**1. Introduction**

Involuntary unemployment in Diamond-type Overlapping Generations (OLG) models seem to be a contradiction in terms. As in Solow [1]'s neoclassical growth model, Diamond assumed full employment of the workforce for the OLG economy with production and capital accumulation. Thus, in this economy, unemployment is purely voluntary. Moreover, fiscal policy does not impact the steady-state growth rate of gross domestic product (GDP) since the output growth is exogenously determined. Both, voluntary unemployment and growth ineffectiveness of fiscal policy, do not accord well with the current state of the pandemic-affected world economy which is characterized by high involuntary unemployment and enormous government expenditures to compensate lockdown-related private losses. To be capable to address the effectiveness of fiscal policy to reduce involuntary unemployment, an additional extension of Diamond [2]'s seminal OLG model towards endogenous growth becomes inevitable.

As is well-known, involuntary unemployment is usually associated with Keynesian macroeconomics [3, 4]. Involuntary unemployment is traced back to lacking aggregate demand. But on the reasons why aggregate demand remains below full employment output in a perfectly functioning market economy, there is no consensus among mainstream macro-economists to this date. The majority view follows the New-Keynesian approach in which prices and wages adapt sluggishly to market imbalances due to imperfect competition and other market failures (for a survey see [5]). In contradistinction to the majority view, a macroeconomists' minority follows [6] and more recently [7] who trace back aggregate demand failures to inflexible aggregate investment demand governed by (pessimistic) "animal spirits" of investors independently from aggregate savings of households. In contrast to the imperfectly flexible-price approach, [6, 7] presume perfectly flexible and perfectly competitive output prices, wage rates and interest rates. Despite this perfect-market setting employees do not become fully employed because an independent investment function makes the general equilibrium equations'system over-determinate. Over-determinacy disappears only if at least one market-clearing condition is cancelled, and it is the labor market clearing condition that is deleted.

Magnani [7] without noting precursor Morishima [6] incorporates a macrofounded investment function into Solow [1]'s neoclassical growth model without public debt. Since the chapter intends to study the effects of public debt on private capital accumulation, GDP growth and unemployment in the long run, the present author switches to Diamond [2]'s OLG model with non-neutral internal public debt. Long-run GDP growth in Diamond [2]'s OLG model is, however, exogenous precluding the analysis of how larger public debt impacts GDP growth and unemployment. Hence, there is a need for a mechanism that endogenizes GDP growth. To this end, we stick to human capital accumulation à la [8, 9].

This chapter pursues several purposes: Firstly, it will be shown how in a loglinear utility and Cobb–Douglas production function version of Diamond [2]'s OLG model with internal public debt, the intertemporal equilibrium dynamics based on household's and firm's first-order conditions, on government's budget constraint and intertemporal market-clearing conditions is modified when aggregate investment demand is governed by a savings-independent investment function. Transcending [7] we secondly intend to rigorously prove the existence and dynamic stability of a steady-state of the equilibrium dynamics in a model which closely follows Farmer [10]'s model setting. Our third purpose is to investigate the effects of a higher public debt to output ratio on the output growth rate, on the capitaloutput ratio, on the interest factor and on the wage tax rate in a steady state of the Diamond OLG model extended by human capital accumulation which is financed by public human capital investment expenditures as in Farmer [11] and in Lin [9]. In extending [9, 11] by an independent aggregate investment function we are capable of exploring analytically and numerically the steady-state effects of a higher public debt to output ratio on the unemployment rate. In particular, we will demonstrate on which factors it depends whether a higher public debt to output ratio raises the output growth rate and decreases the unemployment rate. In contradistinction to the author's contributions in Farmer [10] and Farmer [12] this chapter exhibits the OLG model presented there more completely and succeeds in deriving the steady-state effects of larger public debt more succinctly. This chapter together with Farmer and Farmer [10, 12] can be seen as our contribution to the recent macroeconomic literature.

The structure of the chapter is as follows. In the next section (2.) the model setup will be presented. In section 3, temporary equilibrium relations and the intertemporal equilibrium dynamics are derived from intertemporal utility maximization, atemporal profit maximization, government's budget constraint and the market-clearing condition in each period. In section 4, the existence of a steadystate solution of the equilibrium dynamics and its local dynamic stability is investigated. Section 5, is devoted to the analysis of the comparative steady-state effects of larger public debt. Section 6, concludes.
