![]() ![]() Your task is to fill in the missing Platonic percent change in each row. Perhaps surprisingly, these equations are also very good approximations for other Constant-Returns-to-Scale production functions even when they are not Cobb-Douglas. These equations are exact with Platonic percentage changes and Cobb-Douglas with Constant Returns to Scale. Stay tuned for more on that later on in the semester. But total factor productivity growth %ΔY - %ΔX (= %ΔY - share_K %ΔK + share_L %ΔL when the only inputs are capital and labor) is an imperfect measure of technological change when their are increasing returns to scale (that is, when the degree of returns to scale γ = AC/MC > 1) or when the measures of inputs and outputs used are not comprehensive. It is often treated as a measure of technological change. The percent change in outputs minus the percent change in inputs %ΔY - %ΔX is called total factor productivity growth. Things will get more complicated when there are increasing returns to scale or other issues. It is also a technology improvement if output increases more than inputs. Technology improvements can show up as more output for the same input OR less input for the same output. In words, the change in technology is equal to the percent change in output minus the percent change in inputs overall (%ΔX). (Just to be clear about the notation, share_K and %ΔK are multiplying each other, and so on.) When (a) the degree of returns to scale is equal to 1 ("constant returns to scale"), and (b) the measures of input and output changes include everything, then the measure of technological progress is simply My post " The Shape of Production: Charles Cobb's and Paul Douglas's Boon to Economics" talks about this more in the case of constant-returns-to-scale Cobb-Douglas. s_L = share_L = WL/(RK+WL) is the cost share of labor (the share of the cost of the wages of labor in total cost.).s_K = share_K = RK/(RK+WL) is the cost share of capital (the share of the cost of capital rentals in total cost.).As long as the firm is minimizing costs, the weights will be equal to the share of costs coming from paying for each input: If different inputs change by different percentages, this is a weighted average of the percent changes in each different input. If each input changes by the same percentage, this is always equal to that percentage change in each input. ![]() Let %ΔX be an overall measure of the change in inputs. Here, let me start with the same beginning as to the "Returns to Scale Exercise":
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |