2 Depreciation Depreciation 8=the rate of depreciation per worker,k the fraction of the capital stock that wears out each period Sk 1 Capital per worker,k CHAPTER 4 Economic Growth I slide 11
CHAPTER 4 Economic Growth I slide 11 Depreciation Depreciation per worker, k Capital per worker, k k = the rate of depreciation = the fraction of the capital stock that wears out each period 1 1.2
Change in Capital Stock Change in capital stock investment depreciation 10 △k= Sk Since i=sfk),this becomes: △k=SfK)-6k CHAPTER 4 Economic Growth I slide 12
CHAPTER 4 Economic Growth I slide 12 Change in Capital Stock • Change in capital stock = investment – depreciation k = i – k Since i = sf(k) , this becomes: k = s f(k) – k 1.2
The equation of motion for k △k=sfk)-6k the Solow model's central equation -Determines behavior of capital over time. -.which,in turn,determines behavior of all of the other endogenous variables because they all depend on k.E.g., income per person:y=fk) C consump.per person:c (1-s)fk) CHAPTER 4 Economic Growth I slide 13
CHAPTER 4 Economic Growth I slide 13 The equation of motion for k ▪ the Solow model’s central equation ▪ Determines behavior of capital over time. ▪ .which, in turn, determines behavior of all of the other endogenous variables because they all depend on k. E.g., income per person: y = f(k) C consump. per person: c = (1–s)f(k) k = s f(k) – k 1.2
The steady state △k=SfK)-6k .If investment is just enough to cover depreciation [sfk)=6k], then capital per worker will remain constant: △k=0. This constant value,denoted*is called the steady state capital stock. CHAPTER 4 Economic Growth I slide 14
CHAPTER 4 Economic Growth I slide 14 The steady state •If investment is just enough to cover depreciation [sf(k) = k ], then capital per worker will remain constant: k = 0. This constant value, denoted k * , is called the steady state capital stock. k = s f(k) – k 1.2
