Does this production function exhibit constant returns

Reference no: EM13332642

Assume that an economy has the production function Y = AK1/3L1/3G1/3, whereK is physical capital, L is labor (which
we assume to be equal to population), A is the level of technology, and G is the stock of public infrastructure (G stands
for Government infrastructure).
2

(i) Does this production function exhibit constant returns to scale? Write down the production function in per

capita terms (use the "per capita notation": y = Y/L,k = K/L and g = G/L).
Imagine that the economy is closed, that the saving rate is the constant fraction "s" and the depreciation rate is "δ".
Population growth is an exogenous constant number "n".

(ii)Write down the fundamental equation of Solow-Swan for the GROWTH RATE of capital stock per person, k, as

a function of the parameters A, s, n, δ, the capital stock k, and the level of infrastructures per person, "g".

(iii) Consider the parameters A = 1, s = 0.2, δ = 0.09, n = 0.01. Imagine that the amount of infrastructures per

person is constant at g = 8. Graph the "savings line" and "depreciation line". Is there a steady state? Is it unique?
What is the steady state capital stock per person, k∗, in this economy?
Imagine that the economy is stuck at the steady state with no growth. Imagine that the World Bank gives aid to this
country. We are going to analyze the consequences of this aid.

(iv) Imagine that the aid takes the form of physical capital k (for example, machinery) and in particular, imagine

that g remains constant at g = 8 but, after the aid, the economy has a stock of capital equal to k ∗ +1. How does the
economy behave after this donation? Explain why.

(v) Imagine instead that aid takes the form of public infrastructures. In particular imagine that g increases from

g = 8 to g = 27. How does the economy behave after this donation? Is your answer different from before?

(vi) Imagine now that instead of aid, it is the government of the country that increases the stock of infrastructures

per person. What happens to this economy in the short term and in the long term? Why do you think governments
in developing countries do not continuously invest in infrastructures?

Reference no: EM13332642

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