The impact of taxation on the equilibrium

The impact of taxation on the equilibrium interest rate is given by:This result holds symmetry with Steedman\'s (1973) and Pasinetti\'s (1989a,b), in that the equilibrium interest rate depends positively on the taxation t. In equilibrium, the capital stock of the economy at time t is given by: Assuming that the number of workers and capitalists (who are in the first period of their lives) is equal to 1 and using (2.4), it follows in equilibrium: From (2.7), we obtain: where W=Y−P and assuming that in the long term P/K=r∗, we have: Inserting (2.11) and (2.13) in (2.10), it is verified that the total capital in equilibrium will be: From (2.14) we can get a sense of the importance of inheritance, obtaining the same aspect ratio on the total capital: Admitting that r* (1−t)>b and (Y/K−r*)<1. Differentiating (B/K)* with respect to t: This result is not surprising, because it is expected that if the appearance of a tax decreases (B/K)*, marginal increases in it also exert negative influence on B/K. The effect of government transfers on the distribution of the capital of the capitalist class in relation to the total capital of the economy will be verified now. From (2.13):Differentiating (K/K)* with respect to t:which translates into a lower portion of capital for the capitalists in relation to the total capital of the economy. Thus, we demonstrate that taxation and consequently income transfer to the working class affects the distribution of wealth between the article source because it reduces the share of the capitalist class in the total capital stock of the economy.
The model with government transfers and both classes ensuring intergenerational stock capital If the workers will leave inheritance at the end of period t, then the maximization problem (2.2) will need to incorporate the reason inheritance b, the inheritance received at the end of period and allowed to . The maximization problem of the worker is now:where is the government transfers equal to the tax collected on the inheritance. From the first order conditions, we have: Leaving the right side of the budget constraint of the workers due to and parameters: Inserting (3.3) in (3.4): Assuming the absence of technological progress, it follows that at the equilibrium , implying that: Knowing that W=Y−r, supposing a=0 and using (3.4), it follows that the equilibrium interest rate is given by: Notice that the interest rate arising from the behavior of the capitalists is given by: Eqs. (3.6) and (3.7) indicate that interest rates that maximize the plans of consumption and savings of the working and the capitalist classes cannot be equal. This means that one of the classes can require a different rate of accumulation than the other, causing the class with the lowest rate to disappear from the model. In this case, it would go back to the neoclassical model with only one type of representative agent. Differentiating and with respect to t, we have: The relationships (3.8) and (3.9) show an interesting result compared to the model Steedman (1973). As stated earlier in this paper, by using the same variables of the original models of Kaldor–Pasinetti, it turns out that the introduction of a direct tax on the profit mass will cause the profit rate of the economy (in the long run, supposedly equal to the equilibrium interest rate) to increase its value. The results, now with microfoundations, indicate that in a situation where the capitalist and working classes have their consumption/savings plans with optimized lifecycle and inheritance, they should necessarily follow a relationship of equilibrium, in which the interest rate is positively related to the interest rate. Steedman (1973) also showed that net interest rate of the taxes is exactly equal to the result of Pasinetti (1962). In this model, it can be observed from Eq. (3.7), that:The right side of (3.10) is exactly equal to the interest rate in the model without taxation, found by Baranzini (1991).