  
The Difference ◽  
Growing Economy ◽  
Necessary And Sufficient ◽  
Constant Returns To Scale

Even under constant returns to scale technology there is a positive profit return if the goods are produced in monopolistic competition. By a two-periods overlapping generations (OLG) model with production in monopolistic competition under constant returns to scale in which the economy grows by technological progress and the older generation consumers receive the profits, we consider the problem of budget deficit. We show that the budget deficit equals the difference between the net savings of the younger generation consumers excluding the profits received in the future and that of the older generation consumers in each of the following cases. Also, the following results will be proved. 1) A budget deficit is necessary to realize full employment with constant price when the economy grows. 2) If the budget deficit exceeds the level necessary and sufficient to maintain full employment in a growing economy with constant price, inflation will occur. A stable budget deficit is necessary to prevent further inflation. 3) If the budget deficit is insufficient to maintain full employment, a recession with involuntary unemployment occurs. We can overcome a recession and restore full employment making a budget deficit larger than the one necessary and sufficient to maintain full employment without a recession. Since we can maintain full employment by constant budget deficits, we should not offset the deficit created for overcoming the recession by budget surpluses.

scholarly journals Fiscal Policy as a Solution to Involuntary Unemployment

Ekonomika ◽  
2021 ◽  
Vol 100 (2) ◽  
pp. 63-83
Author(s):  
Yasuhito Tanaka
Keyword(s):  
Fiscal Policy ◽  
Budget Deficit ◽  
Monopolistic Competition ◽  
Full Employment ◽  
Returns To Scale ◽  
Profit Maximization ◽  
Involuntary Unemployment ◽  
Game Theoretic ◽  
Constant Returns To Scale ◽  
Constant Prices

We show the existence of involuntary unemployment based on consumers’ utility maximization and firms’ profit maximization behavior under monopolistic competition with increasing, decreasing or constant returns to scale technology using a three-periods overlapping generations (OLG) model with a childhood period as well as younger and older periods, and pay-as-you-go pension for the older generation, and we analyze the effects of fiscal policy financed by tax and budget deficit (or seigniorage) to achieve full-employment under a situation with involuntary unemployment. Under constant prices we show the following results. 1) If the realization of full employment will increase consumers’ disposable income, in order to achieve full-employment from a state with involuntary unemployment, we need budget deficit (Proposition 1). 2) If the full-employment state has been achieved, we need balanced budget to maintain full-employment (Proposition 2). We also consider fiscal policy under inflation or deflation. Additionally, we present a game-theoretic interpretation of involuntary unemployment and full-employment. We also argue that if full employment should be achieved in equilibrium, the instability of equilibrium can be considered to be the cause of involuntary unemployment.

scholarly journals Involuntary Unemployment in a Neoclassical Model

2020 ◽  
Vol 65 (2) ◽  
pp. 12-28
Author(s):  
Yasuhito Tanaka
Keyword(s):  
Wage Rate ◽  
Utility Maximization ◽  
Overlapping Generations ◽  
Monopolistic Competition ◽  
Returns To Scale ◽  
Profit Maximization ◽  
Nominal Wage ◽  
Olg Model ◽  
Neoclassical Model ◽  
Involuntary Unemployment

AbstractWe show the existence of involuntary unemployment without assuming wage rigidity using a neoclassical model of consumption and production. We consider a case of indivisible labor supply and increasing returns to scale under monopolistic competition. We derive involuntary unemployment by considering utility maximization of consumers and profit maximization of firms in an overlapping generations (OLG) model with two or three generations. In a two-periods OLG model it is possible that a reduction of the nominal wage rate reduces unemployment. However, if we consider a three-periods OLG model including a childhood period, a reduction of the nominal wage rate does not necessarily reduce unemployment.

scholarly journals A Mathematical Model of MMT (Modern Monetary Theory) with Profit Return

2021 ◽  
Vol 11 (4) ◽  
pp. 39
Author(s):  
Yasuhito Tanaka
Keyword(s):  
Technological Progress ◽  
Budget Deficit ◽  
Full Employment ◽  
Returns To Scale ◽  
Perfect Competition ◽  
Budget Deficits ◽  
Price Inflation ◽  
The Difference ◽  
Growing Economy ◽  
The One

Even in perfect competition there is a positive profit return if the good is produced with decreasing returns to scale technology. Using a two-periods overlapping generations (OLG) model with production under perfect competition with decreasing returns to scale technology in which the economy grows by technological progress and the older generation consumers receive the profit returns, we consider the problem of budget deficit under economic growth. We will show the following results. 1) We need a budget deficit to achieve full employment under constant price when the economy grows by technological progress. 2) If the budget deficit exceeds the level necessary to maintain full employment in a growing economy under constant price, inflation will be triggered. We need a stable budget deficit to prevent further inflation. 3) If the budget deficit is insufficient to maintain full employment, it will cause a recession with involuntary unemployment. We can overcome a recession and restore full employment caused by insufficient budget deficit by a budget deficit larger than the one necessary and sufficient to maintain full employment without a recession. We should not offset the deficit created to overcome the recession by subsequent surpluses because we can maintain full employment through constant budget deficits. Also, we show that in each case the budget deficit equals the difference between the net savings of the younger generation consumers and that of the older generation consumers.

scholarly journals INDIVISIBLE LABOR SUPPLY AND INVOLUNTARY UNEMPLOYMENT: MONOPOLISTIC COMPETITION MODEL

2020 ◽  
pp. 1-14
Author(s):  
YASUHITO TANAKA
Keyword(s):  
Labor Supply ◽  
Utility Maximization ◽  
Overlapping Generations ◽  
Monopolistic Competition ◽  
Returns To Scale ◽  
Profit Maximization ◽  
Wage Rigidity ◽  
Overlapping Generations Model ◽  
Involuntary Unemployment ◽  
Constant Returns To Scale

This paper is an attempt to provide a micro-theoretical basis for Keynesian economics while maintaining as much of the neoclassical framework as possible, such as utility maximization for consumers and profit maximization for firms. We show the existence of involuntary unemployment without assuming wage rigidity when labor supplies of individuals are indivisible. We derive involuntary unemployment using an overlapping generations model under monopolistic competition with constant returns to scale technology and indivisible labor supply.

scholarly journals Debt to GDP Ratio from the Perspective of MMT

2021 ◽  
Vol 13 (1) ◽  
pp. 1
Author(s):  
Yasuhito Tanaka
Keyword(s):  
Economic Growth ◽  
Budget Deficit ◽  
Full Employment ◽  
National Income ◽  
Monetary Theory ◽  
Macroeconomic Model ◽  
National Debt ◽  
Government Bonds ◽  
Interest Payments ◽  
Over Time

In this note we examine the debt to GDP ratio from the perspective of MMT (Modern Monetary Theory) by a simple macroeconomic model with savings by government bonds instead of money. Mainly we will show the following results. 1) In order to maintain full employment under economic growth, the budget deficit, including interest payments on government bonds, must be positive; and if the budget deficit is smaller than this value, there will be recession with involuntary unemployment. 2) Under full employment the debt to GDP ratio approaches to a finite value over time. 3) In the underemployment case the national income is determined by the budget deficit. 4) The excessive budget deficit causes inflation. 6) In order to recover full employment from recession we need budget deficit larger than that when full employment is maintained. 5) The budget deficit, including interest payments on government bonds, equals the increase of the savings of consumers between periods (generations); and this result holds whether we have full employment or not, whether we have inflation or not. Then, the ratio of the national debt to GDP in a period is smaller than one, and even if one period constitutes of several years, the debt to GDP ratio in a year is finite.

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