The fundamental flaw of your argument is to take National Accounting at face value. With this, you, unfortunately, share a logical error with standard economics that is ultimately fatal for MMT. The root cause of the accounting error/mistake is a complete lack of understanding of what profit is. Total income is NOT the sum of wage income and profit but of wage income and distributed profit (2013). The conceptual error carries over to National Accounting (2012).
Already your first equation GDP=C+I+G+(X−M) is logically defective and by consequence the rest of your argument. This holds in particular for the sectoral balances equation (I−S)+(G−T)+(X−M)=0 which boils for the most elementary case down to Keynes' I=S (Keynes, 1973, p. 63).
To make it short, what, then, is the — minimal, objective, consistent, testable — common conceptual ground of all of the economics?
Total period income in the elementary production-consumption economy with only one giant firm is given by the sum of wage income and distributed profit, i.e. (1) Y=Yw+Yd. Total consumption expenditures are equal to the product of price and quantity sold, i.e. (2) C=PX. That's all for a start.
Monetary profit of the business sector as a whole is then defined as the difference between consumption expenditures and wage costs, i.e. Q≡C−Yw. Monetary saving of the household sector is then defined as the difference between total income and consumption expenditure S≡Y−C. Hence, S≡−Q if, for a start, Yd=0. In simple words: saving S is equal to loss −Q, or, dissaving −S is equal to profit Q. From this follows immediately that all I=S or IS-LM models are false — irrevocably in all eternity.
Generally speaking, it holds for the elementary production-consumption economy that Qre≡−S, i.e. retained profit Qre is equal to dissaving −S. And for the investment economy holds Qre≡I−S, i.e. retained profit is equal to the difference between investment and saving (for details see 2014).
There is no need at the moment to include net government spending and the trade balance. It suffices to prove that already the elementary macroeconomic accounting equations are defective.
Because the MMT profit theory is false, the theory of money and all the rest are false. (2015, Sec. 7).
Kakarot-Handtke, E. (2012). The Common Error of Common Sense: An Essential Rectification of the Accounting Approach. SSRN Working Paper Series, 2124415: 1–23. URL
Kakarot-Handtke, E. (2013). Debunking Squared. SSRN Working Paper Series, 2357902: 1–5. URL
Kakarot-Handtke, E. (2014). Economics for Economists. SSRN Working Paper Series, 2517242: 1–29. URL
Kakarot-Handtke, E. (2015). Major Defects of the Market Economy. SSRN Working
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Keynes, J. M. (1973). The General Theory of Employment Interest and Money.
The Collected Writings of John Maynard Keynes Vol. VII. London, Basingstoke: Macmillan.