ECON 715 Final: ECON715 FinalFall2018Solution
Document Summary
Instructions: one double-sided sheet with any content is allowed, calculators are not allowed, show all the calculations, and explain your steps, if you need more space, use the back of the page, fully label all graphs. Suppose that gdp as a function of time t is modelled according to the. Y (t) = a (t) k (t)(cid:18) l (t)1(cid:0)(cid:18) , 0 < (cid:18) < 1. The inputs are capital k and labor l, and a is productivity parameter. Prove that the growth rate of gdp, is given by: ^y = ^a + (cid:18) ^k + (1 (cid:0) (cid:18)) ^l where the "hat" on top of a variable indicates the growth rate of that variable. ^y = d dt d dt d dt ln y (t) [ln a (t) + (cid:18) ln k (t) + (1 (cid:0) (cid:18)) ln l (t)] ln a (t) + (cid:18) d dt ln k (t) + (1 (cid:0) (cid:18)) d dt ln l (t)
