2. Solow Model {3D points total] Time is continuous. and output t} is given by the neoclassical production function Fit] = KquiuLfrnl-. where Kit} is capital, Aft] is technology. 12(1) is labor. and the capital elasticity satisfies ii a: e.- a: 1. The exogenous laws of motion for technology and labor are 3%; = g and g = to. investment is a constant fraction of output Wilh fit} = 5Y3): and the law of motion for capital is given by Kit} = Ift] Hair}. To fix terminology. g :5 is the technology growlh rats, n c c is the population growth rate. I) c: s c: 1 is the savings rate. and u c: s c: 1 is the capital depreciation rate. Let Ht] = 2%,?\" and grip} = 3: l t be capital and output per efficiency unit of labor, resMively. gm = cm\" is the intensive form of the production function. Note that the law of motion for felt} is given by in) = some {n + g + print. a result which you may take as given. {a} {5 points} Draw a figure plotting the rate of change of left} with respect to time. lift}. as a function of left]. Label your axes. On the horizontal axis. mark the steady state level If such that left] = I] whenever left} = .t:*. Explain the shape of the gure intuitively. {b} in the long am, the level of capital per efficiency unit of labor approaches the steady state level. i.e. kit} i fr\". Similarly. if g* = if\". then output per efficiency unit of labor approaches y'. is. gqjt} It 3;". tic-u may take these results as given. i. {5 points} Derive an expression for the ratio of steady-state level of capital per effi- ciency unit of labor st to the steady-state level of output per efficiency unit of labor 3;". i.e.. derive an expression for :- as a function of exogenous model parameters. ii. {5 points} Derive the long run growth rate of capital per capita . {c} Assume the economy begins at steady state with km = is\". Then, suddenly. a disaster instantaneously destroys half of the labor force. Note that this results in a drop in the level of Lft} at the moment of the disaster, but the disaster does not directly change the population growth rats it nor anything else in the economic environment. i. (4 points} In the long run, does the disaster increase, decrease. or leave un- changed the level of output 11:}? Explain your answer intuitively. ii. {4 points} In the long run. does the disaster increase. decrease. or leave un- changed the growth rate of output Fit}? Explain your answer intuitively. iii. (4 points} In the long run. does the disaster increase. decrease. or leave un- changed the level of living standards %? Explain your answer intuitively. iv. (3 points} In the long run. does the disaster increase. decrease. or leave un- changed the growth rate of living standards {3}? Explain your answer intuitively