The production function Output per worker,y f(k) MPK=f(k+1)-f(k) Note:this production function exhibits diminishing MPK. Capital per worker,k CHAPTER 4 Economic Growth I slide 6
CHAPTER 4 Economic Growth I slide 6 The production function Output per worker, y Capital per worker, k f(k) Note: this production function exhibits diminishing MPK. 1 MPK =f(k +1) – f(k) 1.1
1.1 The national income identity 。Y=C+I(remember no G) In "per worker"terms: y=c+i where c=CL and i=IL
1.1 The national income identity • Y = C + I (remember, no G ) • In “per worker” terms: y = c + i where c = C/L and i = I/L
1.1 The consumption function 。s=the saving rate, the fraction of income that is saved (s is an exogenous parameter) Note:s is the only lowercase variable that is not equal to its uppercase version divided by L Consumption function:c=(1-s)y (per worker)
1.1 The consumption function • s = the saving rate, the fraction of income that is saved (s is an exogenous parameter) • Note: s is the only lowercase variable that is not equal to its uppercase version divided by L • Consumption function: c = (1–s)y (per worker)
1.2 Saving and investment saving (per worker)=y-c=y -(1-s)y=sy National income identity is y=c+I Rearrange to get:i =y -c =sy (investment saving ! Using the results above, i=sy =sf(k)
1.2 Saving and investment • saving (per worker) = y – c = y – (1–s)y = sy • National income identity is y = c + I Rearrange to get: i = y – c = sy (investment = saving !) • Using the results above, i = sy = sf(k)
1.2 Output,consumption,and investment Output per f(k) worker,y Ci yi- sf(k) K1 Capital per worker,k CHAPTER 4 Economic Growth I slide 10
CHAPTER 4 Economic Growth I slide 10 Output, consumption, and investment Output per worker, y Capital per worker, k f(k) sf(k) k1 y1 i1 c1 1.2