Economic Growth II — Work It Out Question 2 In the nation of Wooknam, the capital...

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

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

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.