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Advanced Macro (Subject) / VL6 (Lesson)
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- Constant returns and Learning-by-Doing We assume that labor productivity is proportional to the existing stock of capital Et=EKt Many endogenous growth models assume technological progress is the outcome of "activities", such as R&D
- A Two-sector model Firms produce goods Research units (universities) produce knowledge Knowledge increases labor productivity in firms u = share of labor force employed in research units (exogenous) Y = F[K, (1-u)EL] Production function for research units: ΔE = g(u)E Capitl accumulation ΔK = sY - δK
- The Romer Model Further subdividing inputs into objects and ideas Objects: land, cell phone, oil, jet planes as well as capital and labor (from the Solow model) Ideas: instructions, recipes. ideas include designs for making objects, blueprints Ideas are not just created by engineering, also management techniques and just-in-time methods new ways of arranging raw materials Sustained growth occurs because of the discovery of new ideas to use the finite resources available to us
- Rivalry and non rivalry of objects and ideas Objects are rivalrous one person's use reduces the usefulness to someone else most goods in economics are rivalrous objects the principle of scarcity comes from that fact Ideas are non-rivalrous one person's use does not reduce the usefulness to someone else new ideas are sacarce; existing ideas are not scarce once an idea has been introduced it can be employes by an arbitrary number of people without anyone's use being degraded non-rivalry implies we do not need to reinvent ideas for additional use
- How a fixed cost leads to increasing return Antibiotic example High initial costs in developing the idea - then only manufacturing costs with ideas being there if doubling the objects or the ideas doubles outputs, doubling both will more than double production
- Problems with pure competition Pareto optimal allocation Cannot make someone better off without making someone else worse off Perfect competition results in pareto optimality because P = MC Under increasing returns to scale, no firm will invest in new ideas if P = MC there is an initial fixed cost of production firms will not have an incentive to engage in R&D if there is no return Thus, there must be a wedge between P and MC to make R&D worthwhile Patents: grant monopoly over a good for a period government funding prizes
- The Romer model there are constant returns to workers alone Yt=AtLyt production of new ideas depends on the existing ideas and the number of R&D workers producing ideas ΔAt+1=z*AtLat z = worker productivity Lyt =(1-l)L labor that produces output and Lat=lL Labor that produces ideas (resource constraint) l share how make ideas, L total workforce
- Solving the Romer Model 4 Equations Yt= AtLyt ΔAt+1=zAtLat Lyt+Lat= L Lat= lL 4 unknowns Yt, At, Lyt, Lat Parameters z L l A0
- Solving the Romer Model 4 Equations Yt= AtLyt ΔAt+1=zAtLat Lyt+Lat= L Lat= lL 4 unknowns Yt, At, Lyt, Lat Parameters z L l A0 Output per person depends on the stock of knowledge. new ideas benefit from all producers yt=Yt/L = At(1-l) The growth rate of knowledge is constant over time an is proportional to the number of researchers in the economy, which in turn is proportional to the population of the economy
- Why is there growth in the Romer Model? The Romer model generates long.run growth does not have diminishing returns to ideas because they are non-rivalrous as the economy accuulates new ideas, the returns to knowledge do not fall old ideas help in the production of new ideas that allow for sustained growth
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- Balanced growth Difference in Solow and Romer Solow (transition dynamics) has diminishing growth with getting closer to steady state Romer does not exhibit transition dynamics - the growth rate is constant at all points in time Economic can be said as to be in steady state from the very beginning - better being on a balanced growth path where the growth rates of all endogenous variables are constant
- Sensitivity analysis: Changing the population Changing the parameters in the romer model will alter the balanced growth path Suppose change in L leads to faster growth when rising (l constant) changing l will also increase growth rate but not output, that only in the long run