Suppose that the net investment flow is described by the equation I(t) = 3t/2 and that %3D the initial capital stock, at time t = 0, is K(0). What is the time path of capital K?

Exploring Economics
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ISBN:9781544336329
Author:Robert L. Sexton
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Chapter16: The Markets For Labor, Capital, And Land
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Suppose that the net investment flow is described by the equation I(t) = 3t/2 and that
the initial capital stock, at time t= 0, is K(0). What is the time path of capital K?
If net investment is a constant flow at I(t) = 1000 (Ghana Cedis per year), what will be
the total net investment (capital formation) during a year, from t= 0 to t= 1?
If I(t) = 3t/2 (thousands of Ghana Cedis per year) – a nonconstant flow – what will be
the capital formation during the time interval [1, 4], that is, during the second, third, and
fourth years?
i) Show that the Cobb-Douglas production
Q=AK*L-a
where Q is total output, Kis capital stock, Lis labour stock and A and a are positive
stants, exhibit constant returns to scale.
ii) What returns to scale does Q=5K025 L06 exhibit?
Transcribed Image Text:Suppose that the net investment flow is described by the equation I(t) = 3t/2 and that the initial capital stock, at time t= 0, is K(0). What is the time path of capital K? If net investment is a constant flow at I(t) = 1000 (Ghana Cedis per year), what will be the total net investment (capital formation) during a year, from t= 0 to t= 1? If I(t) = 3t/2 (thousands of Ghana Cedis per year) – a nonconstant flow – what will be the capital formation during the time interval [1, 4], that is, during the second, third, and fourth years? i) Show that the Cobb-Douglas production Q=AK*L-a where Q is total output, Kis capital stock, Lis labour stock and A and a are positive stants, exhibit constant returns to scale. ii) What returns to scale does Q=5K025 L06 exhibit?
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