A Norwegian translation follows below. En norsk oversettelse følger under. This problem set consists of two (2) pages. You should complete ALL of the problems. 1. (10 points) The table below gives GDP per capita in PPP-adjusted US dollars for 1990 and 2012, and the average growth rate over the period. Country GDP 1990 GDP 2012 Average growth rate India 1,174 5,138 0.069 Germany 18,533 42,700 0.039 (a) Assume first that the growth rate remains constant at the average 1990 2012 level. Rougly how many years does it take for India s GDP per capita to double? Explain your method. We can apply the rule of 70 (the candidate is not expected to derive this), So doubling time of India is approximately (1 + g) t = 2 t ln(1 + g) = ln(2) t = ln(2) ln(1 + g) 70 g 100 70/15 = 4.67 (b) Explain briefly what we mean when we say that GDP is PPP-adjusted. What do you expect would happen to the GDP measure for India relative to the GDP of Germany if we did not PPP-adjust? See Ray pp. 12 16. We expect that GDP falls in India compared to Germany if we do not PPP-adjust. (c) Do you think that it is likely that the growth rate in India relative to the growth rate in Germany remains as in 1990 2012? Why or why not? See Ray ch. 3 5, in particular the Solow model in 3.3.3 and the discussion on convergence in 3.5. 2. (10 points) Consider a society (call it Society A) composed of six equal-sized income groups with 100 individuals in each. Let the income in each group be 100 units higher than in the previous group, such that the members of the poorest group earns 100 units, the next group earns 200 units and so on. 1
(a) Show how one could redistribute income (from some group/s to other group/s) so that you end up with only two income groups: one that earns 200 and one that earns 500. group n A Transfer B 1 100 100 +100 200 2 100 200 200 3 100 300-100 200 4 100 400 +100 500 5 100 500 500 6 100 600-100 500 So, transfer 100 from group 6 to group 4 and 100 from 3 to 1. Call this new society Society B. (b) Based on the above, can you immediately tell which society is more unequal? Verify your answer by drawing the Lorenz curves for Societies A and B, and explain how you use these to conclude. Yes, B is derived from A using progressive transfers, so B must be less unequal than A. The Lorenz curve can be drawn from the below table. That the income shares are always above (or equal) in B, indicates Lorenz dominance of B over A. group Cum. pop. share Cum. Income Share, A Cum. Income Share, B 1 1/6 1/21 2/21 2 2/6 3/21 4/21 3 3/6 6/21 6/21 4 4/6 10/21 11/21 5 5/6 15/21 16/21 6 6/6 21/21 21/21 (c) Say that the poverty line is 250. Which society would you say is poorer, A or B? Calculate some relevant poverty measures to support your discussion. 2
See Ray pp. 253 256. The candidate should calculate at least the HCR and a gap measure, like the PGR (or the IGR), to emphasize that there are less poor in A, but that the poor are poorer in B. It could be relevant to discuss the bang for the buck problem. A good candate might also mention that with the same mean income and less inequality, B must be better according to any reasonable social welfare criterion. HCR(A) = 200/600 = 0.33 HCR(B) = 300/600 = 0.50 PGR(A) = 150 100 + 50 100 = 0.095 2100 100 PGR(B) = 50 300 2100 100 = 0.071 IGR(A) = 150 100 + 50 100 = 0.4 250 200 IGR(B) = 50 300 250 300 = 0.02 (d) Which society do you think is more polarized? Briefly explain what this implies for the potential for conflict? Society B is more polarized, with two big income groups, as compared to the six smaller in A. High polarization implies that groups can be more easily organized around a common cause and adversary, which may increase the potential for conflict. 3. (15 points) Under a share cropping contract, the land owner and the tenant share the output from production. (a) Explain how share cropping may cause production to be inefficiently low. should also explain what we mean by inefficiently low. Optimally, the effort expended in production equates the marginal product of effort with the marginal cost of effort. Under a share cropping contract, the tenant only reaps a fraction of the benefits of his efforts, and therefore sets effort too low. This is what we call a moral hazard problem, and is also called marshallian inefficiency in the context of share cropping. If the contract is w = αg(e) + F where w is the wage to the tenant, g(e) is production as a function of effort e, and α is the share to the tenant, then pure share cropping implies α (0,1) and F = 0. Then effort from the perspective of the tenant is set such that αg (e) = c (e), while g (e) = c (e) maximizes the joint surplus. If the land owner cannot observe effort, then production will be low. Candidates are expected to show sound understanding of share cropping, preferably using a graph/graphs or a simple model like the above. Good candidates should also discuss observability and/or enforcement. (b) Explain how fixed rent tenancy could restore efficiency. 3 You
Under pure fixed rent tenancy, F < 0 and α = 0. The tenant then reaps the full product of his efforts, there is no moral hazard problem, he sets g (e) = c (e) and production is optimal. An issue might be that the tenant has low capital and limited liability, such that he cannot pay up front and he cannot pay if production fails. In this context, there is still inefficiency in production, though whether production is too high or too low depends on the punishment that the land owner can and will inflict on the tenant in case of non-payment. (c) If share cropping contracts are less efficient than fixed rent tenancy, why might land owners/tenants still choose to write share cropping contracts? Share cropping contracts transfer some risk from the tenant to the land owner. A fixed rent contract leaves all the risk with the tenant. If tenants are more risk averse than land owners, it is optimal to transfer some risk to the land owner, implying that the land owner in effect insures the tenant against unexpectedly low production. (d) Imagine a society with two types of tenants, one with high ability and one with low ability. The tenant knows his own ability, but the land owner cannot observe it. Explain how a contract with a combination of share cropping and fixed rent can help the land owner screen the potential tenants. Because the high ability tenants will be more comfortable assuming risk than the low ability tenants, the land owner can in principle fix a contract with α (0,1) and F < 0 such that the high ability tenants are willing to take the contract while the low ability tenants are not willing to take it. 4. (15 points) Discuss the statement: Trade with developed nations helps developing countries exploit their comparative advantages, grow their economy and escape poverty. Candidates are expected to show sound understanding of basic trade theory and comparative advantages. Candidates should also discuss issues with this basic trade theory, and how countries could or could not exploit trade policy to promote development. See Ray Ch 16 17. 4
Dette oppgaveheftet består av to (2) sider. Du skal svare på ALLE oppgavene. 1. (10 poeng) Tabellen under gir BNP per innbygger i PPP-justerte US dollar for 1990 og 2012, samt gjennomsnittlig vekstrate over perioden. Land BNP 1990 BNP 2012 Gjennomsnittlig vekstrate India 1,174 5,138 0.069 Germany 18,533 42,700 0.039 (a) Anta først at vekstraten forblir konstant på 1990 2012-nivå. Omtrent hvor mange år tar det for Indias BNP per innbygger å bli fordoblet? Forklar framgangsmåten du bruker. (b) Forklar kort hva vi mener når vi sier at BNP er PPP-justert. Hva tror du skjer med BNP for India relativt til Tyskland hvis vi ikke PPP-justerer? (c) Tror du at det er sannsynlig at veksten i India relativt til veksten i Tyskland holder seg på nivået for 1990 2012? Hvorfor eller hvorfor ikke? 2. (10 poeng) Tenk på et samfunn med seks like store inntektsgrupper, med 100 personer i hver, kall det samfunn A. La inntekten i hver gruppe være 100 enheter høyere enn i den forrige, slik at medlemmene i den fattigste gruppa tjener 100 enheter, den neste tjener 200 enheter, også videre. (a) Vis hvordan en kunne omfordele inntekt (fra noen gruppe/r til noen andre gruppe/r) slik at man ender opp med bare to inntektsgrupper: En som tjener 200, og en som tjener 500. Kall dette nye samfunnet for samfunn B. (b) Basert på det ovenstående, kan du umiddelbart avgjøre hvilket samfunn som har høyest ulikhet? Kontroller svaret ditt ved å tegne Lorenz-kurvene for samfunn A og B, og forklar hvordan du bruker disse til å konkludere. (c) Si at fattigdomsgrensen er 250. Hvilket samfunn ville du si er fattigst, A eller B? Regn ut noen relevante fattigdomsmål for å underbygge diskusjonen. (d) Hvilket samfunn tror du er mer polarisert? Forklar kort hva dette betyr for potensialet for konflikt i de to samfunnene. 3. (15 poeng) I en share cropping-avtale deler landeieren og leietakeren produksjonen. (a) Forklar hvorfor share cropping kan føre til ineffektivt lav produksjon. Forklar også hva vi mener med ineffektivt lav produksjon. 5
(b) Forklar hvordan en leieavtale med fast leiepris kan gjenopprette effisiens i produksjonen. (c) Hvis en share cropping-kontrakt er mindre effisient enn en leieavtale med fast pris, hvorfor kan landeiere/leietakere likevel foretrekke å skrive share cropping-kontrakter? (d) Tenk på et samfunn med to typer leietakere, en med høy arbeidsevne og en med lav arbeidsevne. Leietakeren kjenner sin egen arbeidsevne, men landeieren kan ikke observere den. Forklar hvordan en kontrakt med en kombinasjon av share cropping og fast leie kan hjelpe landeieren med å sortere mulige leietakere. 4. (15 poeng) Drøft utsagnet: Handel med utviklede land hjelper fattige land å utnytte sine komparative fordeler, skape vekst i økonomien og komme ut av fattigdom. 6