43. Causation: ____

44. Due Process: ____

45. Employment discrimination: ____

(1) Suppose you earn $1,000,000 over your working life, and the real interest rate is 50%. How much will you save and how much will you consume in each part of your life? (5 分)

(2) Suppose a social security system will pay you 25% of your working income when you are retired. Now, with \( y = \)1,000,000, as in part (a), how much will you save and how much will you consume each period? (5 分)

(3) Suppose the interest rate rises, starting from the situation in part (a). Will you save more or less in your working period? Discuss the change of your saving plan based on the substitution effect (SE) and income effect (IE), separately. (5 分)

2. "The Federal Open Market Committee (FOMC) outlined its approach to monetary policy normalization in the Policy Normalization Principles and Plans that it issued after its September 2014 meeting. The FOMC indicated that there would be two main components to policy normalization: gradually raising its target range for the      federal funds rate      to more normal levels and gradually reducing the Federal Reserve's       securities holdings     . The Committee augmented these Principles and Plans at its March 2015 FOMC meeting by announcing more details about the approach it would use to raise the federal funds rate and other short-term interest rates." Based on the above announcement by FOMC, please discuss, in detail with macroeconomic theory, the impacts on (a) the prices and yield rates of government securities, (b) the (nominal) exchange rates, and (c) the aggregate economic activities in the United States.(15 分)

(1) Let \( k_{t} = K_{t} / L_{t} \) and \( y_{t} = Y_{t} / L_{t} \) be capital-labor ratio and output per worker, respectively, find the first-order difference equation for \( k_{t} \), that is \( k_{t + 1} = g(k_{t}) \). (5 分)

(2) Find the steady-state capital-labor ratio \( (k^{*}) \) and output per worker \( (y^{*}) \) with the combination of defined parameters in the question. (5 分)

(3) To maximize steady-state consumption per worker, \( c^* = (1 - s)y^* \), one must choose the golden-run saving rate. Please prove that this golden-run saving rate must be equal to the capital share, \( \alpha \). (5 分)

(4) When \( \alpha = 1 \), the steady-state values of capital-labor ratio \( (k^{*}) \) and output per worker \( (y^{*}) \) fail to exist so please derive the long-run growth rates of \( k_{t} \) and \( y_{t} \). (5 分)

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