ECON 313 Lecture Notes - Lecture 6: Scale Parameter, Production Function, Diminishing Returns

• School: McGill University
• Department: Economics
• Course: ECON 313
• Professor: Sonya Laszlo

Document Summary

Solow growth model: capital accumulation: capital stock at time t: kt, depre(cid:272)iatio(cid:374): (cid:1004) (cid:1005, capital stock at time t+1, kt+1 = kt + it - kt. = it + (1 - )kt: rearranging: Solow growth model: production function: suppose z = 1/lt, then average labor productivity (productivity/unit of labor), (cid:3013)=(cid:4672)(cid:3012)(cid:3013),(cid:3013)(cid:3013)(cid:4673, yt = f(kt) = (cid:3047) St = syt = it: combine with capital accumulation, kt+1 = it + (1 - )kt. If k" < k*: (cid:894)(cid:1005)+(cid:374)(cid:895)k" < sa(cid:894)k"(cid:895) + (1 - (cid:895)k": accumulate more capital/worker. If k"" > k*: (cid:894)(cid:1005)+(cid:374)(cid:895)k"" < sa(cid:894)k""(cid:895) + (1 - (cid:895)k"": reduce capital/worker. Implications for growth: output per worker in equilibrium is constant, but the total output (y) grows at rate n. Implications for savings: an increase of savings rate leads to higher steady state levels of k and y. Implications for population: high population growth rates lead to lower steady state levels of k and y.