Suppose GDP in Penntopia is well approximated by a Solow Model with production function Yt = AKαt L1-αt.
As usual, population grows according to a constant growth rate n. There is depreciation of old capital according to rate d. The capital accumulation equation is standard.
(a) Derive the expression for the steady state capital and output per capita from the 5 basice quations.
(b) Suppose A = 10, α = 1/3, d = 0.1, s = 0.2, n = 10%. Compute the steady state level ofoutput and capital per capita.
(c) Suppose Penntopia it is in a steady state situation i.e. the current levels of output andcapital are the ones that you derived in part (b). Suppose now that an earthquake hitsPenntopia, reducing capital by 50%. What is consumption per capita right after theearthquake? Compute the steady state after the earthquake.
(d) Suppose underneath the rubble, blueprints for a new laser technology are found. Thisincreases technology A by 100%. Furthermore, this discovery also changes the depreciationrate in the economy. Find the new depreciation rate d that will guarantee that thesteady state after the discovery is the same as before.
(e) What is the GDP per capita growth rate in the economy right after the earthquake (i.e.from the period right after the earthquake to the next period after that) if the lasertechnology had not been found? What about if it has been found (with new A0 and d0)?Explain the difference.
(f) Suppose there is another country with the same technology that did not get hit with anearthquake. In the time right after the earthquake, in which country would you generallyexpect the growth rate to be higher. Explain why.
A sentence or two is sufficient.2. Consider the following production function:Yt = A[αKρt + (1 - α)Lρt]1ρ , where A > 0 is TFP, L is labor and K is capital. The other parameters are restricted to be0 α 1, ρ ≤ 1. Find the expression for the steady state level of physical capital per persononly as a function of A, α, n, d, s, ρ. Show your work.