Kindly .solve the following questions.

1. A 10 year bond, which has just been issued, provides semiannual coupons of 6% a year in arrears. It is redeemed at par. What price is paid (per $100 nominal value) if bond yields an annual effective rate of interest of 8%? Ans: $87.37 2. A 20-year zero-coupon bond is redeemed at par. If the price paid per $1,000 face amount is $538.76, determine the annual effective yield rate. Ans: 3.14% 3. A bond pays semi-annual coupons at an annual rate of 10% of the nominal value. The annual effective yield to maturity is currently 4%, and the price paid per $1,000 par value is $1,404.06. If the bond is redeemed after 7 years, calculate the redemption payment. Ans: $1,050.00 4. An n-year bond pays annual coupons of 5% semiannually. The annual effective yield is 8% and the price per $100 par value is $86. The bond is redeemed at 110%. Find n. Ans: 10.7. Use (1) to derive the capital-share in the economy, i.e. 44. Here R is the rental rate of capital, which firms have to pay to use a unit of capital in production. In the data, this capital share is equal to 1/3. What does this imply for o? 8. Solve for the marginal product of capital (MPK = ) ) as a function of the capital-labor ratio k (t), which is not necessarily equal to the steady-state level k*. How does it depend on A? Now calculate the marginal product, when k (t) is equal to the steady-state value k*, which you computed above. How does it depend on A? Can you give an intuition for this surprising result? Now suppose that s = 0.1, 6 = 0.1, n = 0.02 and o = 1/3. What is the marginal product of capital in the steady-state? 9. Now we want to check whether this model can explain a ten-fold difference in per capita GDP between two countries, only based on differences in the propensity to save s. Consider two countries, 1 and 2, that have the same technology (1) and are in their steady state. Let the saving rate in country 1 be given by $1 = 0.1. Let per capita-income in country 1 be 10 times as high as in country 2 and normalize A = 1 in both countries. (a) Assuming the same parameters as in Question 8, solve for $2. (b) Let MPK, and MPK2 be the marginal product of capital in country 1 and 2. Solve for marginal products MPK, and MPK2 in the respective steady-states of the two countries. If you had some money to invest, where would you invest it? Would such investments tend to increase or reduce income differences across countries?1 Analytics of the Solow Model In the Solow economy, people consume a good that firms produce with technology Y = Af (K, L), where A is TFP (which we assume to be constant) and f is a Cobb-Douglas production function f ( K, L) = KOL-a. (1) Here K is the stock of capital, which depreciates at rate o e (0, 1) per period, and L is the labor force, which grows exogenously at rate n > 0. Here employment is always equal to the labor force L, because the L workers alive supply their labor services inelastically, whatever the wage rate. All L individuals alive and working at a point in time are identical, own equal shares of the aggregate capital stock, thus earn the same income, and save the same fraction s E (0, 1) of total income, consuming the rest. So total savings are a fraction s of total gross output (GDP) Y. 1. Write the accumulation equation for the aggregate stock of capital K (), namely K (t + 1) as a function of K (t), L (t) and parameters. 2. Write the accumulation equation for the stock of per capita capital k, namely k (t + 1) as a function of k (t) and parameters. To do so, you have to find the production function in the intensive form function / (#) = f (7,1) for the Cobb-Douglas case (1). 3. Write the equation that determines a steady state &*. 4. In a graph with per capita capital & (t) on the horizontal axis, plot the per capita savings function sAf (k ()) and effective depreciation schedule (n + 6) k (). Relate the graph to the change in per-capita capital k (t + 1)- k (t). How many steady states k* can you see? Explain. 5. Compute steady state per capita income y" and steady state per capita consumption c* as a function of parameters. 6. Suppose that that the economy is in steady state when, suddenly, the government implements a one-child policy, in order to slow population growth down. This policy reduces n to zero. Use a similar plot as in Question 4, to show the steady state both prior and after the new policy. Does the steady-state capital-labor ratio increase or decline? Also draw a graph, which traces out the evolution of capital per-capita (Hint: the graph should have "time" on the x-axis). Describe in words the resulting dynamics of per-capita output and consumption.(15 pts.) Christina enjoys her expresso with chocolate. She always consumes 4 pieces of chocolate with 2 cups of coffee. a) (4 pts.) Using x1 to represents pieces of chocolate and x2 to represents shots of expresso, write down the Christina's utility function. b) (6 pts.) Christina spend $100 per week on her choice. When price of a piece of chocolate is $1 and price of a cup of coffee is $4, how many cups of coffee and pieces of chocolate will she consume? c) (5 pts.) Graph Christina's optimal choice. Your graph should include: the budget line, the indifference curve and the optimal consumption point