Suppose yt=5kt 0.5 (the per worker production function), d=0.1,n n=0.05, and the aggregate savings function is given by St=0.3Ytn (note that the savings rate is 0.3).

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a. Solve for the steady state level of capital per worker (k),n the steady state level of output per worker (y), the steady staten level of consumption per worker (c), the steady state level ofn investment per worker, and the steady state level of savings pern worker. SHOW ALL WORK as done in lecture (do not use a formula forn k* and then just plug in for the values, unless you specificallyn derive k* first).

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b. Suppose that the savings rate falls. What will be the impactn on the steady state values of k, y, and c? Use a diagram ton illustrate the fall in the savings rate and then state the impactn on k, y, and c. Just state. Label everything: including all axesn and all curves.

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c. Continue with b. Provide an intuitive discussion of then impact of the FALL in savings rate on the economy; elaborate onn what is the economic reasoning for the changes, especially changesn in k, y, and c.

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d. Extra credit: Use the information provided above ton derive/calculate the maximum consumption per worker possible atn steady state and the capital-per-worker that yields this maximumn steady state consumption (c_max) [the answers to part a. are notn the answer to this question, you must use calculus to solve thisn problem] 

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[0, 0] [1, 0] [2, 0] [3, 0] [4, 0] [0, 1] [1,1] [2, 1] 1 [3, 1] 9 [4, 1] 42 138 [0, 2] 1 [1, 2] 7 [2, 2] 26 [3, 2] 70 [4, 2] Starting cell is [0, 5] and journey ends at [4, 0]. The following moving constraints are valid for any REACHING CELL [i, j]: (REACHING CELL [i, j] means you want to reach cell [i, j] - If the j value of any REACHING CELL [i, j] is ODD, then you can COME TO/REACH that CELL FROM the CELLS situated STRAIGHT to its RIGHT and STRAIGHT to its UPWARDS - If the j value of any REACHING CELL [i, j] is EVEN, then you can COME TO/REACH that CELL FROM the CELLS situated STRAIGHT to its RIGHT, DIAGONALLY UPWARDS to its RIGHT and STRAIGHT to its UPWARDS 1 [0, 3] Now if I Calculate how many ways are there to reach the BOTTOM LEFT CELL from the TOP RIGHT CELL using the Dynamic Programming approach, I may get an output something like this: 6 [1, 3] 19 [2, 3] 44 [3, 3] 363 155 85 [4, 3] 1 [0, 4] [1,4] [2, 4] 4 [3, 4] 9 [4, 4] 16 25 1 [0, 5] [1, 5] [2,5] [3, 5] 3 [4, 5] 5 7 9 1 1 1 1 1 Now, write down a code with the proper deployment of the given moving constraints as the logic of your code in any of your preferred programming Language (C/C++/Java) that implements the above scenario. [0, 0] [1, 0] [2, 0] [3, 0] [4, 0] [0, 1] [1,1] [2, 1] 1 [3, 1] 9 [4, 1] 42 138 [0, 2] 1 [1, 2] 7 [2, 2] 26 [3, 2] 70 [4, 2] Starting cell is [0, 5] and journey ends at [4, 0]. The following moving constraints are valid for any REACHING CELL [i, j]: (REACHING CELL [i, j] means you want to reach cell [i, j] - If the j value of any REACHING CELL [i, j] is ODD, then you can COME TO/REACH that CELL FROM the CELLS situated STRAIGHT to its RIGHT and STRAIGHT to its UPWARDS - If the j value of any REACHING CELL [i, j] is EVEN, then you can COME TO/REACH that CELL FROM the CELLS situated STRAIGHT to its RIGHT, DIAGONALLY UPWARDS to its RIGHT and STRAIGHT to its UPWARDS 1 [0, 3] Now if I Calculate how many ways are there to reach the BOTTOM LEFT CELL from the TOP RIGHT CELL using the Dynamic Programming approach, I may get an output something like this: 6 [1, 3] 19 [2, 3] 44 [3, 3] 363 155 85 [4, 3] 1 [0, 4] [1,4] [2, 4] 4 [3, 4] 9 [4, 4] 16 25 1 [0, 5] [1, 5] [2,5] [3, 5] 3 [4, 5] 5 7 9 1 1 1 1 1 Now, write down a code with the proper deployment of the given moving constraints as the logic of your code in any of your preferred programming Language (C/C++/Java) that implements the above scenario.

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