Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
Publisher:NICHOLSON
Chapter9: Production Functions
Section: Chapter Questions
Problem 9.2P
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Please, I urgently need this exercise. Area of expertise is macroeconomics: Solow growth model. 

Consider land as an additional productive factor and assume that the
production function is:
Y = A Xa L-a, 0< a <1
where 0 < a < 1, and X is a factor composed of the factors land (D) and capital
(K), such that:
X = DB K1-B ,
0 < B < 1
Capital can be produced while the land factor cannot be increased, i.e., it
remains in time. Let s,n and & be positive constants.
(a) Express the production function per worker in terms of land per worker (d)
and capital per worker (k).
b) Write the equation for the increase in capital per worker (k).
(c) Show that this model implies that the level of output per worker tends to zero
over time. Why does this result obtain?
(d) Suggest some modification in the production function that maintains the
productive factor land but prevents the result in (c) from being obtained,
showing that result.
Transcribed Image Text:Consider land as an additional productive factor and assume that the production function is: Y = A Xa L-a, 0< a <1 where 0 < a < 1, and X is a factor composed of the factors land (D) and capital (K), such that: X = DB K1-B , 0 < B < 1 Capital can be produced while the land factor cannot be increased, i.e., it remains in time. Let s,n and & be positive constants. (a) Express the production function per worker in terms of land per worker (d) and capital per worker (k). b) Write the equation for the increase in capital per worker (k). (c) Show that this model implies that the level of output per worker tends to zero over time. Why does this result obtain? (d) Suggest some modification in the production function that maintains the productive factor land but prevents the result in (c) from being obtained, showing that result.
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