Consider the two-sector macroeconomic model of a fictitious country: dy dt C = 0.5 Y + 540 I = 425 Where C = consumption; I = investment and Y = national income. = = 0.034(C + 1 – 0.6 Y) Determine the following: (a) If Y(0) = 14,000, find an expression for y(t) by solving the differential equation.
Consider the two-sector macroeconomic model of a fictitious country: dy dt C = 0.5 Y + 540 I = 425 Where C = consumption; I = investment and Y = national income. = = 0.034(C + 1 – 0.6 Y) Determine the following: (a) If Y(0) = 14,000, find an expression for y(t) by solving the differential equation.
Chapter1: Making Economics Decisions
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![Consider the two-sector macroeconomic model of a fictitious country:
dy
dt
C = 0.5 Y + 540
I = 425
Where C = consumption; I = investment and Y = national income.
= 0.034(C+I - 0.6 Y)
Determine the following:
(a) If Y(0) = 14,000, find an expression for Y (t) by solving the differential equation.
(b) Find the time taken for income to fall to 13,000.
(c) Is the system stable or unstable? Explain your answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6ebc874b-7ada-4b34-8f4d-6cf62146e8c5%2F1a5223ed-5372-4f44-aeef-39156591bd1a%2F8vk1l1g_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the two-sector macroeconomic model of a fictitious country:
dy
dt
C = 0.5 Y + 540
I = 425
Where C = consumption; I = investment and Y = national income.
= 0.034(C+I - 0.6 Y)
Determine the following:
(a) If Y(0) = 14,000, find an expression for Y (t) by solving the differential equation.
(b) Find the time taken for income to fall to 13,000.
(c) Is the system stable or unstable? Explain your answer.
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