In the consequence of the fiscal policy after the Oil-crisis, the government bond was accumulated up to ¥133 trillion at the end of F.Y. 1985. It will make the big burden to the Japanese public finance in the future. It is very important to decide every year's national budget considering the next generation's burden of the government bond. This paper's purpose is to seek the optimal way to minimize the social cost in the infinite horizon by using the optimal control theory. The optimal ratio of the every year's expenditure for the interest payment and the reduction of bond by the tax revenue to the government bond balance, depends on the difference between the interest rate and the growth rate. Considering the relation between the reduction of bond and the economy, the ratio which is decided by the non-linear optimal control rule, becomes smaller.

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The purpose of our paper is to investigate the aggregative structure of assets in Keynes' General Theory and to investigate the relation between this structure and Keynes' view about the effectiveness of monetary policy. According to Leijonhufvud, Keynes aggregated the long-term assets including financial assets and physical assets as non-money assets. Then relative price of bonds and capital goods is constant, and the interest elasticity of investment is high. We examine Leijonhufvud's this view, and investigate how Keynes considered the differences in non-money assets.
In General Theory, as a basic model, the relative prices of non-money assets are not treated as endogenous variables, then in this sense, non-money assets are aggregated, but this is rather convenient treatment for simplicity, and this does not mean the differences in non-money assets are not important. We consider that changes in estimate of risk and liquidity of non-money assets are important factors in Keynes' view about the effectiveness of monetary policy, even if these are not theoretically analyzed.

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Keynes' argument that income can change without any change in the quantity of money appears in his Treatise on Money. This argument is essentially concerned with the theory of interest and the equilibrium condition in the money market, but Keynes' argument in the Treatise concerning these matters has not been sufficiently analyzed. The purpose of this paper is to clarify these matters and investigate the significance of the argument in the Treatise.
In the Treatise, the total demand function for money is not specified and the money market is not theoretically related to the goods market. Then the theory of interest in the Treatise is not complete, but it can be regarded as a theory which necessarily developed into the liquidity preference theory of interest in the sense that the interest rate is governed by the excess demand for money. Furthermore, the Treatise contains valuable analysis of many subjects which are not covered in the General Theory, such as the transaction demand for money in disequilibrium and the behavior of banks.

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1. The Theory of Interest in Marx’s Capital
　One of characteristic theoretical contributions in Marx’s Capital is its systematic attempt to focus upon money and finance as a social mechanism for both flexible growth and instability of capitalist market economies. This was rarely recognized by Anglo-Saxon political economists in the initial phase of the Renaissance of Western Marxian Economics until the 1980s, as Lapavitsas (2017) states. With the financialization of capitalism, a steady output of articles and books on money and finance is found among Western Marxian economists. In contrast, Japanese Marxian economics has long accumulated studies of money and finance, even forming the Academic Association for the Study of Credit Theory as early as the 1950s.
　However, not a few interesting problems still remain about how to read and apply Marx’s theory of interest. They originate from the fact, among others, that Marx’s draft for Part V of Capital Ⅲ on Interest-Bearing Capital was mostly unfinished and difficult even for Engels to edit.
　Otani (2016) carefully exerted a remarkable effort over many years to translate and interpret Marx’s original draft of Part V and he commented on every difference that he found in the existing version edited by Engels. We learn at least three main points from his effort, as follows.
　First, Marx’s complete draft for Part V of Capital Ⅲ, which was edited to form 16 chapters (chapters 21–36) by Engels, was divided into three different segments. The first segment comprises the somewhat completed first four chapters on the abstract notion of interest-bearing capital. The second segment is an unfinished draft of the concrete forms of interest-bearing capital in the credit system. The title, “Credit and Fictitious Capital” represented this segment as a whole, not just the initial chapter 25. The third segment is titled “Pre-Capitalist Relations,” which was edited by Engels as chapter 36.
　Second, in Engels’ edition, the distinction between Marx’s draft of the main text and the notes or collection of materials that required further editing is not clearly made. This confusion might have resulted from the fact that Engels did not use Marx’s original hand-written draft, but a copy made by someone after hearing Engels’ oral presentation of the draft.
　Third, the draft pages from which Engels wrote chapters 30–32 on “Money Capital and Real Capital Ⅰ,Ⅱ,Ⅲ” are most important in the second segment. In the complete volumes of Capital, Marx treats here the capitalist mechanism of industrial cycles and crises to the greatest degree by stressing the roles of rises in wages and interest rates, along with the ongoing speculative trading of fictitious capital toward the end of prosperity.
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In this paper, a theoretical hypothesis that public works would have deterrence effects of deflation under the situation that deflation-gap exists was tested empirically. For testing this hypothesis empirically, we used macro-economics data in Japan since 1991 when the huge deflation-gap was brought by the collapse of the babble economy. As a result, we found that 1,000 billions yen's public works increases the GDP deflator by 0.2-0.8 % and increases nominal GDP by about 2,430 billions yen - 4,550 billions yen. This results support the hypothesis that public works would have deterrence effects of deflation under the situation that deflation-gap exists. It was also found that the deflation deterrence effects by the public works was larger than that by the in-crease export.

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