The technological progress is stated as the engine of economic growth in the neoclassical growth model, but some models like Solow model, always set the technological progress as an exogenous variable with a constant rate g. Romer model indigences the technological progress, and also shows the relationship between population growth and economic growth, with the effect of labor force allocation taken into account. This assay is trying to analyze the micro foundations of the Romer model 1990, assess its conclusions, and discuss the allocation of labor in the model.
In 1980s, after the better understanding of modeling imperfect competition in a general equilibrium setting, economists was trying to develop growth models with micro foundations to explain the technology progress as an endogenized variable. Romer made an important contribution for explaining how to construct an economy of profit-maximizing agents that endogenizes technological progress, in 1990. The model consists of three sectors: the final goods sector, the intermediate goods sector and the R&D sector.
[...] - Large number of capital / intermediate goods - Constant return to scale (CRTS) The production function is exhibit as: < α < ( 1.1 ) In this function the output level is produced by using labor involved in the production LY, and a number of different capital goods xj. The capital goods are produced by intermediate sector, and the number of them here is treated as given. With constant return to scale, then the output function can be exhibit in a Cobb-Douglas form The maximisation If we assume the price of the final output, is normalize to unity, and then we can derive the following profit maximizing function: ( 1.2 ) pj: rental price for capital good j w : wage paid for labor Revenue Labor cost Cost of capital / intermediate goods Basically, this expression tells us to maximize the revenue minus the cost of labor and take out the cost of capital, we should be able to maximize the profit of the final goods sector. [...]
[...] ( 3.5 ) Because r is constant along balance growth path, then = 0 in the long- run, thus and must grow at the same rate, Therefore, Hence: ( 3.6 ) Assessment After detailed study of the market structure and the micro foundation in Romer model, we can see although the output function in final goods sector exhibit constant returns to scale, if we take the ideas A as an input, then the aggregate production function exhibits increasing rate of returns. [...]
[...] Therefore we can state the features of intermediate goods sectors as: - Monopolist -each producing only one capital good - Monopoly power derived from patent ownership purchase patent at fixed cost - Simple production function one unit of raw capital can be translated into one unit of the capital / intermediate good at marginal cost, r. If we also assume that the cost of purchasing the patent is fixed, then we can solve the maximization problem from: ( 2.1 ) pj is the demand function for the capital good from the equation ( 1.4 ) above: Then the first-order condition: ( 2.2 ) This derived expression shows us a very important relationship, which is the price p is the mark-up over the marginal cost r. [...]
[...] Empirical evidence Zvi Griliches and Edwin Mansfield, and others, estimated the ‘social' rate of return to research performed by firms, with the social rates of return on the order of 40 to 60 percent, which is far exceeding the private rates of return. As an empirical matter, this suggests that the positive externalities of research outweigh the negative externalities so that the market, even in the presence of modern patent system, tends to provide too little research. Conclusion After detailed study and deriving the micro foundation of the Romer model, and assessed its conclusions, what I am trying to solve here, is the problem of allocating labor force properly. Under the given assumptions, in final goods sector, intermediate goods sector, and R&D [...]
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