Exogenous Growth Models

Consider the following numerical example using the Solow growth model. Suppose thatF(K,N) =zK^3/5N^2/5

where the capital depreciation rate isd= 0.1, the savings rate iss= 0.25, the population growth rate isn= 0.075, and the productivity isz= 1.5.

1. Find the steady state per-capita capital stock (k), output per capita (y), and consumption per capita (c).
2. Assume the economy is in the steady state of Question 1 and the government wants to implement a policy that will increasethe long run per capita capitalby 10%. Determine the percentage change in thepopulation growth nthat is required to achieve this goal.
3. Assume the economy is in the steady state of Question 1 and the government wants to implement a policy that will increasethe long run per capita outputby 10%. Determine the percentage change in theproductivity zthat is required to achieve this goal.
4. Assume the economy is in the steady state of Question 1 and the government wants to implement a policy that will increasethe long run per capita consumptionby 10%. Determine the percentage change in thesavings rate sthat is required to achieve this goal and get a higher level of per capita capital for the next generation.