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Models for dynamic macroeconomics phần 7

Tập thể dục 18 dòng chảy doanh thu của công ty được đưa ra bởi R (K, N) = 2K 1 / 2 N 1 / 2, trong đó N là một yếu tố tự do điều chỉnh, đã trả một mức lương w (t) tại thời điểm t; K là tích lũy theo ˙ K = I - ‰ K, và dòng chảy đầu tư chi phí G (I) = I + 1 I 2. 2 (Lưu ý rằng Vn = 1, do đó q = Î.) (A) (b) | EQUILIBRIUM GROWTH 155 sion would complicate the analysis without providing substantially different results. Much more important is the implicit assumption that the efficiency of each unit of labor does not depend on its own productive activity but rather on aggregate economic activity. Agents in this economy learn not only from their own mistakes so to speak but also from the mistakes of others. When deciding how much to invest agents do not consider the fact that their actions affect the productivity of the other agents in the economy the economic interactions are thus affected by externalities. These externalities are similar albeit with an opposite sign to the externalities that one encounters in any basic textbook treatment of pollution or to those that we will discuss in Chapter 5 when we consider coordination problems. If we retain the assumptions that firms produce homogeneous goods with the constant-returns-to-scale production technology F Kj ANj that A is non-rival and non-excludable and that all markets are perfectly competitive then output decisions can be decentralized as in Section 4.3. In particular the marginal productivity of capital needs to coincide with r t the rate at which it is remunerated in the market . . dF _ . __ r t dTF2 F1 . f K L d K and the dynamic optimization problem of households implies a proportional growth rate of consumption equal to r t p ơ if the function of marginal utility has constant elasticity. Hence recalling that L AN it follows that both individual and aggregate consumption grow at a rate C t C t If as in the case of a Cobb-Douglas function the economy distributes a constant or non-vanishing share of national income to the non-accumulated factor then limj TO f k 0 p and consumption growth can remain positive only if A and L grow together with K which would prevent the marginal productivity of capital from approaching zero. However since A is a function of k in the model of this section the growth of A itself .