0, show the step-by-step derivation ofthe fundamental equation of growth (using per worker capital, k). Hint: Firstderive per worker production function.b. Find the steady-state values of capital...

Extracted text: 1. Suppose that the production function of an economy is characterized by the following Cobb-Douglas production technology Y = Ka L*1, where Y is the aggregate output, K is the capital stock, L is the labor and 0< a=""><1. a="" assuming="" dosed="" economy="" with="" no="" govemment,="" labor="" growth="" rate="" being="" constant="" (gs)="" and="" depreciation="" rate="" is="" positive="" ô=""> 0, show the step-by-step derivation of the fundamental equation of growth (using per worker capital, k). Hint: First derive per worker production function. b. Find the steady-state values of capital per labor (k), output per labor (), and consumption per labor (c). Hint: use the fact: k= 0. What would be the effect of changes in s, gs and a on kf 2. Recall that general form of fundamental equation of growth in Solow model is described as follows: k = s - f(k.) – (gs + 6)ka Noting that at steady-state kss = 0 and hence a Using the fact kes= 0, show the steady-state graphically and provide economic interpretation of the steady-state condition s- f(k s) = (gs + 6)k * b Using the same graph you draw in part (a) explain the transitional dynamics of the Solow. Hint: Defime what happens if k. k s- 3. Assume that production fumction takes the form Y = (K'0.5) + L'as)E, Show if this production function obeys neoclassical assumptions. 4. Lets assume that the time derivative of a continuous variable Xa is defmed as X = M+N where, M: and N: are also continuous variables defined by following functions: N: = ekt & M, = et and k is a constant. Find the grow th rate of x at the steady state in terms of k.