Let an economy be given by:
Y = AK + R
Where A and K are technology and capital, respectively, applied in a non-resource sector of the economy. R is the exogenously determined value of resource production. Let the savings rate be given by s and let capital depreciate at rate?. Assume there is zero growth in technology.
a) Is it possible for this economy to grow perpetually into the future?
b) Solve for the capital accumulation equation?.
c) Let the growth rate of the economy be given by G, noting that
and hence that
solve for G.
d) How does a one time positive resource shock (an increase in R) effect i) income levels and ii) income growth?
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