4. Explain what the Laffer curve is and why it is an Inverted-U shape. [10 pts]

(a) Write down the consumer's current period budget constraint and its future-period budget constraint. Also, derive the (present-value) lifetime budget constraint of the consumer. [10 pts]

(b) Use the graphical approach to show the optimal consumption/saving bundle for the consumer to be a lender. The figure should have C' on the vertical axis and C on the horizontal axis. It should also contain the lifetime budget of the consumers, and the indifference curve (IC). Make sure you mark the slope of the budget line, its endpoints, the endowment point, the equilibrium current and future consumption (C* and C'*), and the equilibrium saving (s*). [10 pts]

(c) Consider an increase in the real interest rate. Draw the new budget constraint in the figure, and show how it affects the consumer's intertemporal decisions on C, C', and s? Explain your answer with income and substitution effects, and show how it matters whether the consumer is initially a borrower or a lender. [10 pts]

(d) Suppose that the ratio of good borrowers is 2 (0<λ<1) and that of bad borrowers is (I-λ) in the credit market. The good borrowers are all identical, and always repay their loans. Bad borrowers never repay their loans. Banks issue deposits that pay a real interest rate "p" to a lender, and make loans to borrowers. Banks cannot tell the difference between a good borrower and a bad one. Consider that banks are in a perfectly competitive market and make zero profits. Find the interest rate on loans (i.e., the interest rate paid by a borrower) determined by banks. Explain the details how you derive it, and whether it is higher or lower than r. Besides, show the consumer's lifetime budget constraint in a figure with C' on the vertical axis and C on the horizontal axis. [10 pts]

(e) Use the figure in (d) to show that Ricardian equivalence theorem may not hold under the asymmetric information. Explain clearly how a tax cut in the current period will affect the lifetime income for a borrower given that the government's spending is unchanged. [10 pts]

2.Consider a two-period real model with investment. The consumer chooses consumption (C and C') and labor supply (Ns and Ns) in the current and future periods, and determines saving (s) in the current period. The firm chooses labor demand (Nd and Nd') in the current and future periods, and determines investment () in the current period. The capital accumulation is formulated by K'=(1-δ)K+I where K and K' are the capital stock in the two periods, and O is the depreciation rate. The production functions in the two periods are Y = F(K, N) and Y' = F(K', N') and they follow the standard properties with decreasing marginal product of labor and decreasing marginal product of capital. Now, suppose there is a natural disaster that destroys part of the nation's capital stock "K" in the current period. Use the two figures of the labor market and product market in the current period to show how the decrease in current capital stock K impacts the equilibrium real wage w, labor employment N, real interest rate r, and aggregate output Y in the current period. [20 pts]Hint: Plot the supply and demand of the current labor market (with the real wage "w" on the vertical axis and the labor employment "N" on the horizontal axis) and the supply and demand of the current product market (with the real interest rate "y" on the vertical axis and the aggregate output "Y"' on the horizontal axis). Then, show how the decrease in K affects the supply and demand in the two markets and how the equilibrium outcomes in the two markets change. (Two more questions on the next page)

Consider the Solow growth model without population growth or technological change. The parameters of the model are given by s = 0.2 (savings rate) and S= 0.05 (depreciation rate). Let k denote capital per worker, y denote output per worker, c denote consumption per worker. [20 pts] (a) Suppose that the production function of aggregate outputs is Y = where K denotes capital inputs, and N denotes labor inputs. Rewrite the production function in per-worker terms, and find the steady-state level of capital per worker. [8 pts]

(b) The golden rule level of the capital per worker,, maximizes consumption per worker in steady-state. To obtain , should citizens save more or less? [12 pts]

(C)給定民眾相信央行的承諾,預期通膨為零,請問央行是否有動機偏離零通膨的政策規劃?(7分)

(b)若民眾不相信央行未來可以信守零通膨的承諾,且大眾為理性預期,請問央行所能選擇的最適通膨為何?(4分)此對應損失函數值為何?其比(a)的損失函數值大或小?(3分)

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