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4. (a) y(t) = K₂( AE(t)) Fd E(t)= (1-Ø I(+)) | Ka [Ā (1-Ø I(t)) L] 1-2 In (Y₁x)) = b[ Rα [Ã (1-PI(+)) L]~*I 1-2

4. (a) y(t) = K₂( AE(t)) Fd E(t)= (1-Ø I(+)) | Ka [Ā (1-Ø I(t)) L] 1-2 In (Y₁x)) = b[ Rα [Ã (1-PI(+)) L]~*I 1-2

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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question a) only :)

I am thinking sub E(t) into Y(t), take log and do the partial derivative. But I am stucking in doing the partial derivative.

Appreciate your help.

E(t)= (1-Ø I(+)) L Ka [Ã (1-Ø Ict)) L] 1-2 m(Y₁t)) = m ( Kα [Ã (1-p Ict))L] 1-2) 2 4. (a) y(t) = K₂( AE(t)) ³d 3
Transcribed Image Text:E(t)= (1-Ø I(+)) L Ka [Ã (1-Ø Ict)) L] 1-2 m(Y₁t)) = m ( Kα [Ã (1-p Ict))L] 1-2) 2 4. (a) y(t) = K₂( AE(t)) ³d 3
4. The Covid Economic Slump: Let's consider the economic impact of the pandemic on the economy. Assume that the pandemic evolves according to the basic SIR model: S and i R = = = -BS(t)I(t) BS(t)I(t) — YI (t) yI(t) with initial conditions S(0), I(0), and R(0), satisfying S(0) + I(0) + R(0) = 1 (1) (2) (3) S+I+R=0⇒ S(t) + I(t) + R(t) = 1 for all t≥ 0. Assume that some fraction 0 < ¢ ≤ 1 of infected people are too sick to work. This implies that during the pandemic the effective labour force E(t) is given by E(t) = (1 − þI(t))ī, where we assume the labour (Ī) is fixed and does change over time. Finally, assume that production is Cobb-Douglas such that Y(t) = Kº(ÃE(t))¹-α, where capital is fixed (K) and technology (Ā) are fixed. (a) Find an expression for the growth rate of output in terms of the growth rate of infections 91 = İ/I(t). Is output growth positively or negatively related to infection growth?
Transcribed Image Text:4. The Covid Economic Slump: Let's consider the economic impact of the pandemic on the economy. Assume that the pandemic evolves according to the basic SIR model: S and i R = = = -BS(t)I(t) BS(t)I(t) — YI (t) yI(t) with initial conditions S(0), I(0), and R(0), satisfying S(0) + I(0) + R(0) = 1 (1) (2) (3) S+I+R=0⇒ S(t) + I(t) + R(t) = 1 for all t≥ 0. Assume that some fraction 0 < ¢ ≤ 1 of infected people are too sick to work. This implies that during the pandemic the effective labour force E(t) is given by E(t) = (1 − þI(t))ī, where we assume the labour (Ī) is fixed and does change over time. Finally, assume that production is Cobb-Douglas such that Y(t) = Kº(ÃE(t))¹-α, where capital is fixed (K) and technology (Ā) are fixed. (a) Find an expression for the growth rate of output in terms of the growth rate of infections 91 = İ/I(t). Is output growth positively or negatively related to infection growth?
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