Answer to Question #294440 in Macroeconomics for Bunny

Question

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

Answer 1

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