Question

3. Given the Solow Growth Model (SGM), where ? = 0.1, s= 0.2, n = 0.01 and g = 0.01 set up an excel sheet program to a) The starting value of k= 2 and also has a starting value of 15. Compute the two different scenarios as each economy moves to the steady state. Discuss intuitively what is going on in these scenarios. (10 points) b) Suppose n increases to 0.2 due to changes in migration policy and the government is considering changing incentives to increase the savings rate so that the steady state capital labor ratio will not change. Use the SGM (in excel) to determine the new savings rate and explain the underlying intuition of why this policy should work. (15 points)

Answer 1

Find the current steady state kss. Per worker production function is y = k^0.3

At te steady state we have

k* /y* = s/(n + d)

k*/k*^0.3 = 0.2/(0.01 + 0.07)

k* = 3.702

Now at the golden rule kg, the cosumption is maximum. Find the consumption function and maximize the same

c = y - sy

c = k*0.3 - (n+d)k

dc/dk = 0.3k^(-0.7) -  (0.01 + 0.07)

For maximization, dc/dk = 0

0.3k^(-0.7) = (0.01 + 0.07)

This gives kg = 6.6 which is the golden rule quantity of capital per worker.

Since kss < kg, there is currently underinvestment.