In this problem, you are asked to derive the Solow growth model and some of its implications. The model is a model of capital accumulation, and it consists of a production technology, a law of motion for capital, and a rule that decides how to split output between consumption and investment.
Timing and initial condition: The variable t indexes time. The economy starts in period t=0, and continues through periods t=1,2,3,dots and so on. In period t=0, the economy starts with a given amount of capital K_(0).
Production technology: Every period, output Y_(t) is produced using capital K_(t) and labor L_(t) with a Cobb-Douglas production technology:
Y_(t)=AK_(t)^(alpha )L_(t)^(1-alpha ).
Law of motion for capital: Capital depreciates every period at rate delta , and every period, new investment I_(t) adds to the capital stock that is available next period:
K_(t+1)=(1-delta )K_(t)+I_(t).
Resource constraint: Every period, output is divided for use as consumption or Investment:
Y_(t)=C_(t)+I_(t)
Savings function: The amount of output used for investment is given by a fixed saving rate s. Remember that the saving rate is the share of investment in output: s=(I_(t))/(Y_(t)). Therefore
I_(t)=sY_(t).
Fixed labor supply: The number of workers available for employment is fixed at /bar (L) :
L_(t)()/(b)=ar (L)
Question 1.8 Into the same graph, sketch the depreciation delta K_(t) as a function of K_(t). What is the slope of this function?
Question 1.8 Into the same graph,sketch the depreciation &K as a function of K. What is the slope of this function?