Steady-State Growth Rates in the Solow Model with Tech.Progress Variable Symbol Steady-state growth rate Capital per effective worker k=KW(L×E) 0 Output per 0 effective worker y=YY(L×E) Output per worker (YML)=y×E Total output Y=y×E×L n+g CHAPTER 5 Economic Growth Il slide 10
CHAPTER 5 Economic Growth II slide 10 Steady-State Growth Rates in the Solow Model with Tech. Progress Total output Y = y E L n + g Output per worker (Y/ L) =y E g y =Y/(L E ) 0 Output per effective worker k =K/(L E ) 0 Capital per effective worker Steady-state growth rate Variable Symbol 1
The Golden Rule To find the Golden Rule capital stock, express c*in terms of k*: c*=y* * In the Golden Rule Steady State, =f(k*)-(δ+n+g)* the marginal c*is maximized when product of capital MPK=8+n+g net of depreciation equals the or equivalently, pop.growth rate MPK-6=n+g plus the rate of tech progress. Return CHAPTER 5 Economic Growth ll slide 11
CHAPTER 5 Economic Growth II slide 11 The Golden Rule To find the Golden Rule capital stock, express c * in terms of k* : c * = y* − i * = f (k* ) − ( +n +g)k* c * is maximized when MPK = + n + g or equivalently, MPK − = n + g In the Golden Rule Steady State, the marginal product of capital net of depreciation equals the pop. growth rate plus the rate of tech progress. 1 Return
2.1 Evaluating the Rate of Saving Use the Golden Rule to determine whether our saving rate and capital stock are too high, too low,or about right. To do this,we need to compare (MPK-6)to (n +g). ·If(MPK-δ)>(n+g),then we are below the Golden Rule steady state and should increase s. -If (MPK-6)<(n+g),then we are above the Golden Rule steady state and should reduce s. CHAPTER 5 Economic Growth ll slide 13
CHAPTER 5 Economic Growth II slide 13 Evaluating the Rate of Saving ▪ Use the Golden Rule to determine whether our saving rate and capital stock are too high, too low, or about right. ▪ To do this, we need to compare (MPK − ) to (n + g ). ▪ If (MPK − ) > (n + g ), then we are below the Golden Rule steady state and should increase s. ▪ If (MPK − ) < (n + g ), then we are above the Golden Rule steady state and should reduce s. 2.1