3 child takes intermediate values In this case the bubble raises capital

3 child takes intermediate values in this case the

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child takes intermediate values. In this case, the bubble raises capital because a larger amount of productive investment is required to finance savings at the middle-age. Our model also allows us to contribute to the debate on the link between population size and the asset price. We associate the asset price to the bub- ble on the speculative asset and a larger ratio of adult over young households means that the main buyers of the speculative asset are relatively more. The comparison of the bubbly and bubbleless BGPs allows us to observe the same link than Geanakoplos et al. (2004) find between the asset price and the demog- raphy, i.e. the BGP associated with the larger value of the asset (the bubbly one) is also characterized by a larger ratio of adult over young households. How- ever, our result should be interpreted in a different way: in our framework with endogenous fertility, the fall of the price of the speculative asset that follows a market crash of the bubble explains the smaller ratio of adult over young rather than the opposite. This paper is organized as follows. In the next section, we present the model. In Section 3, we analyze the economy without bubble. In Section 4, we characterize an equilibrium with a bubble. In Section 5, we show the ex- istence of an asymptotic bubbly BGP. We analyze whether a bubble may be productive in Section 6. In Section 7, we interpret our results according to the crowding-out versus crowding-in effects. Concluding remarks are provided in Section 8, while some technical details are relegated to an Appendix. 2 Model Time is discrete ( t = 0, 1, ..., + ) and there are two types of agents, households and firms. 2.1 Firms Aggregate output is produced by a continuum of firms, of unit size, using la- bor, L t , and capital, K t , as inputs. This capital can be interpreted broadly to include human capital (training, master programs). In addition, production benefits from an externality that summarizes a learning by doing process and allows to have sustained growth. Following Frankel (1962) or Ljungqvist and Sargent (2004, chapter 14), this externality depends on the average capital-labor ratio. Letting k t K t / L t , k t represents the average capital-labor ratio. Firms pro- duce the final good with the following technology: Y t = F ( K t , ¯ k t L t ) The technology F ( K t , ¯ k t L t ) has the usual neoclassical properties, i.e. is a strictly increasing and concave production function satisfying the Inada conditions, and is homogeneous of degree one with respect to its two arguments. 4
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Profit maximization under perfect competition implies that the wage w t and the return of capital q t are given by 4 w t = F 2 ( K t , ¯ k t L t ) ¯ k t (1) q t = F 1 ( K t , ¯ k t L t ) (2) 2.2 Households We consider an overlapping generations economy populated by agents living for three periods. An agent is young at the first period of life, adult at the second period and old at the third period. As it is argued by Geanokoplos et al. (2004), such a demographic structure is a reasonable representation of the households’ life-cycle.
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  • Spring '10
  • Economics, Capital accumulation

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