Question

Use a production function and the subsistence line from the Malthusian model to show that an advance in technology does not affect output per worker in the long run. Explain your diagram clearly.  

Answer 1

WK 4/819-04b Malthus To Perove model : & Technological Advance & Increase in Population & No long run • Assumptions. (1) Production function: Y22. FCL N e Total factor Land is Total No. of Workers Productivity " Function has constant retuans to scale and is increasing in both its arguments at a decreasing rate (2) Growth of Population depends on consumption per capital I AN = N + births - deaths. N+N( birth rate death rate) N'AN,) where N is population in Mont Period g is an increasing function of a : Rekets Using CRs property of production function, we can express output per capita as: yo řez. f(x) = 2 FALLIN), 2.5(45.2) ozf@) a output Evolution of per capita depends on hand per ofita. population can then be written as: N: N.ge) - N.goy) = mig (2ogle) CS Scanned with CamScanner

M T W T F S S M T W T F S S ZU Steady 320-045/Wk 46 state: Given the evolution of population, we can draw the following diagramta future population - g (2 F(2011) 'N s - Current population - 2 N* is a steady state; N=NEN" Here, it ih teme that Ni NigeCk) legeek) + (0* 27.9 (I) / At this lenel per capita consumption we know how much land per capita there & Sunday C* y* I = 2 (* = 2. f(l) & l Sunday ( * = L y ) DECEMBER Scanned with CamScanner

Diagramat ** population Growth e_popular wilN) E ngen und bestimmen -mx f ex e hard neu worker 2 So, improvements in the production of technology Cincrease in z) or the acquisition of more land 3 Cincrease in L lead to higher aggregate labore, & higher aggregate consumption, but donot lead to a A change in the long-run Standard of living, On cs Scanned with CamScanner