Assume an output production function Y(t) = A(t)(1 - aL) L(t) and a production function of new ideas A(t) = B[aLL(t)] A(t) - SA9A(t)A(t) where бA is the rate at which the current stock of ideas becomes obsolete over time. Also, assume population grows at rate n. This setup of the endogenous growth model implies that ġ₁(t) = yng₁(t) + (0 − 1)gå(t)², where gд(t) is the growth rate of knowledge. (a) [TYPE IN TEXT EDITOR] Suppose that is greater than zero. What does this imply for the relationship between the current level of technology and the growth rate of ideas? (b) [UPLOAD WORKING] If = 1 and n = 0, derive the steady-state growth rate of ideas. How, if at all, does a decrease in the rate of obsolescence A affect the steady-state growth of knowledge in this case?
Assume an output production function Y(t) = A(t)(1 - aL) L(t) and a production function of new ideas A(t) = B[aLL(t)] A(t) - SA9A(t)A(t) where бA is the rate at which the current stock of ideas becomes obsolete over time. Also, assume population grows at rate n. This setup of the endogenous growth model implies that ġ₁(t) = yng₁(t) + (0 − 1)gå(t)², where gд(t) is the growth rate of knowledge. (a) [TYPE IN TEXT EDITOR] Suppose that is greater than zero. What does this imply for the relationship between the current level of technology and the growth rate of ideas? (b) [UPLOAD WORKING] If = 1 and n = 0, derive the steady-state growth rate of ideas. How, if at all, does a decrease in the rate of obsolescence A affect the steady-state growth of knowledge in this case?
Chapter1: Making Economics Decisions
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![Assume an output production function Y(t) = A(t)(1 – aL)L(t) and a production function of new ideas A(t) = B[aLL(t)]" A(t)º – 849A(t)A(t) where d4 is the rate at which the
current stock of ideas becomes obsolete over time. Also, assume population grows at rate n. This setup of the endogenous growth model implies that ġ A(t) = yngA(t)+(0 – 1)gA(t)²,
where ga(t) is the growth rate of knowledge.
(a) [TYPE IN TEXT EDITOR] Suppose that 0 is greater than zero. What does this imply for the relationship between the current level of technology and the growth rate of ideas?
(b) [UPLOAD WORKING] If 0 = 1 and n = 0, derive the steady-state growth rate of ideas. How, if at all, does a decrease in the rate of obsolescence 8A affect the steady-state growth of
knowledge in this case?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6c4ae283-2192-496d-bd83-1077decf4882%2Ff5f5d06e-19e2-4f38-a9cc-555752cd6286%2Fuh8465g_processed.png&w=3840&q=75)
Transcribed Image Text:Assume an output production function Y(t) = A(t)(1 – aL)L(t) and a production function of new ideas A(t) = B[aLL(t)]" A(t)º – 849A(t)A(t) where d4 is the rate at which the
current stock of ideas becomes obsolete over time. Also, assume population grows at rate n. This setup of the endogenous growth model implies that ġ A(t) = yngA(t)+(0 – 1)gA(t)²,
where ga(t) is the growth rate of knowledge.
(a) [TYPE IN TEXT EDITOR] Suppose that 0 is greater than zero. What does this imply for the relationship between the current level of technology and the growth rate of ideas?
(b) [UPLOAD WORKING] If 0 = 1 and n = 0, derive the steady-state growth rate of ideas. How, if at all, does a decrease in the rate of obsolescence 8A affect the steady-state growth of
knowledge in this case?
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