B and Lemma II are crucial. For expository reasons those are sufficient, but not as sharp as they could be. For example, we might accept a small loss in H(1)
H(0), as long as net N(1)
N(0).
However, even then the analytical structure remains, that productivity L is assumed, so that it doesn’t come as a big surprise that employment is possible. This actually is similar to the Arrow-Debreu setting, where endowments are assumed, and full employment appears to be possible. The modern reader might be inclined towards assumptions that generate the impossibility of full employment. (See for example the Grandmont (1983) setting of expectatory mismatch.) However, each impossibility can be questioned too. It is up to reality what model applies. Stated differently: the value of above tautological theorem is that it helps us to understand what is implicit in our concepts, so that we may be more aware in observing whether these concepts apply. This fits in with our concept of a proposition.
Remark: The reduced form also captures the ‘physical tax’. The lack of infrastructure, machines or tools may ‘tax’ people - and once these have been provided, they could start earning income, and their earnings would, crucially, be larger than needed to pay for the equipment. Economists of course understand this concept of a physical tax - as the lack of efficient capital markets, or the frustration of those by taxes - but the crucial point is the abstract one. When people don’t earn anything, and the economist suggests to abolish some tax, then a listener may become upset, since how can you abolish something that people don’t pay ?
Graphical presentation
Diagrams help understanding the analysis. Figure 42 shows two tax regimes, T(y, 0) and T(y, 1), characterized by different exemptions X(0) and X(1), and different critical incomes M(0) and M(1). The main difference is net income at L. In regime 0, net income at L falls below subsistence, causing unemployment and higher taxes to pay for benefits.
