Tech.progress in the Solow model A new variable:E=labor efficiency Assume: Technological progress is labor-augmenting: it increases labor efficiency at the exogenous rate g. △E E CHAPTER 5 Economic Growth ll slide 5
CHAPTER 5 Economic Growth II slide 5 Tech. progress in the Solow model ▪ A new variable: E = labor efficiency ▪ Assume: Technological progress is labor-augmenting: it increases labor efficiency at the exogenous rate g: E g E = 1
1 Tech.progress in the Solow model -We now write the production function as: Y=F(K,L×E) where LxE the number of effective workers. Hence,increases in labor efficiency have the same effect on output as increases in the labor force. CHAPTER 5 Economic Growth ll slide 6
CHAPTER 5 Economic Growth II slide 6 Tech. progress in the Solow model ▪ We now write the production function as: ▪ where L E = the number of effective workers. – Hence, increases in labor efficiency have the same effect on output as increases in the labor force. Y F K L E = ( , ) 1
1 Tech.progress in the Solow model ■Notation: y=YLE output per effective worker k=KLE capital per effective worker Production function per effective worker: y=f(k) -Saving and investment per effective worker: sy=sf(k) CHAPTER 5 Economic Growth Il slide 7
CHAPTER 5 Economic Growth II slide 7 Tech. progress in the Solow model ▪ Notation: y = Y/LE = output per effective worker k = K/LE = capital per effective worker ▪ Production function per effective worker: y = f(k) ▪ Saving and investment per effective worker: s y = s f(k) 1
1 Tech.progress in the Solow model (+n+g)k break-even investment: the amount of investment necessary to keep k constant. Consists of: k to replace depreciating capital n to provide capital for new workers gk to provide capital for the new "effective"workers created by technological progress CHAPTER 5 Economic Growth ll slide 8
CHAPTER 5 Economic Growth II slide 8 Tech. progress in the Solow model ( + n + g)k = break-even investment: the amount of investment necessary to keep k constant. Consists of: k to replace depreciating capital n k to provide capital for new workers gk to provide capital for the new “effective” workers created by technological progress 1
i Tech.progress in the Solow model Investment, △k=sfk)-(6+n+g)k break-even investment (6+n+g)k sf(k) K* Capital per worker,k CHAPTER 5 Economic Growth ll slide 9
CHAPTER 5 Economic Growth II slide 9 Tech. progress in the Solow model Investment, break-even investment Capital per worker, k sf(k) ( +n +g)k k * k = s f(k) − ( +n +g)k 1