according to the following law of motion: K'=(1-d]K+I, where oi is the depreciation rate and I is the investment. Consumers receive exogenous income 1", and save a fraction of the income and consume the rut, i.e. I = 31' and C = (1 sjY. (a) Derive the law of motion for capital. Hint: Use the capital per e'iciency units of labor rather than capital per labor, i.e derive the law of motion for k = KEN instead of g. (h) Does the econom3,r have a. steadystate? If so, what is the growth rate of output, consumption, investment and per capital income at the steady-state? (c) What is the effect of an increase in f on the growth rate of per capita. income