Economics 302 Summer 2007 Answers to Homework 3 Homework 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 Initial Levels at Beginning of Year Change due to committing to a relationship Sub total Change due to leaving committed relationship Total 400 000 Free from Relationships F Total Adult Population 100 000 10000 10000 XXX 410 000 80000 90 000 80000 XXX 330 000 170 000 500 000 500 000 500 000 c At the end of the first year what is the percentage of people in committed relationships in this country 1 Percentage 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 Initial Levels at Beginning of Year Change due to committing to a relationship Sub total Change due to leaving committed relationship Total 330 000 Free from Relationships F Total Adult Population 170 000 500 000 17000 17000 XXX 347 000 66000 153 000 66000 XXX 500 000 281 000 219 000 500 000 e 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 and s and the values you calculated in part d Use the following table to report your answers Committed Relationships C Initial Levels at Beginning of Year Change due to committing to a relationship Sub total Change due to leaving committed 281 000 Free from Relationships F Total Adult Population 219 000 21900 21900 XXX 302 900 56200 197 100 56200 XXX 500 000 500 000 2 relationship Total 246 700 253 300 500 000 g At the end of the third year what is the percentage of people in committed relationships 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 rise when sC mF An alternative way to way to convey this idea is to say that the 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 67 500 000 333 333 k 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 Initial Levels at Beginning of Year 166 667 Change due to committing to a relationship 33333 3 Sub total 200 000 Free from Relationships F Total Adult Population 333 333 500 000 33333 3 XXX 300 000 500 000 3 Change due to leaving committed relationship Total 33333 4 166 667 33333 4 XXX 333 333 500 000 l 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 12 m 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 Initial Levels at Beginning of Year Change due to committing to a relationship Sub total Change due to leaving committed relationship Total 300 000 Free from Relationships F Total Adult Population 200 000 500 000 60000 60000 XXX 360 000 60000 140 000 60000 XXX 500 000 300 000 200 000 500 000 2 You are given the following information about a small open economy Y F K L A Ka L1 a C C Y T 20 6 Y T 4 I I r 100 1000r Y C I G NX Y C SP T G 20 T 20 K 100 L 100 a 25 A 2 M P S 1000 M P D 2000 20000r a 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 200 b Find the level of consumption spending in this economy C 20 6 Y T C 20 6 200 20 C 20 6 180 C 128 c Find the level of private saving SP for this economy SP Y C T SP 200 128 20 SP 52 d Find the level of government saving SG for this economy SG T G SG 20 20 SG 0 e Find the level of national …