Notes on an Endogenous Growth Model with two Capital Stocks II: The Stochastic Case



stock of human capital is equal to zero. The schooling technology implies that the
potential marginal and average product of human capital coincide and are equal to
B ,
whereas the realized marginal and average products are equal to
B (1 - ut). Note that
the depreciation rate of human capital is 100 percent per period.

2.3 The goods sector

We assume an infinitely large number of profit-maximizing firms producing a single good.
They are using a Cobb-Douglas technology in physical capital
kt and effective work htut .
Furthermore, the average skill of workers
ha,t has a positive influence on total factor
productivity. Hence, output
yt is determined by:

yt = Atktα (utht)1 hγa,t.                                   (5)

The parameter α is the output elasticity of physical capital and we assume α (0, 1).
The parameter
γ is non-negative and measures the degree of the external effect of human
capital. If we set
ut equal to one, we get the potential output in the goods sector. The
homogeneity of the agents implies that:

ha,t =ht,     tN0.                                  (6)

The state variable At denotes total factor productivity. Throughout this chapter, we
assume that ln
At follows a first-order autoregressive process, i.e.:

ln At+1 = ρln At + εt,     t N0    and ε ~ N (0,σ2) .         (7)

This assumption is a generalization of Bethmann (2002), where A was taken as fixed.
The firm has to rent physical and human capital on perfectly competitive factor markets.
In the decentralized economy, the representative firm’s profit Π in period
t is given by:

Π (kt, ht ; At, ha,t) = Atktα (utht)1 hγa,t - rtkt - wtutht,

where the semicolon indicates that the whole paths of ha,t and At are treated as exogenous
by the representative firm. The first-order necessary conditions for the profit-maximizing
factor demands are:

_ ∂yt _ αyt   sιnd   ,,,x = dyt   (1 (1-α)yt                        (8)

rt ∂kt = kt   and  wt (utht) = utht .                    (8)

These market-clearing factor prices ensure that the zero-profit condition holds. Inserting
the prices into the agent’s budget constraint (3) yields:

τrαyt + τw(1 - α)yt = ct + kt+1,     t N0.                   (9)

2.4 The state sector in the decentralized economy

In each period t, we require the state’s budget to be balanced. Therefore:

(τr - 1) rtkt = (1 - τw) wtutht                            (10)

must hold for all t N0 . This means that if we consider a tax on physical capital returns,
we are subsidizing work effort at the same time and vice versa. This remark ends the
presentation of the model. In Section 3, we solve the centralized version of this model.



More intriguing information

1. Segmentación en la era de la globalización: ¿Cómo encontrar un segmento nuevo de mercado?
2. Models of Cognition: Neurological possibility does not indicate neurological plausibility.
3. Imperfect competition and congestion in the City
4. The Value of Cultural Heritage Sites in Armenia: Evidence From a Travel Cost Method Study
5. Impacts of Tourism and Fiscal Expenditure on Remote Islands in Japan: A Panel Data Analysis
6. The name is absent
7. The Distribution of Income of Self-employed, Entrepreneurs and Professions as Revealed from Micro Income Tax Statistics in Germany
8. The name is absent
9. The name is absent
10. Analyse des verbraucherorientierten Qualitätsurteils mittels assoziativer Verfahren am Beispiel von Schweinefleisch und Kartoffeln
11. The name is absent
12. Innovation Trajectories in Honduras’ Coffee Value Chain. Public and Private Influence on the Use of New Knowledge and Technology among Coffee Growers
13. IMPLICATIONS OF CHANGING AID PROGRAMS TO U.S. AGRICULTURE
14. Industrial districts, innovation and I-district effect: territory or industrial specialization?
15. The duration of fixed exchange rate regimes
16. Understanding the (relative) fall and rise of construction wages
17. Towards a Mirror System for the Development of Socially-Mediated Skills
18. The Composition of Government Spending and the Real Exchange Rate
19. Strategic Planning on the Local Level As a Factor of Rural Development in the Republic of Serbia
20. The name is absent