Assume we have two economies. Economy A has a level of GDP per capita of Ya(0) which is higher than Yb(0) but it is growing at a yearly rate of ga which is lower than that of B, gb. \

a) Use the rules of the logs to find an expression in terms of Ya(0), Yb(0), ga, and gb for the period, t*, where the poor economy catches up with the rich economy, i.e. when GDP per capita in both economies coincide. Show your derivations.

b) Explain the effect on t* of a decrease in the growth rate of the initially rich country, ga.

c) Assume Ya(0) = 100, ga = 2%, Yb(0) = 25 and gb = 8%. Calculate how many years does it take for B to catch up with A?