Consider the Solow-Swan growth model, with a savings rate, s, a depreciation rate,8, and a population growth rate, n. The production function is given by: Y = AK + BK¹/2 H¹/4L¹/4 where A and B are positive constants. Note that this production is a mixture of Romer's AK model and the neoclassical Cobb-Douglas production function. (f) What will be the growth rate of consumption and investment under these Parameters in the long term? g) Imagine that we have two countries with the same parameters (same A, B, s, d, and n). One of them is rich and the other is poor. Which one of the two will grow faster? Why? Will those two countries eventually catch up? (h) Suppose now that sA > d+ n. Draw the savings and depreciation curves. Under these circumstances, will there be positive growth in the long run? Why? (i) If s = 0.52, A = 1.5, B = 1, d= 0.15, h*= 10000 and n = 0.2, the growth rate converges to some value as time goes to infinity. What is this value? (j) For these specific parameters, say that this country has a GDP (Y) value of $ 300 billion. What is the level of consumption? (k) What will be the GDP next year?

ENGR.ECONOMIC ANALYSIS
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Consider the Solow-Swan growth model, with a savings rate, s, a depreciation
rate,8, and a population growth rate, n. The production function is given by:
Y = AK + BK1/2 H1/4L1/4
where A and B are positive constants. Note that this production is a mixture of
Romer's AK model and the neoclassical Cobb-Douglas production function.
(f) What will be the growth rate of consumption and investment under these
Parameters in the long term?
g) Imagine that we have two countries with the same parameters (same A, B, s,
d, and n). One of them is rich and the other is poor. Which one of the two will
grow faster? Why? Will those two countries eventually catch up?
(h) Suppose now that sA > d+ n. Draw the savings and depreciation curves.
.I
Under these circumstances, will there be positive growth in the long run? Why?
(i) If s = 0.52, A = 1.5, B = 1, d= 0.15, h*= 10000 and n = 0.2, the growth rate
converges to some value as time goes to infinity. What is this value?
(j) For these specific parameters, say that this country has a GDP (Y) value of $
300 billion. What is the level of consumption?
(k) What will be the GDP next year?
Transcribed Image Text:Consider the Solow-Swan growth model, with a savings rate, s, a depreciation rate,8, and a population growth rate, n. The production function is given by: Y = AK + BK1/2 H1/4L1/4 where A and B are positive constants. Note that this production is a mixture of Romer's AK model and the neoclassical Cobb-Douglas production function. (f) What will be the growth rate of consumption and investment under these Parameters in the long term? g) Imagine that we have two countries with the same parameters (same A, B, s, d, and n). One of them is rich and the other is poor. Which one of the two will grow faster? Why? Will those two countries eventually catch up? (h) Suppose now that sA > d+ n. Draw the savings and depreciation curves. .I Under these circumstances, will there be positive growth in the long run? Why? (i) If s = 0.52, A = 1.5, B = 1, d= 0.15, h*= 10000 and n = 0.2, the growth rate converges to some value as time goes to infinity. What is this value? (j) For these specific parameters, say that this country has a GDP (Y) value of $ 300 billion. What is the level of consumption? (k) What will be the GDP next year?
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