Thank you..

Consider a two-period economy that has at the beginning of period 1 external wealth of 100. GDP in both periods is 120. The interest rate in periods 1 and 2 is 10 percent. In period 1, the country runs a current account decit of 5 percent of GDP. At the end of period 2, the external wealth must be equal to zero. 1. Find the level of the trade balance in period 1, the level of the current account balance in period 1, and the country's external wealth at the beginning of period 2. 2. Is the country living beyond its means? To answer this question, nd the country's current account balance in period 2 and the associated trade balance in period 2. Is this value for the trade balance feasible? [Hintz Keep in mind that since expenditures cannot be negative, the trade balance cannot exceed GDP]. 3. Now assume that in period 1, the country runs instead a much larger current account decit of 10 percent of GDP. Find the country's external wealth at the end of period 1. Is the country living beyond its means? If so, why? 4. What is the maximum current account decit (as a share of GDP) that this country can have at time 1 and still live within its means? 6 In a certain country, all civil servants are recruited on their 25th birthdays. (Birthdays are assumed to occur uniformly over the calendar year). Of those who reach exact age 40, 10% obtain employment in private companies and leave the civil service immediately. All remaining civil servants retire when they reach age 60 or die in service before this age. Civil servants have for many years experienced the mortality of English Life Table No. 12 - Males, and will do so for the indefinite future. The population of civil servants has been stationary for many years, and civil servants are recruited at the rate of 3,000 each year. (i) How many civil servants are in service at any given date? (ii) The government of the country has just decided to reduce the size of the civil service by 10%. This is to be done by immediately lowering the retirement age of civil servants. Find the new retirement age (to the nearest month), assuming that there are no other changes. 7 In a mortality table with a one-year select period, the following relationships apply at age r: (0 0, a > 0, and 3 > 0 are constants. Recall that a production function exhibits constant returns to scale if f(AL, AK) = Af(L, K) for any > > 1. It has decreasing returns if f(AL, AK) Af( L, K). (a) For what values of o and 3 does f (L, K) have constant or decreasing returns? (b) Show that f ( L, K ) is concave if it has constant or decreasing returns to scale. (c) Show that f( L, K) is quasiconcave regardless of its returns to scale. (Hint: any monotonic transformation of a concave function is quasiconcave.)Question Four Order statistics are very useful tools for analyzing the properties of samples. 1. Write down the general formula of the pdf and cdf for the th order statistic of a sample of size n of a random variable X with CDF Fx(x). Question Five (Bain/Engelhardt p. 229) Let X] and X2 be a random sample of size n = 2 from a continuous distribution with pdf of the form f(x) = 2x if 0