Consider an economy that is characterized by the Solow Model. The (aggregate) production function is given by: Y = 4K^1/4 (LxE)^3/4 Note: Keep your answer to 4 decimal places if needed. Be sure to show your work. In this economy, workers consume 90% of income and save the rest. The labour force is growing 3% per year. The annual rate of capital depreciation is 5% per year. Initially, the economy is endowed with 4000 units of capital, 100 workers, E is 1.0 & constant, and there is no government.

a) Solve for the steady state levels of capital, output & consumption (all in per worker terms)

b) Is the economy initially at its steady state? Explain. If the economy is not in its steady state, what happens to the capital-labour ratio and output per worker in the economy during very long-run transition. The economy is in a steady state as described above from part a). A new government is introduced. The government levies a tax on the economy collecting 5% of output.

c) After this tax is collected you can assume that these funds are gone, (no goods or services are purchased with them), and no government employees are paid with the tax revenue. Determine the impact the tax has on the steady state levels of capital per worker & consumption per worker. Sketch a diagram showing the impact of this shock. Explain what impact the shock has on the level and growth rate of the standard of living (as measured by output per worker) in steady state.

d) Suppose as an alternative after the tax is collected, the government is able to use these funds to create and a plan that causes the growth rate of labour augmenting technological change to rise to 3% per year. Determine the impact the tax has on the steady state levels of capital, output, and consumption (all per effective worker)

Sketch a diagram showing the impact of this shock.

Explain what impact the shock has on the level and growth rate of the standard of living (as measured by output per worker) in steady state.