Government policy to reduce pollution emissions within the overlapping generations model

Abstract

This article develops an overlapping generations model with multiple categories of capital. The importance of this article is in its ability to analyse changes in the distribution of various categories of capital along the growth path of the economy. Economic growth is accompanied by capital growth as well as increase in pollution emissions. Implementing a government policy to reduce pollution emission would change the equilibrium path of capital distribution. Within the model, the government builds a corporate tax function that defines the tax rate as a function of a ‘desired’ pollution level. The tax rate decreases as the ‘desired’ pollution level is higher. When the ‘desired’ pollution level is higher than the actual pollution level, production is subsidized and pollution levels rise. An example and a simulation are presented in order to confirm the theoretical results and demonstrate that the model can be used for empirical analysis.

Notes

¹ Y_t is production after covering depreciation, (1 + r)dK_t (notice that depreciation here is in terms of future value).

² This assumption enables us to avoid the discussion on prices of each category of capital. Measuring by constant dollars does not mean that the various kinds of capital are sold for the same price, but that their economic dollar value represents quantities and not nominal value.

³ We can define the productivity of each kind of capital according to its relative contribution to output F_Kit K_{i , t} /Y_t . We can expect that capital K_p would be employed more intensively than K_p−1 , so that its relative contribution to output would be larger.

⁴ I used the simplifying assumption that government savings, as well as government product equals zero. This assumption means that the government uses all tax income to buy services and products and does not produce by itself.

⁵ The entrepreneurs maximize PV:

and we get: dPV/dK _i,t + 1 = [(MPK _i,t + 1 + (1 − d _t + 1))(1 + r _t + 1)] − 1 = 0⇒MPK _i,t + 1 = r _t + 1 + d _t + 1.

⁶ Producers would decide the distribution of capital by maximizing the following expression:s

⁷ We should notice that K_p is more productive then K _p−1,… etc.

⁸ MPK _{i , t +1} is calculated by differentiating Equation 4a in respect to K_{i , t +1}.

⁹ Vardanyan and Dong-Woon (2006) demonstrated that different parameterization methodologies can produce different shadow prices of socially undesirable outputs.

¹⁰ We can define δ in many ways, for example,

In this case the size of δ would represent an average of the λ's.

¹¹ We should notice that it's a constant return to scale production function.

¹²

¹³ If emission is not positively connected to productivity, we should define a higher λ for a more polluting capital.