Question

Consider an economy that is characterized by the Solow Model. The (aggregate) production function is given by: Y = 6K1/3L2/3

In this economy, workers consume 80% of income and save the rest.

The labour force is growing at 2% per year while the annual rate of capital depreciation is 5.5%.

a) Solve for the steady state capital-labour ratio and consumption per worker.

The economy is in its steady state as described in part (a). Suppose both the stock of capital and the number of workers double. b) What happens to the capital-labour ratio and output per worker when the economy reaches its new steady state? Explain. (5 points)

c) Suppose instead of the doubling of both capital and workers, the depreciation rate increases by 3.75 percentage points and, at the same time, the saving rate increase by ten percentage points. What happens to the capital-labour ratio, output per worker, and consumption per worker when the economy reaches its new steady state? Also, show your answer in an appropriate diagram (and be sure to identify the initial and new steady states).

d) The economy is in its steady state as described in part (a). Suppose the government wants to set the level of investment per worker to 9.375 via a change in saving rate. Find the saving rate that will achieve this goal. What happens to the steady-state level of consumption per worker? Explain your answer with the aid of ONE appropriate diagram. Be sure to explain what happens to the variables during transition to steady state.

Answer 1

So, here the initial equilibrium is "E1". Now, the required savings rate for "i=9.375" is "s2=31.25%". So, as the savings rate increases implied "k" increases to "125".