Consider an economy that with an aggregate production function is given by: Y = K1/3(LxE)2/3 Where: K = the aggregate real quantity of capital utilized or employed L = the aggregate real amount of labour employed E = the effectiveness of labour Note: Keep your answer to 2 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 at 3% per year while the annual rate of capital depreciation is 5%. The growth rate of labour augmenting technological progress is 2% per year. The nominal money supply is growing at 8% per year. Suppose the rate of job separation is 2 % per period and the rate of job finding is 38% per period. Presently the inflation rate is 4% per year. Initially, the economy is in long-run and very long-run equilibrium endowed with 125,000 units of capital, and employs 125,000 workers, it makes 500,000 real units of output, and there is no government. Hint: If A = BxC, then the growth rate of A is equal to the sum of the growth rates of B & C. Similarly, if H = (I/J), then the growth rate of H is equal to the growth rate of I minus the growth rate of J. Also, if A = B, then the growth rate of A is equal to times the growth rate of B. a) Solve for the present (or initial) long-run equilibrium level of labour effectiveness (E) and the labour force (LF). (4 marks) b) Write down expressions for the marginal products of labour and capital and calculate their initial long-run equilibrium levels. (2 marks) c) Determine the growth rates of the marginal products of labour and capital in the very long-run. Explain in words what this means for standard of living of workers and owners of capital. (4 marks) d) Determine the very long-run growth rate of the (income) velocity of money. Show your work. (2 marks) e) Suppose the central bank finds the present inflation rate unacceptable and decides to lower it to 1.5% per year. Explain in words what the central bank needs to do. Suppose agents believe the central bank's announced change in its policy. Then as a result explain in words what the impact is on the real rate of interest. (3 marks)