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# The Solow-Swan model

Consider the Solow-Swan model in continuous time with the Cobb-Douglas aggregate production function, y = k
α, constant savings rate s, depreciation rate δ, productivity growth g
and population growth n.
(a) Show that f
0
(k) > 0, f
00(k) < 0, and the Inada conditions limk→0f
0
(k) = ∞ and
limk→∞f
0
(k) = 0 are satisfied.
(b) What are the steady-state values of k

, y
∗ and c

(c) Why is the steady state unique?
Now consider country A with α = 0.3, saving rate s = 15%, population growth n = 3%,
technology growth g = 2%, and depreciation δ = 10%. Assume labour and capital are paid
their marginal products and that the country is on its balanced growth path at t = 0.
(d) Solve for the numerical vales of k

A
, y

A
and c

A
(e) What is the growth rate of capital K˙A/KA in country A at t = 0?
(f) What are the growth rates of wages ˙wA/wA and return to capital ˙rA/rA in country A
at t = 0?
(g) Can country A achieve a higher c

than for s = 15%? Why or why not?

Sample Solution

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