Question

Economic Growth II — Work It Out Question 2 In the nation of Wooknam, the capital share of GDP is 35 percent, the average growth in output is 3.0 percent per year, the depreciation rate is 5.0 percent per year, and the capital-output ratio is 4.5. Suppose that the production function is Cobb- Douglas and that Wooknam has been in a steady state. Round answers to two places after the decimal when necessary. a. In the initial steady state, what is the savings rate (8)?

Answer 1

According to the question, the given informations are,

The production function is Cobb-Douglas production function where the capital share of output(GDP) is given by 35%. In other words,

we know from a Cobb-Douglus production function of the form

Y = K71-

Here 'a' is the capital share of output i.e. a = 0.35. We can get the MPK from Y i.e.

$MPK=a(L/K)^1^-^a$

or, MPK = a/(K/Y)

or, a = MPK×(K/Y)..........(1)

Also we are given, average growth in output(g) is 3% per year i.e. g=0.03. And depriciation rate(d) is 5% per year i.e. d=0.05. Also given that K/Y = 4.5. Now we will move on to the questions one by one.

(a) We know, the Solow model steady state growth is determined from the equation of capital stock change,

∆K = sY-(g+d)K, where s=savings rate.

Now at steady state,

∆K = 0

or, sY = (d+g)K

or, s = (d+g)×(K/Y)...........(2)

or, s = (0.03+0.05)×4.5

or s* = 0.36

Hence, the steady state growth rate is 36%(Answer)

(b) Now from equation 1, we get

MPK = a/(K/Y)

or, MPK = 0.35/4.5

or, MPK = 0.0778

Hence, at steady state MPK = 0.0778(Answer)

(c) Now, when we consider the Golden Rule level of capital, we maximize the consumption of the nation. Here investment = I = (g+d)K and consumption = C = Y-I.

now, when consumption is maximized,

dC/dK = 0

or, MPK*gold = (g+d)

or MPK*gold = (0.03+0.05) = 0.08.

Hence, Golden Rule MPK*gold = 0.08(Answer)

(d) Now, from equation 1, at Golden Rule capital level,

a = MPK*gold×(K/Ygold)

or, 0.35 = 0.08×(K/Ygold)

or, K/Ygold = 4.375

Hence, at Golden Rule level of capital, K/Ygold = 4.375(Answer)

(e) From equation 2 we , we can use it in Golden Rule level of capital,

s*gold = (d+g)×(K/Ygold)

or, s*gold = (0.05+0.03)×4.375

or, s*gold = 0.35

Hence, Golden Rule savings rate s*gold = 35%(Answer)

Hope the solution is clear to you my friend.