together y Show more show your work completely but succinctly. While you are welcome (and encouraged) to work together your submission and writeup must be yours alone. 1. Suppose your bank account has a balance today of $100. Consider the following time periods: t = 0 t = 1t = 2t = 12t = 24t = 48t = 60. (If you like use a spreadsheet program to help you with these questions). ?(a) Compute your bank balance for these time periods assuming the interest rate is 1% (b) Do the same thing for an interest rate of 6% ?(c) Plot your bank balances for these two scenarios on a standard scale (d) Do the same thing with a ratio scale 2. Consider the basic Cobb-Douglas production function we used as the basis for our first model. Modify it to the more general form Y = A ?K?L1?? . (a) Write down the new model and identify specifically the: Equations (by name) ? Endogenous variables ? Exogenous variables . (b) Find the solution to the model (i.e. expressions for the endogenous variables in terms of the exogenous). ?If you are having trouble with the factor market clearing conditions ask me. . (c) Find y? for this model. 3. Using our standard production function (Y = A ?K1/3L ?2/3) . (a) Write down the growth rate of GDP gY as a function of the growth in capital stock (remember that ?labor is fixed). You can use the growth rate relationship approximations provided in class/textbook. . (b) Does your answer to (a) change if were looking at per-capita GDP? If so how? If not why not? (c) In the context of the Solow model find a measure for gy as a function of current capital stock Kt. The ?Kt Y? ??(K?)2/3 ?? growth rate of capital stock is Kt = s ?K? K2/3 ? 1 . Weve already written down the steady state t solution K?. Your answer should only contain exogenous variables/parameterslabor is exogenous here. (d) Based on your solution to part (c) what happens to the growth rate as Kt gets really small? What happens to the growth rate when Kt gets really large? 4. Suppose were modeling an economy using the Solow model. It begins in steady state. By what proportion does y? (the post-change steady-state per capita GDP) change in response to the following changes? Show your work/reasoning (a solution for y? will be a useful starting point). (a) The investment rate doubles?(b) The depreciation rate falls by 15% (c) Productivity rises by 15% 5.Aneconomyhasthefollowingparametervalues:s ?=.3d ?=.1A ?=1andL ?=100.2 Theeconomybegins at steady state but at some point is attacked by Godzilla destroying 70% of the capital stock. Calculate the growth of per-capita GDP in the period immediately following the Godzilla attack. 1The Dropbox will not close but your score will be reduced by the amount described in the syllabus depending on how late it is uploaded. 2Note that the presence of savings and depreciation rates mean that this problem involves the Solow model. Show less