Economic growth and economic development 586

Introduction to Modern Economic Growth 13.1 The Lab Equipment Model of Growth with Product Varieties We start with a particular version of the growth model with expanding varieties of inputs and an R&D technology such that only output is used in order to undertake research This is sometimes referred to as the lab equipment model, since all that is required for research is investment in equipment or in laboratories–rather than the employment of skilled or unskilled workers or scientists 13.1.1 Demographics, Preferences and Technology Imagine an infinitehorizon economy in continuous time admitting a representative household with preferences (13.1) Z∞ C (t)1−θ − dt exp (−ρt) 1−θ There is no population growth, and the total population of workers, L supplies labor inelastically throughout We also assume, as discussed in the previous chapter, that the representative household owns a balanced portfolio of all the firms in the economy Alternatively, we can think of the economy as consisting of many households with the same preferences as the representative household in each household holding a balanced portfolio of all the firms The unique consumption good of the economy is produced with the following aggregate production function: (13.2) Y (t) = 1−β "Z N(t) 1−β x(ν, t) # dν Lβ , where L is the aggregate labor input, N (t) denotes the different number of varieties of inputs (machines) available to be used in the production process at time t, and x (ν, t) is the total amount of input (machine) type ν used at time t We assume that x’s depreciate fully after use, thus they can be can be interpreted as generic inputs, as intermediate goods, as machines, or even as capital as long as we are comfortable with the assumption that there is immediate depreciation The assumption that the inputs or machines are “used up” in production or depreciate immediately after being used makes sure that the amounts of inputs used in the past not become additional state variables, and simplifies the exposition of the model (though the 572