Consider a closed economy. The production function per capita given by the following expression: 3h = Ak Where k, and ye are capital per capita and output per capita respectively at date t. a. Describe as accurately as possible the various properties of this function. What does the term A, represent? b. Plot this function in the plane (key) c. Suppose that in the long run, the capital per capita is constant and has a value k. It is known as the steady state of the economy. Represent graphically the steady state in the plane (ke, t). e. On the same graph as above, show the consequences of an increase in A, on k and f(k). Explain the impact of an increase in A, on income per capita. f. Let two countries, A and B, be represented by the production function given above and assume that A, is the same in both countries at each date t. It is also assumed that the savings rate and capital depreciation rate are identical in both countries. Initially, both countries' capital stock per capital is less than k, but country A has more capital per capita than country B. In which country is the growth rate of y, faster in the short run? In the long run? g. Suppose that in country A the term A, is growing faster than in country B. How does it change the answer you gave to the previous question?