Free response question

IEO past paper: 2018 International Economics Olympiad, open questions

The degree to which members of society have equal opportunity of success, irrespective of their family background, is often measured by intergenerational elasticity of income. Roughly, it measures what percentage of inequality between members of the generation is passed on to the members of the next generation. Here is a definition from The Economy by CORE: "[C]onsider two pairs of fathers and children. The father in the first pair is richer than the father in the second. The intergenerational elasticity measures how much richer the child of the well off father will be than the child of the poorer father. An elasticity of 0.5, for example, means that if one father is 10% richer, then his child, when grown up, will be on average 5% richer than the other child." The following graph shows the relation between inequality and intergenerational income elasticity. Sometimes it is called The Great Gatsby Curve (a term attributed to Alan Krueger). It is a scatter plot of countries with inequality (Gini coefficient) on the horizontal axis and intergenerational income elasticity on the vertical axis, with an upward-sloping line of best fit. Approximate values read from the graph: $$\begin{array}{lcc} \text{Country} & \text{Gini} & \text{Elasticity} \\ \hline \text{Denmark} & 25 & 0.15 \\ \text{Norway} & 26 & 0.17 \\ \text{Finland} & 27 & 0.18 \\ \text{Sweden} & 25 & 0.27 \\ \text{Germany} & 28 & 0.32 \\ \text{Japan} & 25 & 0.34 \\ \text{Canada} & 32 & 0.19 \\ \text{Australia} & 35 & 0.26 \\ \text{New Zealand} & 36 & 0.29 \\ \text{France} & 31 & 0.41 \\ \text{Spain} & 35 & 0.40 \\ \text{Pakistan} & 33 & 0.46 \\ \text{Switzerland} & 34 & 0.46 \\ \text{United Kingdom} & 36 & 0.50 \\ \text{Italy} & 36 & 0.50 \\ \text{United States} & 41 & 0.47 \\ \text{Singapore} & 43 & 0.44 \\ \text{China} & 42 & 0.60 \\ \text{Argentina} & 53 & 0.49 \\ \text{Chile} & 55 & 0.52 \\ \text{Brazil} & 59 & 0.58 \\ \text{Peru} & 53 & 0.67 \end{array}$$ Source of the graph: Corak, M. (2012). Inequality from generation to generation: The United States in comparison.