辅导案例-OCTOBER 20

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IN CLASS ASSIGNMENT – 5 – OCTOBER 20

QUESTION-1:

Consider the below model:

    1YALKY

Where A is the stock of ideas, LY is the amount of labour used in the production of the final
good, K is the stock of capital and,  is the constant between 0 and 1. the law of month of A is:
 ALAA  ,  is constant between 0 and 1, LA is the labour devoted in the production new ideas.
We assume 0 and 1

The resource constraint of the economy is: LLL YA  and proportion devoted to both activities
is constant: RA sL
L  and RYY ssL
L  1 . The population grows at the rate of n i.e.:
nLLL YA  ˆˆˆ
The capital accumulation for the physical capital stock is: YsK K . Depreciation is assumed to
be zero.


(a) Show that, at any time, the growth of technology, gA, is:   LsAg RA 1 . Explain for
each of the two cases: 1 and 1 how the output of the research sector A , the
technological level A, and the technological growth rate Ag evolve over time when the
labour input into the research sector LsL RA  is constant.

(b) Derive the equation for the growth rate of capital per worker as: n
A
kssk YK 





1




(c) Give an intuitive explanation of what the parameters  and  between zero and one
imply.

(d) Assume now that  = 1 and  =0. Write down the equation for the growth rate of A at
the aggregate level, the growth rate of k =K/L and the growth rate of y=Y/L.

(e) Define a balanced growth path (BGP) in this model. Assume that along a BGP the growth
rates of LA and LY equal the rate of population growth (n). Derive the growth rate of A
and y along the BGP.




QUESTION-2:

A) Suppose economy’s output is produced according to the production function given as:
= ఈఊଵିఈିఊ
where B is an index of technology change, E is energy (extracted) input in production which
is equal to ௧ = ௘ . ௧ where se is energy extraction rate and Rt is initial energy stock, L is
labor. Parameters  and γ both are positive and between zero and one. Production function
exhibits constant returns to scale in K, L and E. And, BgB
BB 
ˆ , n
L
LL 
ˆ , and capital
accumulation equation is dKsYK  . From the bove model derive the growth rate of
output per worker along the BGP as: ො஻ீ௉ = − ഥ[௘ + ] where 

1
Bgg and
̅ = ቀ ఊ
ଵିఈ

B) Provide explanation by examining the growth rate of output per worker at the BGP for:
(i) = 0 (ii) > 0 (iii) g = 0 i.e. no technological progress (iv) as population growth (n)
increases.


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