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? 6. (15%) Consider a world with two economies, Domestic and Foreign, with the following data