Suppose that total factor productivity, A,, fluctuates in the Solow model. In particular: A₁ = A=1 if t = 0,3,6,... A₁ A1 ift-1,4,7,... A₁ = AL < 1 if t = 2,5,8,... Also suppose that the saving and depreciation rate are some positive constants s and 6, re- spectively, and that population and labor force remain constant over time. Finally, the aggregate production function is given by: Y₁ = A₁ KoN- a) Solve for GDP per worker, y=Y₁/N₁. Like we did in last class, show in a dynamic diagram how the economy will experience fluctuations in real income, i.e., "business cycles". What do these artificial cycles look like and in what ways do they resemble real macroeconomic

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)
14th Edition
ISBN:9781305506381
Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Chapter5: Business And Economic Forecasting
Section: Chapter Questions
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Suppose that total factor productivity, A, fluctuates in the Solow model. In particular:
if t = 0,3, 6, ...
if t = 1,4, 7,...
if t = 2, 5, 8, ...
A = Ã = 1
A, - An >1
A - AL <1
Also suppose that the saving and depreciation rate are some positive constants s and 6, re-
spectively, and that population and labor force remain constant over time. Finally, the aggregate
production function is given by:
Y; = A, Kª N}-a
a) Solve for GDP per worker, y := Y;/N. Like we did in last class, show in a dynamic diagram
how the economy will experience fluctuations in real income, i.e., "business cycles". What
do these artificial cycles look like and in what ways do they resemble real macroeconomic
fluctuations?
b) Show how the values (Ỹ , Y1, Yu) depend on the parameters (a, 8, 6, Ā, AL, Aµ). Explain
carefully.
c) Solve for the capital to output ratio and show how it depends on the parameter space
(a, s, 6, Ā, AL, Au). Explain carefully.
Transcribed Image Text:Suppose that total factor productivity, A, fluctuates in the Solow model. In particular: if t = 0,3, 6, ... if t = 1,4, 7,... if t = 2, 5, 8, ... A = Ã = 1 A, - An >1 A - AL <1 Also suppose that the saving and depreciation rate are some positive constants s and 6, re- spectively, and that population and labor force remain constant over time. Finally, the aggregate production function is given by: Y; = A, Kª N}-a a) Solve for GDP per worker, y := Y;/N. Like we did in last class, show in a dynamic diagram how the economy will experience fluctuations in real income, i.e., "business cycles". What do these artificial cycles look like and in what ways do they resemble real macroeconomic fluctuations? b) Show how the values (Ỹ , Y1, Yu) depend on the parameters (a, 8, 6, Ā, AL, Aµ). Explain carefully. c) Solve for the capital to output ratio and show how it depends on the parameter space (a, s, 6, Ā, AL, Au). Explain carefully.
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