Economics 302Summer 2007Answers to Homework #3Homework will be graded for content as well as neatness. Sloppy or illegible work will not receive full credit. You will find it helpful to do this work using Excel.1. The total adult population in your country is constant and equal to 500,000 people. In your country there are initially 400,000 people in committed relationships (C) and 100,000 people who are not in committed relationships (F). In this example, “C” stands for committed and F for “free”. There are pros and cons to being in either group and in your country there is substantial movement between these two categories.a. What is the initial percentage of people in committed relationships in this country? Initial percentage of people in committed relationships = (400,000/500,000)(100) = 80%.Now, suppose that each year the rate of commitment to committed relationships , m, is 10% of the previous year’s free population while the rate of separation, s, is 20% of the previous year’s committed population. Use this information to answer the following questions. Note: the adult population in your country is unchanging and should therefore always sum to 500,000.b. Calculate the values for the end of the first year given the values of m and s. You can do this without Excel, but you will find it infinitely easier to do this problem using Excel. Committed Relationships (C)Free from Relationships (F)Total Adult PopulationInitial Levels at Beginning of Year400,000 100,000 500,000Change due to committing to a relationship10000 -10000 XXXSub-total 410,000 90,000 500,000Change due to leaving committed relationship-80000 80000 XXXTotal 330,000 170,000 500,000c. At the end of the first year, what is the percentage of people in committed relationships in this country?1Percentage of people in committed relationships = (330,000/500,000)*100 = 66%.d. Calculate the values for the end of the second year given the values of m and s, and the values you calculated in part (b). Use the following table to report your answers. Committed Relationships (C)Free from Relationships (F)Total Adult PopulationInitial Levels at Beginning of Year330,000 170,000 500,000Change due to committing to a relationship17000 -17000 XXXSub-total 347,000 153,000 500,000Change due to leaving committed relationship-66000 66000 XXXTotal 281,000 219,000 500,000e. At the end of the second year, what is the percentage of people in committed relationships in this country?Percentage of people in committed relationships = (281,000/500,000)*100 = 56.2%.f. Calculate the values for the end of the third year given the values of m ands, and the values you calculated in part (d). Use the following table to report your answers. Committed Relationships (C)Free from Relationships (F)Total Adult PopulationInitial Levels at Beginning of Year281,000 219,000 500,000Change due to committing to a relationship21900 -21900 XXXSub-total 302,900 197,100 500,000Change due to leaving committed -56200 56200 XXX2relationshipTotal 246,700 253,300 500,000g. At the end of the third year, what is the percentage of people in committedrelationships in this country?Percentage of people in committed relationships = (246,700/500,000)*100 = 549.34%.h. Do you see any pattern emerging from this exercise? Briefly describe the pattern you see and its implications.The number of people in committed relationships is decreasing while the number of people not committed to relationships is increasing. But, with each year the changes are getting smaller suggesting that at some point there will be a steady state.i. The rate of commitment to relationships will neither rise nor fall when risewhen sC = mF. An alternative way to way to convey this idea is to say thatthe steady rate of relationship commitment (C/adult population)SS, equals m/(m+s). In this example, what is the steady state of relationship commitment? (C/adult population)SS = m/(m + f) = .1/(.1 + .2) = .1/.3 = 33.33%j. If this economy is at its steady state of relationship commitment, what do C and F equal?C = .33(500,000) = 166,667 people; and F = .67(500,000) = 333,333k. Using the figures you gave in part (j), verify that your answers really do identify the steady state of relationship commitment by filling in the table below. Committed Relationships (C)Free from Relationships (F)Total Adult PopulationInitial Levels at Beginning of Year166,667 333,333 500,000Change due to committing to a relationship33333.3 -33333.3 XXXSub-total 200,000 300,000 500,0003Change due to leaving committed relationship-33333.4 33333.4 XXXTotal 166,667 333,333 500,000l. Suppose as a policymaker you determine that the rate of commitment to relationship is too low and leads to instability in your economy. You decide to offer a variety of programs and incentives to encourage a greater level of commitment to relationships. Suppose you decide that ideally 60% of the adult population in your economy should be in committed relationships. Furthermore, suppose that you cannot alter the rate of separation through public policy. To reach your policy goal of 60%, what would the rate of commitment to relationships need to be in your economy?Desired Percentage of people in committed relationships = 60% So, percentage of people in committed relationships = m/(m + f) Or, .6 = m/(m + .2).6(m + .2) = m.6m + .12 = m.4m = .12m = .3 or 30%m. Using the information you calculated in part (l), verify that your answers really do identify the steady state of relationship commitment by filling in the table below. Committed Relationships (C)Free from Relationships (F)Total Adult PopulationInitial Levels at Beginning of Year300,000 200,000 500,000Change due to committing to a relationship60000 -60000 XXXSub-total 360,000 140,000 500,000Change due to leaving committed relationship-60000 60000 XXXTotal 300,000 200,000 500,0002. You are given the following information about a small, open economy. Y = F(K, L) = A Ka L1-aC = C(Y – T) = 20 + .6(Y – T)4I = I(r) = 100 – 1000r Y = C + I + G + NXY = C + SP + TG = 20T = 20K = 100L = 100a = .25A = 2 (M/P)S = 1000(M/P)D = 2000 – 20000ra. Find the level of aggregate output, Y , for this economy.Y = F(K, L) = A Ka L1-a Y = 2(100).25(100).75 Y = 200b. Find the level of consumption spending in this economy.C = 20 + .6(Y – T)C = 20 + .6(200 – 20)C = 20 + .6(180)C = 128c. Find the level of private saving, SP , for this economy.SP = Y – C – TSP = 200 – 128 – 20SP = 52d. Find the level of