Please, I urgently need this exercise. Area of expertise is macroeconomics: Solow growth model. Consider land as an additional productive factor and assume that theproduction function is:Y = A Xa L-a, 0< a <1where 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 < 1Capital can be produced while the land factor cannot be increased, i.e., itremains 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 zeroover time. Why does this result obtain?(d) Suggest some modification in the production function that maintains theproductive factor land but prevents the result in (c) from being obtained,showing that result.

Start by setting up the model. The production function is given by Y=AXαL1-α; X=DβK1-β We are told…

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Chapter1: Making Economics Decisions

Section: Chapter Questions

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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.

Branch of economics that analyzes the behavior and performance of an economy as a whole. It focuses on the study of aggregates and evaluates changes related to unemployment, gross domestic product, inflation, monetary and fiscal policies of the government.

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