[Solved] Assignment 219497

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Assignment Details

Subject: Economics    / General Economics
Question
III-III TELUS ‘2"? T513244 L G} 39% 1-:1’5′ ? Queens University at KingstonConsider a simple growth model with population growth, labour-augmenting tech-
nology growth, and human and physical capital. Suppose that the aggregate production
function takes the following form:W) = KGVHUW [A{f)N(t)]’_"_?- {2)where Y0) denotes output, K (t) physical capital, and H (t) human capital. N0} is labour,
and AU) denotes the level of technology. Note that A(I)N(t) is commonly referred as
effective labour. Assume a > 0, ,6 :r- U and or + ,6 c 1. Output can he used on a one-for-
one basis for consumption or investment in either type of capital. Let y{t) = %, k-{r} = 3%, and so) = ,??g?, . ta}Derive the intensive form of the production function in terms of effective labour. N and A grow at constant rates it and g, respectively {i.e. W = n, and ”limit—Am = g ]. Both types of capital depreciate at the rate d. Assume that gross invest- ment in physical capital is a fraction as of output and that gross investment in human
capital is a fraction 3H of output Also physical capital accumulation and human capital
accumulation are: to +1)— Kn)
H(r+1)—H(t) Mt) – dtKitl)
IHU) – leUl}(b) Use the laws of motion for k and h to obtain the steady state conditions for this
economy (the steady state conditions for both physical and human capital stocks).(c) What are the steady-state values of physical capital, human capital, and output, all in
per unit of effective labour?(d) Given the result in (c), solve for the steady state level of consumption per unit of
effective worker. Now consider the growth model with population growth, labour-augmenting tech-
nology growth, and only physical capital. Therefore the aggregate production function
takes the form; W) = KU)” [I‘lltflx’t-‘(IllHI 2 (simply remove H from the production function and set {3 equal to zero.) where, as before,
denote the population growth rate as n, technology growth rate as g, and the depreciation
rate as d.(e) Solve for the Golden rule level of capital per unit of effective worker, k5.

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