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1)Use the Solow model to evaluate this question

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1)Use the Solow model to evaluate this question. You are the chief economic advisor to a small Caribbean country with an aggregate per capita production function of y = 3k%. The savings rate is 6%, and the rate of depreciation is 10%. Population grows at a rate of 4%. There is no technological progress. a. (3) On a graph, show the output, break-even investment, and savings functions for this economy (as a function of capital per worker). Denote steady-state capital per worker k* and steady-state output per worker y*. Label your graph completely for full credit. b. (2) Write down the equation used to solve for the steady state, and find the numerical values of this economy's steady-state levels of capital per worker and output per worker. (fractions or decimals are fine) C. (2) If capital per worker equals four units (k=4), explain in words how the economy works its way toward the steady state. d. (3) lf k-4, write down the equations for and find the numerical values of: (1) investment per worker; (ii) break-even investment per worker; (ii) output per worker, and (iv) consumption per worker. Identify each of these on your graph (draw a new graph if necessary to see clearly). e. (2) If k-0, explain in words what happens. f. (1) How fast is output per worker in this economy growing in the long run? Explain how you know this.

2)Use the Solow model to evaluate this question. You are the chief economic advisor to a small Caribbean country with an aggregate per capita production function of y - 3k". The savings rate is 6%, and the rate of depreciation is 10%. Population grows at a rate of 4%. There is no technological progress
f. (1) How fast is output per worker in this economy growing in the long run? Explain how you know this. 8. (1) If the rate of technological progress in this country were 5%, at what rate would output per worker grow in the steady state? h. (2) Say that the economy is originally in the steady state identified in part b when population growth decreases to 2%. Explain in words what happens to the growth rate and level of output per capita, being sure to address what happens both in the short run and in the long run. 1. (2) Say that the economy is in its original steady state (part b), when a hurricane destroys 1/3 of its capital stock. How does this change the steady-state level of output per capita? 1. (2) While the Solow model does not directly include any government policies, name one specific government policy that could increase long-run growth in output (income) per capita as described by the Solow model.
Use the Solow model to evaluate this question. You are the chief economic advisor to a small Caribbean country with an aggregate per capita production function of y = 3k%. The savings rate is 6%, and the rate of depreciation is 10%. Population grows at a rate of 4%. There is no technological progress.
f. (1) How fast is output per worker in this economy growing in the long run? Explain how you know this. 8. (1) If the rate of technological progress in this country were 5%, at what rate would output per worker grow in the steady state?

3)

Suppose that Maggie cares only about chai and bagels. Her utility function is U= CB, where C is the number of cups of chai she drinks in a day, and B is the number of bagels she eats in a day. The price of chai is $3, and the price of bagels is $1.50. Maggie has $6 to spend per day on chai and bagels.

1. State the objective function
2. State the constraint
3. Solve for MU_C and MU_B and state if utility function exhibits diminishing MU for each good
4. Interpret the value of your MU_C and MU_B at C=2 and B=6
5. Solve for MRS_CB and state if the utility function exhibits diminishing MRS
6. Interpret the value of your MRS_CB if P=2 and S=1
7. Write down the optimality condition. Express it using the utility function and prices given above.
8. What is the economic meaning of the optimality condition applied specifically to the chai and bagels. Equality of slopes of IC and BL are not acceptable answers- these are not economically relevant terms
9. Solve for optimal level of chai and bagels.
10. Draw your optimal solution by drawing an IC (convex one) and BL, and make sure you label your optimal levels of B and C as well as the intercepts of your BL.