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Consider the full version of the Solow model with both population growth and technology: Yt = F(Kt,LtEt). We will extend this version of Solow to also explicitly include the government. The national income accounts identity becomes: Yt = Ct + It + Gt where Gt is government spending in period t. In order to fund its spending the government collects a tax Tt. Suppose for simplicity that the government runs a balanced budget Gt = Tt and that the tax collected is a constant fraction of output: Gt = Tt = Yt. The remaining disposable income for households each period is (1 )Yt. As in Solow we still assume that households save/invest a constant fraction s of their (now disposable) income. The population growth rate is n, techonology grows at g, and the depreciation rate is . (a) Assume for now that there is only private and no public investment (i.e all government purchases are spent on consumer goods and none of Gt is used to invest in capital). Write down the standard system - the equations for output, consumption, investment, and the capital accumulation equation. Define: yt = Yt/EtLt,

kt = Kt/EtLt,

it = It/EtLt,

ct = Ct/EtLt,

gt = Gt/EtLt.

(b) Transform the model from part (a) in per- effective worker form and derive the steady-state equation for capital per effective worker. Draw a graph depicting the steady state.

(c) What is the effect of higher tax rate on the steady state? Show the effect on your graph and explain the intuition for your answer.

d) Now suppose that, in addition to the case in part (a), a fraction of Tt is also invested in the capital stock, i.e. public investment equals Tt = Yt. What is total investment equal to now? Similarly to part (b) derive the steady-state equation for capital per worker and depict your answer on a graph.

(e) Show that if is sufficiently high (i.e. you will need to find a specific threshold value), then the steady state capital per effective worker will increase as a result of higher taxation.

The government wants to encourage technological innovation all across the US. The government thinks that with better technology, the US economy could become again the greatest economic power by far.

1. What would you do in order to encourage firms and/or households to invent/develop new technologies that would help produce more output (and thus create more employment)?

2. State Three (3) possible ways (policies) to encourage technological innovation.

3. Be specific on your recommended policy and Explain each.

Suppose Canada is a closed economy and in its long-run equilibrium initially. The government increases its subsidy to new capital investment projects. At the same time, the shortage of computer chips/semiconductors forces many manufactures to delay their spending on replacing depreciated machinery and equipment.

In the context of the long-run classical model, examine the effects of the above events on the following variables in the long run:

output real interest rate national savings real rental price of capital price level Explain and support your answer by ONE diagram for the market of loanable funds and ONEdiagram for the rental market for capital.

Consider the plant 31447080 in a closed loop with unitary feedback and a controller Gc(s). Answer the following:

(a) Determine the angle deficit for the point s = 1.60 + 1.60j to belong to the root locus. (b) Design a lead compensator such that s = 1.60 + 1.60j is a closed loop pole. (c) Determine the |ess| of the closed loop system with the previous controller. (d) To the previously designed lead compensator add a lag compensator with a pole at pc = 0.10 such that |ess| is 30.00 percent. Provide the transfer function of the lag part. (e) Design a PD Controller such that s = 1.60 + 1.60j is a closed loop pole. (f) Design a PI Controller such that s = 0.80 + 1.00j is a closed loop pole.

Suppose that the Ohorongo Cement made an offer to acquirer Cheetah Cement Company that consists of the purchase of 4 million shares at $10 per share. The value of Cheetah Cement Company stock before the bid was made public was $9 per share. Ohorongo Cement Company stock is trading at $20 per share, and there are 8 million shares outstanding. Ohorongo Cement Company estimates that it is likely to reduce costs through economics of scale with this merger of $1 million per year, forever. The appropriate discount rate for these gains is assumed to be 12%. Answer the following question.

What are the synergistic gains from this merger? What parties, if any, share in these gains? What is the estimated value of the Ohorongo Company post-merger? What is likelihood that the Cheetah Company shareholders will support the takeover? Motivate your answer. Briefly discuss if this proposed merger is likely to be approved/rejected by the Namibian competition.