Consider the Cobb-Douglas production function in continuous time, 𝒀(𝒕) = 𝑲(𝒕)
𝟏
𝟒(𝑯(𝒕))
𝟑
𝟒,
𝑯(𝒕) = 𝐀(𝒕)𝑳(𝒕), 𝒌̇(𝒕) = 𝒔𝒇(𝒌(𝒕)) − (𝒈𝑨 + 𝒏 + 𝜹)𝒌(𝒕),
𝑨̇(𝒕)
𝑨(𝒕)
= 𝒈𝑨,
𝑳̇(𝒕)
𝑳(𝒕)
= 𝒏 𝒚(𝒕) = 𝒄(𝒕) +
𝒊(𝒕) + 𝒈(𝒕), where, 𝒈(𝒕) = 𝝈𝒚(𝒕) and 𝝈 > 𝟎. Answer the following questions-
(i) Derive the intensive form production function in per-capita terms. (1 Mark)
(ii) what is the steady-state and Golden-rule level of capital-output ratio and consumption? (2
Marks)
(iii) Explain the effect of government expenditure on output at the golden rule
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