(SOLVED)Consider a version of Solow's Model

Question

Consider a version of Solow's Model: Yt​=AKtα​Lt1−α​sYt​=Kt+1​−Kt​+δKt​Lt​=L0​(1+n)t​ 1

 a) Rewrite the production function and the equation of capital accummulation using variables normalized by the units of labor, i.e. k=K/L;y=Y/L

b) What are the values of k and y in a steady state? What are the growth rates of aggregate output and aggregate consumption? Consider this different version of Solow's Model:

Yt​=AKtα​(Et​Lt​)1−αsYt​=Kt+1​−Kt​+δKt​Lt​=L0​(1+n)tEt​=E0​(1+x)t​

c) Rewrite the production function and the equation of capital accummulation using variables normalized by the units of effective labor, i.e. k=K/(EL);y=Y/(EL).

d) What are the values of k and y along a balanced growth path? What is the growth rate of aggregate output and aggregate consumption along this BGP?

EXPERT SOLUTION PREVIEW

a) The production function and equation of capital accumulation in this version of Solow's model can be rewritten in terms of variables normalized by units of labor as follows:

Explanation

Production Function:

y = Y/L = AK/L^(1-a) = Ak^a, where k = K/L

Capital Accumulation Equation:

dk/dt = sAk^a - (d+g)k, where k = K/L

where y denotes output per hour worked, k denotes capital per hour worked, s denotes savings rate, d denotes depreciation rate, and g denotes population......