Consider a simple variant of the Solow Growth model. The main difference from the standard model...

 

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Consider a simple variant of the Solow Growth model. The main difference from the standard model is in the aggregate production function. All other aspects are the same as in the Solow framework (and the steps in the solution of the model are the same). The aggregate production function is as follows: Y = aK + BN where Y, stands for output, K, for the aggregate capital stock, N for the size of the labor force (there is no unemployment), and a and B are two positive numbers. Notice that the aggregate production function is linear in the inputs (i.e., if you were to graph their marginal products, they would be constant and not decreasing as in the standard Solow case). The labor force grows at rate n, capital depreciates at rate d, and the households save a constant fraction s their income. (a) Manipulate the aggregate production function to express output per worker yt as a function of the capital-labor ratio k. (b) Write the condition for a steady-state and find the expression for the steady-state capital-labor ratio k*, assuming that sa < d+n. Draw a graph representing the steady-state. (c) How much are the steady-state values of output per worker, consumption per worker and investment per worker? (d) Represent graphically the effect of a small increase in a (i.e., in the marginal productivity of capital). Is there any effect on the steady state of the economy? Describe how the economy adjusts after the change in a and if the economy is going to have long run growth in the output per worker yt. Consider a simple variant of the Solow Growth model. The main difference from the standard model is in the aggregate production function. All other aspects are the same as in the Solow framework (and the steps in the solution of the model are the same). The aggregate production function is as follows: Y = aK + BN where Y, stands for output, K, for the aggregate capital stock, N for the size of the labor force (there is no unemployment), and a and B are two positive numbers. Notice that the aggregate production function is linear in the inputs (i.e., if you were to graph their marginal products, they would be constant and not decreasing as in the standard Solow case). The labor force grows at rate n, capital depreciates at rate d, and the households save a constant fraction s their income. (a) Manipulate the aggregate production function to express output per worker yt as a function of the capital-labor ratio k. (b) Write the condition for a steady-state and find the expression for the steady-state capital-labor ratio k*, assuming that sa < d+n. Draw a graph representing the steady-state. (c) How much are the steady-state values of output per worker, consumption per worker and investment per worker? (d) Represent graphically the effect of a small increase in a (i.e., in the marginal productivity of capital). Is there any effect on the steady state of the economy? Describe how the economy adjusts after the change in a and if the economy is going to have long run growth in the output per worker yt.

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Ans This is the hand written answer where at first manipulate the linear production function in ... View the full answer